The returns and volatility of agribusiness stocks; how do they measure up to non-agribusiness stocks.

CHAPTER 1: INTRODUCTION

1.1 Trends in Agribusiness

The market performance of agribusiness firms traded on U.S. exchanges relative to their non-

agribusiness counterparts has been the subject of limited research. The recent downturn in the

overall market caused by the financial crisis has caused many investors to reassess their

investment strategies. A common reaction during uncertain economic periods is to shift money

investments to assets that carry less risk. The historically defensive nature of US food companies

makes them an appealing investment diversification opportunity during a period of high market

volatility (Dirks, 1958). Defensive stocks tend to remain stable under difficult conditions in the

economy as a whole (Ang et al., 2006). Volatility in a specific industry’s stock prices is related

to the level of risk that is associated with investing in the industry. Corporate financial risk can

be estimated by calculating the systematic risk estimator “beta”, as defined in the Capital Asset

Pricing Model (Sharpe, 1964), (Lintner, 1965). According to the New York University Stern

School of Business, the beta value for the US Food Processing Industry was 0.63, as of January

2009 (Damodaran, 2009). Thus, the historical evidence suggests that investing in the U.S. Food

Industry is less risky than investing in a market index.

Various trends in today’s society make investment in food-marketing firms an interesting

topic for research. First, human health education is becoming the subject of much global interest

and the demand for “healthy foods” on both a domestic and international level has increased

significantly. Past research has shown that consumers identify organic food products as having

additional nutritional value over food products grown with traditional methods (Hay, 1989). In

the United States organic food industry, sales have grown from just over $1 billion in 1990 to

approximately $19 billion in 2007 (Dimitri, 2002), (Nutrition Business Journal, 2008). Food

processors, like General Mills, Unilever, and Kellogg have taken notice of this trend and have

introduced their own organic product lines. As of 2006, food retail giant, Wal-Mart, offered more

than 400 organic food products (Associated Press, 2006). The global food market forces

agribusiness firms to constantly search for ways to increase market share (innovation, etc.), if

they are to remain profitable. Furthermore, the introduction of genetically modified (GMO) and

functional food products has been a worldwide topic of debate among producers and consumers.

GMO’s have been the subject of legislation reform in Brazil. As GMO’s become more accepted

worldwide and new markets begin to relax GMO restrictions, agribusiness firms involved in their

production stand to make tremendous profit. There is also an unprecedented demand for the

inputs used in agricultural production and agribusiness processing by non-agricultural industries.

The increase in competition for these inputs may influence the profitability of agribusiness firms,

which ultimately affects their share prices and dividend streams. For example, the increasing

demands for corn, sugarcane, and soybeans by firms involved in the production of ethanol and

biodiesel has decreased the available supply of these inputs for those agribusiness firms who

traditionally use these inputs in their production process. Consequently, companies that engage

in oil/gas exploration, alternative fuels, and other commodity related companies have been

reporting record profits over the past few years. Recent volatility in the crude oil market has only

strengthened this trend. Finally, the recent slump in the financial and banking sector has acted to

reinforce this movement towards stocks that are more defensive in nature (Kahn, 2008). That is

to say, defensive stocks lag behind downturns in the general market, i.e. have a beta value of less

than one.

There are, however, certain risk factors that are unique to the agricultural industry that

add uncertainty to investing in the sector. These include but are not limited to, weather and

natural disasters, biological and environmental factors, and the industry’s policy sensitive nature,

as a large portion of farm income are solely dependent on Farm Bill Policy, which is typically

renewed every seven years (Beierlein et al., 2003). The aforementioned factors provide a signal

for the need in understanding the sector specific risk and performance of agribusiness firms

relative to their non-agribusiness peers.

1.2 Goals

Two objectives are accomplished through this work. First, to provide a thorough review of the

limited existing literature that compares the financial performance of agribusiness firms relative

to non-agribusiness firms. Second, to contribute original research on the returns and risks

associated with a large-cap index of publicly traded US agribusiness companies. The second task

will be accomplished in two stages. First, a large-cap index of US agribusiness stocks using the

Economic Research Service’s definition of agribusiness as the framework for selection. Firms

eligible for inclusion in the index have US Economic Census Standard Industrial Classification

Codes (SIC codes) (US Census Bureau, 2009) that correspond to the ERS classification of firms

that are related to agriculture (Economic Research Service, 2005). The sample will be restricted

to large-cap domestic agribusinesses, traded on the three major US exchanges, and that have data

available from The Center for Research in Security Prices Daily Stock Price Dataset (CRSP)

(Center for Research in Security Prices, 2009). A large-cap company is defined as a firm ranking

in the top 70th percentile of the industry, by market capitalization. Second, the calculated risk and

return associated with the agribusiness index will be compared to that of the market as a whole.

Implications and further extensions of this research will also be provided.

CHAPTER 2: LITERATURE REVIEW

The literature review will be organized in three sections. First, literature that examines

agricultural businesses as an investment strategy; the attitude towards investment in agricultural

related companies in the investment and academic community will be explored. Second, this

section will cover the literature concerning stock index creation. In particular, in depth coverage

will be given to the mathematical methods for creating indices. The final section will provide a

review of the literature regarding proper means of comparing indices. For example, industry

accepted risk and return methods are explored.

2.1 Investing in Agribusiness

2.1.1 Unique to Agriculture

Much of the risk agribusinesses face is unique to the industry as it is subject to an unusual set of

external factors. Weather, environmental concerns, biological factors, and governmental policy

all affect the profitability of firms in the sector. It is also understood that fluctuations in a

country’s aggregate business cycle are closely related to the share of agricultural output in the

economy (Da-Rocha and Restuccia, 2006) and to farmland value (Bjornson, 1995). Countries

with a high share of employment in production agriculture are subject to higher fluctuations in

aggregate output than countries with little production agriculture employment. In fact, most of

the major American industrial business cycles from 1800 to WWI were caused by fluctuations in

the size of the cotton harvest that resulted from exogenous factors such as weather (Davis et al.,

2009). Therefore, it is important to understand how shocks like weather, international trade

restrictions, domestic farm policy, and the level of employment in the sector affect agricultural

output and cycles. The length these cycles (on input and output market prices) and their

relationship with US Gross Domestic Product is what is important from an investment

perspective.

2.1.2 Organics

Global sales of organic products are estimated to be growing at a rate between 10 and 20 percent

a year. Estimated U.S. sales of organic produce in 2001 ranged between $5.5 and $6.5 billion

dollars, as compared with $2.1 billion in 1995 and $3.3 billion in 1998 (Dimitri and Richman,

2000). The growing concern of fitness, health, toxin exposure, and a recent series of food safety

scares have acted to strengthen the trend towards the consumption of more organically grown

food products (Byrne et al., 1991), (Tregear et al., 1994), (Davies et al., 1995), (Dimitri, 2002),

(Willer and Yussefi, 2004). The North American market for organic products is experiencing the

highest growth worldwide. Organic food and drink sales in the US were estimated to be

approximately 14.5 billion in 2005. US consumer demand for organic products is expected to

remain strong and account for most global organic food revenues going forward (Willer and

Yussefi, 2004). This growth has occurred despite the fact that organic product premiums have

been estimated to range from 50 percent to 75 percent (Willer and Yussefi, 2004). Consequently,

for a family of four to adopt an organic only diet they would increase their annual food

expenditures by almost 50 percent (Brown and Sperow, 2005). Numerous studies have

presented organic consumer profiles and determined characteristics that make a person more

likely to purchase organic products (Byrne et al., 1991), (Govindasamy et al., 2001), (Thompson

and Kidwell, 1998), (Zepeda and Jinghan, 2007). These studies have found that consumers that

purchase organic food products are typically young, highly educated, females, high-income

earners, and have children living at home. Further research shows that parents of young children

are becoming increasingly aware of their children’s organophosphorus pesticide exposure (Hood,

2003). A highly publicized 2003 study of Seattle preschool children, showed that those children

who consumed organically grown produce and juices significantly decreased OP exposure as

compared to children who consumed conventionally grown produce and juices (Curl et al.,

2003). However, recent research indicates that the long-term health benefits of organic food

over non-organic products is inconclusive (Dangour et al., 2009). Given the previous research on

organic food consumption, it is likely that the organic industry will continually grow on both the

domestic and international level. Consequently, agribusinesses that operate in this high margin

industry should expect to see increases in their sales, which should ultimately make them more

profitable.

2.1.3 Growing Global Demand

Global population is expected to increase from 6.5 billion in 2005 to 9.1 billion by 2050. Most of

this growth (97.7 percent) is expected to come from less developed regions in the world (United

Nations, 2008). Population growth India and China alone should account for 22.3 percent of the

expected increase in world population by 2050. At the same time, incomes, measured by per-

capita Gross Domestic Product (GDP), are expected to continue to grow in countries that have

recently enjoyed industrialization. For instance, Korea, India, and Thailand experienced average

annual growth of 11.76, 10.03, and 8.52 percent, respectively, from 1998 to 2007 (United

Nations, 2008b). Indian and Chinese per-capita income is expected to increase by 5.7 and 5.8

percent, respectively, per year between now and 2020 with a similar, but slightly lower, income

growth expectation for Asia in general, Eastern Europe, and Sub-Saharan Africa (Rosegrant et

al., 2001). Research shows that as incomes in these areas rise and as more people move out of

rural areas to more densely populated areas, general food consumption patterns change. A 2001

study showed that, as incomes rise and populations become more urbanized, consumption

patterns shift from basic staple items to diets consisting of more processed foods and meat and

dairy products (Rosegrant et al., 2001). These changes in consumption patterns will put strains

on these developing nations’ agricultural production industry. Countries that are land poor will

become increasingly dependent on food imports to meet the growing demand and changing food

preferences of its citizens, while those countries that have abundant land endowments but are

cash strapped will convert more land in to agricultural use (Rosegrant et al., 2001). Many US

agribusiness firms have the necessary infrastructure and supply chain investments in place to

capitalize on the growing demands that will be placed on the global food and fiber industry by

these developing countries, and therefore they stand to earn large profits.

2.1.4 Biofuels/Ethanol Industry

The rate at which global ethanol production has increased in the last 10 years is remarkable. The

creation of such bio-based combustibles requires large masses of starch or sugar rich crops. In

fact, demand for corn to be used in the production of ethanol is expected to reach 5 billion

bushels by 2015 (United States Department of Agriculture, 2009). A 2007 study projected corn-

based ethanol production to increase to over 14 billion gallons by 2010 (Tokgoz et al., 2007). It

is clear that the global demand for feedstock based biofuels has been a major factor in the current

increase in global grain prices (Trostle, 2008), (Rosegrant, 2008). This increase in prices, has

served as a signal for farmers to increase the production of those crops that can be used in bio-

fuel conversion. In fact, ERS predicts planted acres of corn to increase every year until 2019

(Economic Research Service, 2009). Similar trends exist for other oil crops such as soybeans and

sugar cane. As global demand for these products continue to increase and the governmental

mandates on ethanol/gas mix requirements are maintained, companies involved in their

production will likely see increased revenues.

2.1.5 Impact on Agricultural Inputs Sector

Grain prices have recently reached all time highs. According to an ERS report, world grain

prices increased by 60 percent from 2006 to 2008 (Trostle, 2008). The aforementioned literature

indicates that this trend resulted from growing global demand for food, competition within grain

markets for their alternative uses, and changing tastes and preferences. This translates in to an

increase in farm profits and expected future earnings. In fact, net cash farm income has

established multiple record highs between 2004 and 2008 and reached a peak of more than 89

billion dollars in 2008 (Harris, 2008). Though, net farm income is expected to decline in the

near term from the high levels of 2008, it will remain historically strong and rebound to near-

record levels by the end of the USDA projections in 2018 (United States Department of

Agriculture, 2009). The accompanying increase in demand for agricultural products has

multiplier effect, which is felt throughout the agriculture input sector (equipment/machinery,

seed, fertilizer, pesticide, herbicides, etc…). Increased commodity prices will create derived

demand for farm inputs, which in turn will improve agribusiness input supplier profitability.

Many investors expect farmers to re-invest a portion of their income in on-farm capital

improvements (Shinkle and Marquardt, 2008). If this is the case, manufacturers of tractors,

combines, planters, sprayers, and tillage equipment can expect increased business. A 2008 ERS

report estimated the value of farm equipment purchases in 2008 was 4.8 billion (Harris, 2008).

2.1.6 Investor Interest

Within the past few years, analysts have seriously started examining agriculture stocks as a

potential source of diversification, long-term investment growth, and short-term protection from

downturn in the general market. Jeff Auxier, investor and founder of Auxier Asset Management,

spoke about the investment opportunity in agriculture in a recent interview with U.S. News &

World Report, “I think agriculture looks really bright over the next 10 years, if we maintain the

biodiesel mandates, with the demographics for baby boomers eating healthier, and then the 2-3

billion [new] customers [worldwide]… it looks really good from the investment standpoint”

(Wolgemuth, 2008). In another recent interview, David Fondrie, chief investment officer of

Heartland Advisors spoke of US farmers, “The farmer is now in a great position to spend…

[f]arm balance sheets are in great shape, the land is worth more, and prices are high for crops.

Farmers can now go out and buy more machinery as well as crop inputs like fertilizer and seed”.

In the same article, the author reported on a recent note to Morgan Stanley clients, where analyst

Robert Wertheimer wrote, “[John Deere] is still in the earlier stages of a multi-year boom in farm

equipment” (Marquardt, 2008). In a recent article, Senior Editor of U.S. News and World

Report, Kirk Shinkle, wrote that “despite some recent selling along with the rest of the market,

agriculture remains one of just a few bright spots enjoying solid fundamental growth and some

defensive characteristics” (Shinkle and Marquardt, 2008). These statements are supported by

former analyst and current Barron’s Magazine contributor, Michael Kahn, who noted that despite

recent poor performance in the general stock market, agriculture was a pocket of strength (Kahn,

2008). A 2002 study suggested that farm owners might be better off investing some equity of the

farm in a portfolio of food and agribusiness stocks rather than a well-diversified market based

portfolio (Duval and Featherstone, 2002). They found that even given the systematic and non-

systematic risk associated with such a portfolio, it is still a viable alternative to other value-added

portfolios for all the farms in their sample (Duval and Featherstone, 2002). A similar study

found that livestock farmers could diversify risk and capture value-added profits through

investing in a portfolio consisting of publicly traded value added firms in the meat processing

industry (Detre et al., 2007).

In summary, the US Agriculture sector is believed to carry less risk, enjoy higher risk

adjusted return, be defensive in nature as compared to a market portfolio, and be an area of

growth in the future. However, little research exists that attempts quantify these beliefs. What is

needed from an investment standpoint is an index comprised of agribusiness stocks that

summarizes the historical market performance of US Agribusiness firms. Such an index would

allow investors to understand how these stocks compare to non-agribusiness companies and the

market as a whole. Index and data service firms have recognized this growth in investor interest

in agriculturally related businesses. Two major agriculture-based indices have been published

within the past 6 years. In 2003, the Deutsche Boerse Group, a global exchange organization,

launched the DaxGlobal Agribusiness Index. The index tracks 46 domestic and international

firms in five major sectors; agriculture chemicals, agri-product operations, agriculture

equipment, livestock operations, and ethanol/biodiesel.1 In August 2007 Van Eck Global, a New

York based investment firm, launched the Market Vectors Agribusiness Exchange-Traded Fund

(ETF) which seeks to track, before fees and expenses, the performance of the DaxGlobal

Agribusiness Index. The ETF is publicly traded on the AMEX exchange under the ticker “MOO”

with a beta value of 0.89 and had year-to-date returns of 10.2 percent, as of May 2008. In June of

2009, Standard and Poor’s released the North American Agribusiness Index (S&P-AG) as the

industry’s first index. The S&P-AG index consists of 24 of the largest publicly traded

agribusiness companies trading on the U.S. and Canadian exchanges.2 The constituents of the

S&P-AG index are equally distributed between two clusters; Producers, Distributors, and

Processors; and Equipment and Materials Suppliers (Standard & Poor's, 2009). In an interview

on the day on the index’s launch, Liz Taxin, Director of Strategy Indices for Standard & Poor’s

Index Services, noted, “The Index was created based on external market demand from product

producers and distributers whose clients have voiced a preference for a regional version of the

popular S&P Global Agribusiness Index” (Guarino, 2009).

What is still missing though, is historical back testing of index methodology, as both of

these indices only provide a couple of years of historical data. Therefore, the main contribution

1 Appendix A contains the December 2009 list of constituent firms that make up the DAXGlobal Agribusiness Index

2 Appendix B contains the December 2009 list of constituent firms that make up the S&P North American

Agribusiness Index

of this study is the development of a continuous price series that summarizes the historical

performance and risk of the US agriculture sector during the past 39 years.

2.2 Stock Price Indices

Mathematical stock price indexing is popular means of aggregating stock price movements in

industries or an entire stock market. They are used as benchmarks to evaluate the performance of

professional money managers, create and monitor an index fund, measure market rates of return

in economic studies, for predicting future market movements, and as a proxy for a market

portfolio of risky assets (Reilly and Brown, 2003). U.S. industry indices have been used since

1884, when the Dow Jones Transportation Average was created to track price movements in the

US transportation industry. Today, there are market indices for almost every industrial sector in

the economy. The most widely followed major market indices in the US are the Standard and

Poor’s 500 (S&P 500) and the Dow Jones Industrial Average (DOW). Each index contains a

unique formula of stocks and follows one of two general mathematical weighting schemes. The

S&P 500 is a market-capitalization-weighted index of 500 stocks intended to be a representative

sample of the leading companies in the top US industries. The DOW is a price-weighted index

containing 30 “blue-chip” stocks in the top US industrial sectors. Because of their wide use in

financial and investment literature, these two indices will be used as proxies for the “market as a

whole” in this study.

2.2.1 Types of Indices

Each method consists of three main components: the security price, the security weight, and a

divisor. The security price is the value of the stock being indexed. In the case of a stock price

index, the price is simply the current value of one share of a firms stock. The security weight

depends on the type of index. The weight can be based on the number of outstanding shares for a

security, the market value of the security, the price of the security, or the index can be equally

weighted among all of the securities. The weighting scheme is what distinguishes one type of

index method from another. An index divisor is the basis for comparisons of the index over time

and a starting point to which adjustments must be made as the makeup of the underlying

securities change. In addition, since most indices are an aggregate of stock price values,

sometimes in the trillions of dollars, a divisor can be used to scale an index so that its number is

easier to track. Once the base year of the index is determined, the divisor is used to scale the

index to a base value, usually 10, 100, or 1000. Understanding the divisor is critically important

to understanding how indices are calculated. Further discussion of the divisor and the base year

can be found in the methods section.

The first and simplest method is the price-weighted index. In this method, the price of

each component stock is the only consideration when determining the value of the index. Found

in equation (1) the calculation of the price-weighted index is:

Index Level Divisor

(1)

where the Index Level is determined by the sum of each security’s price, divided by a Divisor.

The Divisor is adjusted to account for changes in share counts and other changes in the sample

over time3. With this method, each company’s weight in the index depends on its price level and

therefore a 10 percent price movement in a $100 security, regardless of the size of the firm, will

have a larger influence in the value of the index than a similar movement in a $10 security.

3 Each index has its own list of events that will result in changes in the divisor.

Because of this flaw, price weighted indices are not widely used – although, with much criticism,

the DOW continues to utilize this method4.

The second type of index weighting method is market-capitalization weighting, also

known as market-cap. The basic formula for a market-cap index is:

Index Level Divisor

(2)

where the Index Level is determined by the sum of each security’s price multiplied by its

respective weight (Qi), divided by a Divisor. This method takes in to account the size of each

firm in the index and weights each security accordingly. The weight is calculated by determining

the percentage market value of each security in the index out of the total value of all securities

included. Daily market value (DMV) is determined by the following equation:

i i i

DMV S P

(3)

where the DMVi is the product of the number of outstanding shares (S) and the current market

price (P) of security “i”. The total market value of the index is given by equation (4) below:

()

IMV DMV

(4)

where the index market value (IMV) is given by the sum of each security’s DMV. The weight of

each stock is given by the ratio of its market value and the total market value of the index:

DMV

QIMV

(5)

where

is the weight assigned to security i,

DMV

is the daily market value of security i, and

IMV

is the total market value of the index. Examples of market-cap indices are the S&P 500

4 For more information about investor criticism of the DJIA and other price-weighted indices, see “100 Years of the

DJIA,” section in The Wall Street Journal, 28 May 1996, R29-R56, and “What’s Behind the Trailing Performance

of the Dow Industrials vs. the S & P 500?” The Wall Street Journal, 20 August 1998, C1, C17.

(US), the Hang Seng Index (Hong Kong), and the FTSE 100 (Britain). This method is more

widely used by index service firms because firm size is accounted for in the index calculation.

Because of this characteristic, the market-cap method is the index calculation used in this study.

There are however, some limitations to this method. Due to the weighting method, the larger

firms in the index can crowd out the smaller ones as they generally carry more weight in the

index. In industries that are highly concentrated this can affect the validity of the index. To get

around this issue, many index managers set a per-firm cap, usually 8 to 10 percent of the total

index value per firm in the index.

2.3 Index Performance and Comparison

A vast body of academic literature exists concerning security price return, risk, and comparison

methods. Additionally, rating agencies, financial analysis firms, and index service providers

publish thousands of documents each year that explain new measures of security performance

and risk. The purpose of this section is to determine the proper measures of risk and return to be

used to analyze and compare stock indices.

2.3.1 Index Performance

Before a discussion of performance measures, it is important to note that the index in this study,

like most stock price indices, ignores dividend payments. Therefore, a true investment return

cannot be calculated, only a measure of price appreciation is calculable. It is possible to make an

adjustment for dividends in some cases by splicing an index with a dividend yield index (Wilson

and Jones, 2002). Recently, many index service and database firms have begun to publish

versions of popular indices that have been corrected for dividends payments5. However, it can be

argued that because dividend payments are somewhat constant and predictable, their value is

5 An example of such an index is the Center for Research in Security Prices indices on the S&P 500 that have been

corrected for dividends CenterforResearchinSecurityPrices. (2009). "CRSP Daily Stock Price Database." from

http://www.crsp.com/products/index.html..

already represented in the company’s stock price, which by definition is the current value of

expected future earnings. In the following discussion, any reference to “return” refers only to

change in the index’s price, not actually total investment return.

Most financial literature primarily involves return data, or change in price, instead of

prices of securities. There are many statistical advantages to using security returns. (Campbell et

al., 1997) argued that for average investors, returns are a complete and scale-free summation of

the investment opportunity and that return series are easier to handle that price series because of

their attractive statistical properties. Return calculation is an active area of academic research and

is an important issue for investors who need to make informed decision for their clients. The next

few sections will discuss simple return measures, holding period return measures, and risk

adjusted performance measures.

2.3.1.1 Simple Return Measures

A simple return measure, or rate of change, can be calculated for one or multiple periods of

investment. From (Tsay, 2005), assuming no dividend payments, a one-period simple gross

return is given by:

(6)

moreover, the equivalent simple return is given by:

(7)

where

is the return on trading day t,

is the security’s price on trading day t, and

is the

security’s price on day t-1. From (Tsay, 2005), the multi-period gross return calculation is given

by:

1 [ ] * *...*

(1 )(1 )...(1 )

(1 )

t t t k

P P P

Rk P P P

R R R

(8)

where the security is held for k periods between the trading day t-k and t, and the k-period simple

gross return is the product of the one-period simple gross returns of all periods within the k

period. Therefore, the k-period simple return is:

()

[] t t k

Rk P

(9)

where

[]

is the simple multi-period return for the period k,

is the security’s price on date

t, and

is the security’s price on date t-k.

2.3.1.2 Geometric Return

A geometric return is considered the industry standard for return reporting when a security is

held for a year or more. The following calculation, from (Campbell et al., 1997), is used to find

the geometric return (GR) of security i in time t:

(1 ) 1

t t j

GR R

(10)

where the geometric return is equal to the multi-period simple gross return to the 1/k power and k

is the number of years in the holding period. The reported returns using this method will always

be smaller than returns calculated with the simple arithmetic method.

2.3.1.3 Risk Adjusted Returns

Investors are not always interested in a security’s return in itself. Rather, they are often

concerned with the security’s relative performance as compared to some risk-less security,

usually U.S. Treasury Bills. The resulting measure is often referred to as the “risk-adjusted

return”. Examples of these types of measures are excess return and the Sharpe Ratio. A

security’s excess return is the difference between the security’s return and the risk free security’s

return and is calculated as:

i i rf

t t t

Z R R

(11)

where

is the excess return for security i on day t,

is the return on security i on day t, and

is the return on the risk free security on day t. Building on the excess return model, (Sharpe,

1966) developed a method that measures a security’s excess return per unit of risk, known as the

reward to variability ratio (R/V), or, the Sharpe Ratio. It is now considered to be one of the

most commonly used measure of risk-adjusted performance (Simons, 1998 and Lo,2002). The

Sharpe ratio at time t for security i can be expressed as:

i rf

itt

SharpeRatio

(12)

where

i rf

is the difference of security i’s return in time t and the risk-free return in time t,

and

is the standard deviation of security i in time t. The Sharpe Ratio essentially represents

the tradeoff between risk and return. Therefore, unlike simple return measures, the Sharpe Ratio

can be used as a standard of performance and risk ranking to compare different investment

options.

2.3.2 Index Risk

2.3.2.1Standard Deviation

When making investment decisions, investors are not only concerned with security performance,

but also with the risk associated with said security. By taking on additional price risk, an investor

will expect higher returns and it is understood that traditionally less risky assets will have lower

returns. Understanding how to measure this risk and the ability to compare assets of differing

configurations is necessary for informed investment decision making. Within the scope of this

study, security risk can be thought of as the uncertainty in price movement. Some of the most

widely used measures of price risk are; standard deviation, beta value, and value at risk. The

most basic measure of stock price variability is the standard deviation. In general, standard

deviation is defined as, a measure of dispersion calculated as the positive square root of variance

(Weiers, 2002). Variance is defined as a measure of dispersion based on the squared differences

between observed values and their mean (Weiers, 2002). In general, variance is given by

equation (13),

2()

(13)

where

is the variance,

is the ith data value, is the population mean, and

is the

number of data values in the population. The square root of the variance is the standard deviation

( ) or,

(14)

When applied to security price analysis, the standard deviation gives investors a measure of

daily, monthly, or annual variability of price movements.

2.3.2.2 Beta Value

In the introductory section of this study, the CAPM, or capital security pricing model was briefly

discussed. Specifically, the “beta” parameter within the CAPM framework was considered. A

security’s beta value gives investors an idea of the security’s returns relative to that of the

financial market as a whole. The beta value of the market portfolio is always one. A security

with a beta value of 1 or -1 means that its price is perfectly correlated with the market, while a

beta value of zero means that the security’s price is not correlated at all with the market. If the

beta value is less than one but positive, it means that the market and the security’s prices move in

similar directions but with dissimilar magnitudes (positive correlation), while a negative beta

that’s greater than -1 means that they move in opposite directions but with dissimilar magnitudes

(negatively correlated). This powerful characteristic makes the beta value is a popular measure of

an assets statistical variance. A beta value can be estimated for individual companies through

simple regression analysis against a market proxy, such as the S&P 500. As previously

mentioned, the beta for the U.S. Food Processing Industry was estimated to be 0.65, indicating

that the sector lags behind market movements but still moves in similar directions. The broader

agricultural sector is believed to have the same characteristics though little research has been

published to test this hypothesis.

2.3.2.3 Value at Risk

Another popular measure of price risk is Value at Risk (VaR). The VaR measure was first used

to evaluate price risk associated with derivatives trading at major banks (Simons, 1998). The

measure was further popularized by the 1993 special report by the Group of Thirty, Derivatives:

Practices and Principles, which further recommended VaR for derivative risk analysis (Global

Derivatives Study Group, 1993). The VaR measure tells an investor how much the value of a

portfolio could decline over a given amount of time based on a given probability. To calculate

VaR, stock prices must be assumed to be distributed normally and, therefore, it is assumed that

95 percent of all deviation around the mean occurs within 1.96 standard deviations. Thus, the 5%

VaR calculation is given by:

1.96*

i i i

t t t

VaR R

(15)

where

VaR

is firm i’s value at risk for time period t,

is firm i’s return for time period t¸ and

is firm i’s standard deviation for time period t. This measure of risk is particularly useful for

investments that have significantly different compositions over time, such as an index or mutual

fund (Simons, 1998). Since this research is primarily concerned with the historical risk of

agriculturally related firms and not future or present risk, a VAR measure will not be calculated.

The measures mentioned above are universal and can be compared across investment

options. When comparing different investment possibilities, it is important to choose options for

comparison that are similar in composition. For instance, if an investor wanted to compare the

risk and return of a collection of small-cap stocks to the performance of small-cap stocks as a

whole, it would not be wise to choose the S&P 500 or Dow Jones Industrial Average, as they are

large-cap indices. A more suitable comparison index would the Standard and Poor’s small-cap

index. For the purposes of this study, the S&P 500 and the Dow Jones Industrial Average are

proper comparison indices, given that the AG Index is comprised of large-cap stocks.

CHAPTER 3: METHODS

3.1 Data

3.1.1 Overview

Daily closing stock prices, returns, and outstanding shares are collected from The Center for

Research in Security Prices Database (CRSP) though the Wharton Research Data Services

(WRDS) database. The CRSP US Stock Database contains end-of-day and month-end prices on

all New York Stock Exchange (NYSE) (December 31, 1925-Present), American Stock Exchange

(AMEX) (July 2, 1962-Present), and the National Association of Securities Dealers Automated

Quotations (NASDAQ) (December 14, 1972-Present) common stocks along with basic market

indices, distribution information, and total return calculations.

3.1.2 Firm Selection

The USDA’s Economic Research Service (ERS) provides a listing of industries closely tied to

production agriculture by the U.S. Economic Census Standard Industrial Classification Code

(SIC codes). SIC codes aggregate industries into related groups. For example; farm production,

agricultural services, forestry, and fishing; agricultural input industries; agricultural processing

and marketing industries; wholesale and retail trade of agricultural products; and indirect

agribusinesses. ERS defines farm and farm-related industries as those industries generally having

50 percent or more of their national work force employed in providing goods and services

necessary to satisfy the final demand for agricultural products and indirect agribusiness are those

industries having between 32 and 50 percent. Appendix C contains ERS’s listing of these sectors.

A list of publicly traded firms with SIC codes that correspond to the ERS classification of

agribusiness firms was generated using the CRSP database. The CRSP database is the leading

provider of the most comprehensive US historical stock market databases and is the most widely

used database in finance literature. The CRSP database contains daily price quotations for

common stocks, excluding preferred stock and including American Depositary Receipts, traded

on the New York and American stock exchanges and NASDAQ. Daily returns provide a more

accurate measure of market efficiency than monthly returns (Henderson, 1990), (Armitage,

1995), (MacKinlay, 1997). Daily data begin in July 1962. While NYSE data are available

throughout the entire period, AMEX data starts in 1962, and NASDAQ data begins in 1972.

For a stock to be eligible for inclusion in this study, the stock must have daily return data

in the CRSP database and have data available for a full year of trading. Any agribusiness firm

that did not have daily return data for the aforementioned dates was excluded from the choice

set. Appendix D provides a list of the firms, by years, which were dropped from the sample due

to missing data. Once a sample of eligible stocks was compiled, the sample was broken up in to

three sub-industry groups based upon the ERS classification grouped according to SIC codes:

farming stocks, closely related to farming, and peripherally related to farming. A full list of the

component industries in each group is provided in Appendix C. Within each industry group, only

the firms that make up the top 70th percentile based on market share were selected for the final

index selection.6 This selection process is repeated on the first trading day of each year in the

index calculation. A list of all firms included in each year’s index is provided, by permanent

number (PERMNO), in Appendices E and F. Finally, the daily closing prices (prc) and number

of outstanding shares (shrout) were obtained for each firm from the CRSP database. “Prc” is

defined by CRSP as the closing price or the negative bid/ask average for a trading day. If the

closing price is not available on any given trading day, the number in the price field has a

negative sign to indicate that it is a bid/ask average and not an actual closing price. If neither

6 The 70th percentile selection process is discussed in length in a later chapter.

closing price nor bid/ask average is available on a date, the value in the price field is set to zero.

Corrections were made to the data to eliminate any negative values, by using the absolute value

function in Microsoft Excel (abs()). When a daily price value was not available, the value for the

previous trading day was used. In the cases where data for consecutive days was not available,

the last available trading day value was used for up to 10 consecutive days of missing data. If

more than 10 consecutive days of data were missing from the dataset, the firm was removed

from the sample. “Shrout” is defined by CRSP as the number of publicly held shares, recorded in

thousands. This is sometimes referred to as the “float” or the number of outstanding shares that

are available to investors. Floated share counts exclude shares closely held by control groups,

other publicly traded companies, or government agencies. Using a floated share count reflects

the value available in the public markets.

The data collection, management, and risk and return calculations were completed in

Microsoft Excel 2007 and Access 2007. In addition to the included statistical functions of these

programs, the DigDB, Excel Analysis Tool Pack, and Macros Add-in tools were used.

3.2 Index Membership

The universe from which firms are selected is all publicly listed companies in the CRSP database

with a SIC code classification that corresponds to the ERS definition of agriculturally related

industries. The list generated via the CRSP database included 374 firms classified as “farming”,

“closely related to farming” or “peripherally related to farming” that were publicly traded at

sometime between January 1970 and December 2008. The universe was then narrowed down to

a set of stocks based on several criteria. First, for a stock to be considered for inclusion in the

index for a given year, say 1970, price and outstanding share count must be available for the full

year of 1970. The sample was then split based on the ERS subcategories of “farm and farm-

related industries”. These include farming, closely related to farming, and peripherally related to

farming. Next, the sample size was reduced to include only the top 70th percentile of firms

among each of the three sub-categories. Please refer to Table 1 for a visual representation of this

step. Each year’s basket of potential firms was filtered to display only the first trading day’s

Table 1: Top 70th Percentile Selection

price and share count. The daily market value (DMV) was calculated for each firm by applying

equation (3) and then sorted from largest to smallest. Next, the total index market value is

determined by using equation (4). Then, the percent market share is calculated for each firm by

equation (16):

DMV

Market Share Total MKTValue

(16)

where the % Market Share for firm i is given by the daily market value of firm i divided by the

total market value of the index on the first trading day of the year. For example, from Table 1,

TRD Day Firm PRC SHROUT DMV

% MKT Share

CMPD Sum

1 A 94

220292000 20707448000 23.4% 23.4%

1 B 33.5

358815000 12020302500 13.6% 37.0%

1 C 28.63

360136000 10308893000 11.7% 48.7%

1 D 28

201187000 5633236000 6.4% 55.0%

1 E 41.38

133862000 5538540250 6.3% 61.3%

1 F 61.5

70860000 4357890000 4.9% 66.2%

1 G 31.38

129590000 4065886250 4.6% 70.8%

1 H 42.5

92244000 3920370000 4.4% 75.3%

1 I 41.25

81734000 3371527500 3.8% 79.1%

1 J 39

79366000 3095274000 3.5% 82.6%

1 K 17.63

162520000 2864415000 3.2% 85.8%

1 L 17.88

159715000 2854905625 3.2% 89.1%

1 M 54

48283000 2607282000 2.9% 92.0%

1 N 28.13

75190000 2114718750 2.4% 94.4%

1 O 29.75

60168000 1789998000 2.0% 96.4%

1 P 43.88

38203000 1676156625 1.9% 98.3%

1 Q 43

34657000 1490251000 1.7% 100.0%

Total MKT Value 88417094500

firm “A” has a DMV of $20,707,448,000 which represents 23.4 percent of the total market value

of all the firms in the index for this year within the same sub-group. Next, a compounding sum is

calculated as:

B B A

CMPDSum MKT Share MKT Share

(17)

where the compounding sum equals the sum of the percent market share of firm “B” and the

percent market share of firm “A”, which is the firm immediately above firm “B” when sorted

from largest to smallest by DMV. This step is repeated until the CMPD Sum reaches 100 percent.

Finally, only those firms making up the top 70th percentile, or as close to it as possible, are

selected for inclusion in the index for the given year. This is illustrated in Table 1 above, by

those firms shaded in gray. In this example, only firms A, B, C, D, E, F, and G are selected for

inclusion; all other firms are dropped from the sample for year t because they are too small. This

procedure is performed separately for each sub-group; farming, closely related to farming, and

peripherally related to farming, so that the index represents the top 70th percentile of firms within

each of the three sub-groups. Once the final firm selections were made, the firms within each

sub-group were combined in to one worksheet. The final dataset was then split in to 39 separate

worksheets, organized by year from 1970 to 2008.

3.3 Index Methodology

The index calculation method utilized in this study is defined as the market-capitalization

method. As mentioned in an earlier chapter, it is the most widely used form of index calculation.

The index calculation is a very straightforward process, the first step of which involves

calculating the daily market value (DMV) for each firm in the index using the following

equation:

( * )

t t t

i i i

DMV P Shares

(18)

where the daily market value for security i in time t is the product of the price and the number of

outstanding shares of security i. The total index market value for a given day is calculated by:

IMV DMV

(19)

where

IMV

is the index market value at time t and

DMV

is the daily market value for firm i, at

time t. The symbol “t” represents the number of trading days in a given year, usually 253 day. A

table containing the number of trading days in each year is available in Appendix G. These steps

were repeated for each year in the study.

3.5 Index Scaling and Rebalancing

3.5.1 Scaling the Index Using a Divisor

On any given day, the total market value of an index of stocks can be in the billions or even

trillions of dollars. For example, on 5/8/1991 the total index value in this study was

$333,644,493,625.00. Tracking a number this large on a day-to-day basis can be a challenge in

itself; therefore, the index value is scaled so that it is easier to track. Many index service

companies utilize what is called a “divisor” to scale the index. To scale an index using a divisor

an index manager must first choose a base date and a base value. The actual base value is

irrelevant because it tells us nothing about the performance of the firms in the index. Investors

are more concerned with the incremental changes in that value. However, the initial value of the

divisor is dependent on the base value and is determined at the base date of the index. For

example, if the base date for an index is January 2, 2003 and the index manager defines the base

value at 100, the initial divisor is calculated by:

2,2003

100

Jan

initial

IndexMarketValue

Divisor

(20)

where

2,2003Jan

IndexMarketValue

is the total market value of the index on the base date.

Therefore, if the total market value of the index on the base date were $25,000,000, the divisor

would be 250,000. To get the scaled index value, simply divide the index market value by the

divisor using:

IndexMarketValue

Scaled IndexValue Divisor

(21)

where the scaled index value at time t is determined by dividing the index market value at time t

by the divisor at time t. Again, if the index market value is $25,000,000 and the divisor is

250,000 then the scaled index value will be 100. The scaled index value will always be the same

as the base value on the base date. Therefore, if the index market value increases to $26,500,000

on the next trading day the scaled index value will be 26,500,000/250,000, or 106, which

represents a 6 percent increase in value from the previous day. Note that the divisor in equation

(21) does have a time notation. This is because the index manager for maintenance purposes can

manipulate the value of the divisor.

3.5.2 Scaling the Index Using the Ratio Method

There are several ways to build and scale a market-value-weighted index. The most

straightforward is to use the method outlined in (Chartered Financial Analyst Institute, 2005),

which will be referred to as the “Ratio Method”. Like the divisor method, the first step is to

choose a base date and base value. In addition, the scaled index value is the base value on the

base date. However, in this case the scaled index value is given by:

IMV

SIV SIV

IMV

(22)

where

SIV

the scaled index value at time t is,

IMV

is the index market value at time t-1,

IMV

is the index market value at time t, and

SIV

is the scaled index value at time t-1. By taking the

ratio of today’s index market value and the previous day’s index market value then multiplying

it by the previous day’s SIV we can achieve the same goal of scaling the index market value to a

more manageable number. With this method, there is no need for a divisor.

3.5.3 Bi-Annual Corrections

3.5.3.1 Mid-Year Update

The number of shares available to the public for a given firm can change from day to day for

several reasons. If a company issues new shares to the public this number will rise, if they buy

back shares the number will reduce. Changes in share count can also occur due to acquisitions,

mergers and spin-offs, and several other corporate actions. All indices must have a clearly

defined method for accounting for these changes as they can drastically affect the accuracy of the

index. For example, the S&P 500 uses what they call the “5 percent rule”, where immediate

corrections to the index are made only when corporate action or any other force causes a firm’s

share count to change by more than 5 percent, (Standard & Poor's, 2009b). All other changes that

result in less than a 5 percent change are accumulated and made on a quarterly basis. For this

study, all changes in share counts, despite size, are accumulated and updated bi-annually. All

changes during trading days 1 through 126 and are updated on day 127 and changes during days

127 to the last trading day of the year and are updated on the first trading day of the next year.7.

This correction is calculated as:

7 Given the time constraints of this study it was not possible to track share count changes as closely as those

published indices like the S&P 500 or Dow Jones Industrial Average.

1 127

127 127

td t

itd t

P Shares if d

DMV P Shares if d

(23)

where

DMV

is the daily market value of firm i on day d in year t,

is the security price of

firm i on day d in year t,

is the share count for firm i on day 1 in year t, and

127t

the share count for firm i on day 127 in year t. For all trading days preceding day 127, the

recorded share count on the first trading day of the year is used. For all trading days on or after

day 127, the recorded share count on the 127th day of trading is used.

3.5.3.2 Beginning of the Year Update

On the first trading day of each year, the index is rebalanced to account for two changes to its

makeup. First, all changes in share counts and second, all additions and deletions are made to the

constituents of the index. In a given year, the firms that make up the top 70th percentile of the

agricultural industry can change. Additions and deletions occur because each year some

companies are shutdown because of bankruptcy, new companies are started, some companies

grow, mergers occur, and others fall in market share. Making annual firm additions and deletions

ensures that the AG Index remains an up-to-date representation of the US agriculture sector.

These changes are only made at the beginning of each year; consequently, if a company is added

to the index in January, it cannot leave the index until the January of the next year.

3.5.4 Rebalancing the Index Using a Divisor

When changes are made to the index’s constituents or if share counts change, the index level

should not move up or down, as this change does not represent market price movement. To

ensure that an index’s level does not change when stocks are added or deleted, an adjustment

must be made to offset the change in market value. In the case of the S&P 500 and many other

indices, the divisor is used to accomplish this (Standard & Poor's, 2009b). The divisor, in this

case, plays a crucial role in the ability to compare index levels over time as changes in the

constituents can affect the reliability of the index measure. For instance, if an index closes on

December 31, 1972 at 450 and after the close a new firm is added to the index, the index should

still open on January 2, 1973 at 450. This offset is accomplished by:

( )* t

IMV

Divisor Divisor IMV

(24)

where

Divisor

is the new divisor at time t¸ is

Divisor

is the old divisor at time t-1,

IMV

is the

index market value at time t, and

IMV

is the index market value at time t-1. This new divisor is

used to scale the index until another rebalancing is required.

3.5.5 Rebalancing the Index Using the Ratio Method

A more general method used to rebalance the index to offset changes in the constituency and

share counts in the index over time is the ratio method (Chartered Financial Analyst Institute,

2005). With indices that are managed daily, this rebalancing is done after the market closes for

the day. Because the price data in this study is daily closing price, the intraday prices are not

available. Therefore, to properly rebalance the index after a constituent or share count change,

the index market value at time t (after the change) must be calculated using the prices from time

t-1 (before the change). This new index market value using the adjusted share counts and

updated basket of firms will be referred to from this point forward as the Adjustment Index

Market Value (AIMV). This adjustment figure must be calculated in the beginning of each year to

offset the change in constituents and the change in share counts, and at trading day 127 when

only the share counts are updated. The AIMV calculated at the beginning of each year is given

by:

1 1 1 1 1 1

11 1 1

( * ) ( * ) ( * )

n n n

y d yd y d yd y d yd

i i j j k k

i j k

AIMV P Shares P Shares P Shares

(25)

where

AIMV

is the adjusted index market value at trading day 1,

11yd

is the price for security

i on trading day d-1 in year y-1,

is the share count for security i on trading day d in year

y, and so forth. The second bracketed section in the equation is the total market value of all the

firms that are being added to the index using the new share counts and the previous trading day’s

prices. The third bracketed section is the total market value of all the firms that are leaving the

index using the new share counts and the previous trading day’s prices. The AIMV at trading day

127 is given by:

126 127

127 *

AIMV P Shares

(26)

where

127

AIMV

is the adjustment index market value at trading day 127,

126

is the price of

security i at trading day 126, and

127

is the updated share count for firm i at trading day

127. The rebalanced and scaled index value for the first trading day of each year is given by:

1 1,253

IMV

SIV SIV

AIMV

(27)

where

SIV

is the scaled index value at the rebalancing trading day 1 in year y,

IMV

is the index

market value on trading day 1 in year y,

AIMV

is the adjustment index market value on trading

day 1 in year y, and

1,253y

SIV

is the scaled index value from the last trading day of the previous

year. The rebalanced and scaled index value for the 127-trading day is given by:

127

127 126

127

IMV

SIV SIV

AIMV

(28)

where

127

SIV

is the scaled index value on trading day 127,

127

IMV

is the index market value on

trading day 127,

127

AIMV

is the adjustment index market value on trading day 127, and

126

SIV

the scaled index value on trading day 126.

3.6 Index Return

Within the contexts of this study, the term “return”, refers only to change in price from one

specified point in time to another, not investment return. That being said, the index’s return is

reported as a geometric return. The first step of this return calculation is to find the holding

period ratio (HPR) for each year of the index by:

Ag Index

yAg Index

HPR P

(29)

where, the HPR for year y is given by the ratio of the price of the Ag Index in year y on day n

(the last trading day of year y) and the price of the Ag Index in year y on trading day 1 (the first

trading day of year y). For example, the holding period ratio in 1970 would be calculated as

follows:

1970

101.589

100

Ag Index

HPR

(30)

Therefore, the holding period ratio for 1970 would be 1.01589. To calculate the geometric return

(GR) for one period (year) you simple subtract 1 from the period’s HPR as:

( ) 1

Ag Index Ag Index

GR HPR

(31)

In the case of 1970, the geometric return was 1.01589 - 1 = 0.01589 or 1.589 percent return. The

geometric return for more than one period is calculated by:

,( * *...* ) 1

Ag Index n

x z x y z

GR HPR HPR HPR

(32)

where

Ag Index

is the geometric return for period x through z,

HPR

is the holding period ratio for

period x,

HPR

is the holding period ratio for period y,

HPR

is the holding period ratio for period

z, and n is the total number of periods within the return calculation. For the period of 1970 to

1974, the geometric return calculation is given as follows:

1970,1974 (1.015894*1.07623*1.01857*0.76175*0.68982) 1

Ag Index

(33)

Therefore, the geometric return for the five-year period of 1970 to 1974 was -0.101625 or -

10.1625 percent. To ensure comparability across indices, the returns for all comparison indices

are calculated using the same methodology.

3.7 Index Risk and Risk Adjusted Performance

The reported measures of risk in this study are standard deviation and beta; and the Sharpe Ratio,

a measure of risk-adjusted returns. The resulting values are compared with those of the two

comparison indices (S&P 500 and Dow Jones Industrial Average).

The standard deviation (STDEV) of the AG Index as well as the comparison indices will

be calculated as:

()

nii

SIV

STDEV N

(34)

where

STDEV

is the standard deviation of index i during period p,

SIV

is the scaled index

value for index i for the tth trading day and

is the mean value of index i for period p, and N, is

the number of data values in period p.

Investors are not only concerned about the price risk of the security itself; rather, they are

also interested in its risk relative to some other securities. A popular measure that summarizes

the correlation between one security and a benchmark is its beta value. As previously mentioned

the beta measure is a component of the capital asset pricing model (CAPM). From (Perold,

2004), the CAPM is calculated by:

()

s f M f

E r E r

(35)

where

and

are the expected return from the security and the market portfolio,

respectively,

is the risk free return, and is the sensitivity of the security’s price to the

market, i.e., the security’s beta value. The security’s beta value is calculated by simply

regressing the security’s return against the market portfolio:

()

(36)

where

and

are the return series from the security and the market portfolio, respectively,

is the slope the regression line and the assets beta value, and is the error term. For the

purposes of this study, the S&P 500 was used as a proxy from the market portfolio. Short and

long-term measures are useful to investors making investment decisions on different time

horizons. Therefore, to test the belief that the U.S. agricultural sector is defensive in nature, the

beta value was calculated for the AG Index for each year in the study, each five-year, and each

10-year holding period.

In the beta calculation, the benchmark security is the market portfolio, which still

contains risk. However, investors are also concerned with a security’s performance and risk

relative to a riskless asset. Excess return measures, like the Sharpe Ratio, provide such

information to investors. Because this study is mainly concerned with the past performance of

US Agribusiness firms relative to the market as a whole, the ex post Sharpe Ratio is provided.

The ex post, Sharpe Ratio is given by:

i rf

SharpeRatio

(37)

where

is the simple return of security i,

is the simple return of the risk free security, and

is the standard deviation of security i. It is important to note that the Sharpe Ratio measure is

not independent of the time period over which it is measured (Sharpe, 1994). The commonly

cited way to annualize the Sharpe Ratio measure (S) is given by:

SharpeRatio T SharpeRatio

(38)

where

SharpeRatio

is the annualized measure over T periods, and

SharpeRatio

is the one

period measure. However, this method has been shown to be correct in only a few rare statistical

circumstances (Lo, 2002). Therefore, from (Sharpe, 1994), the proper way to calculate multi-

period (p) Sharpe Ratio measures is given by,

i rf

GR GR

SharpeRatio

(39)

where,

is the geometric return for security i during period p,

is the geometric return

for the risk free security, during period p, and

is the standard deviation of security i for period

p. When calculating risk adjusted return measures, special attention should be given to selecting

a proper proxy for the risk free security in the equation. Typically, short term (90 day) US

Treasury Bills are used, however, government securities are not entirely riskless, especially when

their maturity period is not matched to the investor’s time horizon (Roll, 1969). Therefore, daily

yield values for one, five, and ten year US Treasury Bills are used based on the corresponding

holding period return.

CHAPTER 4: RESULTS

The results will be organized in to five sections. The first section will discuss the AG Index

continuous price series, general characteristics of returns, and other descriptive statistics. The

second section will discuss the returns of the AG Index relative to the comparison indices.

Annual, 5-year, and 10-year holding period geometric returns will be provided. The third section

will compare the standard deviation of the AG Index and the comparison indices. The fourth

section will provide the results from the Sharpe Ratio calculation and the fifth and final section

will be a discussion of the estimated beta parameters.

4.1 Descriptive Statistics

Figure 1 below, shows the continuous price series of the agribusiness stock index from January

2, 1970 to December 31, 2008. The initial index value is 100, the lowest recorded value

Figure 1: AG Index Value (1970-2008)

was 50.82 on October 3, 1974, and the highest recorded value was 170.55 on November 23,

1998. The average index value was 108.17, median value was 110.54, and had standard

deviation of 27.87. From an investment standpoint, the index price is not as important as the

change in said price over time, or, the returns of the index in question. A larger version of this

figure is provided in Appendix H. Table 2 displays the daily simple return descriptive statistics

Table 2: Daily and Annual Descriptive Statistics

and the geometric annual return descriptive statistics for the AG Index and the two comparison

indices. As expected, daily and annual return calculations for the AG Index were less than that of

the comparison “market” indices while the AG Index daily and annual price variability,

measured by standard deviation, was lower than that of the comparison indices.

4.2 Annual, Five and Ten-Year Geometric Returns

The index of agribusiness stocks shows similar long-term returns to those of the two comparison

indices. Appendix I contains the annual geometric returns for the AG Index and the two

comparison indices for the period of 1970 to 2008. These results show that the values of these

three indices on average from year to year move together. The signs on the return values of the

three indices are identical for 26 of the 39 years of the study. Of the 13 years when the signs

differ, six differ only between the AG Index and one of the comparison indices. The relationship

between the AG Index and the comparison indices is better illustrated in graphical form. Figure 2

shows the annual geometric returns of AG Index and the S&P 500 for the period of 1970 to

Daily Annual Daily Annual Daily Annual

Mean 0.00005 0.01273 0.00029 0.06495 0.00030 0.07476

Standard Error 0.00010 0.02605 0.00011 0.02768 0.00011 0.02655

Median 0.00027 0.02894 0.00039 0.07136 0.00033 0.07179

Mode 0 0 0 0 0 0

Standard Deviation 0.01040 0.16265 0.01056 0.17284 0.01066 0.16581

Sample Variance 0.00011 0.02646 0.00011 0.02987 0.00011 0.02749

Kurtosis 16.86589 0.22506 22.84198 -0.04035 27.87884 -0.23721

Skewness -0.87764 -0.12207 -0.73049 -0.54564 -0.86131 -0.49628

Range 0.26245 0.74971 0.32047 0.71742 0.33691 0.67583

Minimum -0.15904 -0.36769 -0.20467 -0.37585 -0.22610 -0.32717

Maximum 0.10340 0.38202 0.11580 0.34157 0.11080 0.34866

Sum 0.49295 0.49643 2.82639 2.53315 2.94795 2.91576

Count 9845 39 9845 39 9845 39

AG Index Descriptive Statistics

S&P 500 Descriptive Statistics

DOW Descriptive Statistics

Figure 2: Annual Geometric Return, AG Index and the S&P 500 (1970-2008)

2008. The solid series is the annual geometric returns of the AG Index and the long dashed series

is the annual geometric returns of the S&P 500. It is clear that the two indices follow each other

closely, with a few exceptions. The periods of 1987 to 1990, 1992 to 1995, and 1997 to 2000 are

periods where the two series diverge. It is unclear what the cause of the divergence is, but it is

hypothesized that macroeconomic effects or agricultural sector specific effects are to blame.

Further extensions of this research should attempt to determine the effects of agriculture specific

indicators and macroeconomic factors (gross domestic product, inflation, and the value of the US

dollar) on the value of the AG Index. Figure 3 shows the annual geometric returns of AG Index

and the Dow Jones Industrial Average (DOW) for the period of 1970 to 2008. The short dashed

series is the annual geometric return for the DOW index and the solid series is the annual

geometric return of the AG Index. It is clear from the graph that the AG Index and the DOW

geometric return series follow each other closely with only two exceptions. During the periods of

-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

10%

15%

20%

25%

30%

35%

AG Index -Geometric Return

S&P 500 - Geometric Return

Figure 3: Annual Geometric Return, AG Index and the Dow Jones Industrial Average (1970-

2008)

1992 to 1994 and 1999 to 2002, the two return series diverge. Again, it is hypothesized that

macroeconomic effects or agricultural sector specific effects are the cause of the divergence.

Figure 4 shows the annual geometric returns for the period 1970 to 2008 for the AG Index and

both of the comparison indices. It is clear from the graph that the three indices follow each other

with the exception of two periods. The periods of 1992 to 1994 and 1996 to 2000 show a clear

divergence between the three series. Specifically, the AG Index annual geometric returns are

lower than that of the two comparison indices during these periods. For a better look at the long-

term performance of the AG Index, the return series was split in to five and ten-year holding

return periods. Table 3 contains the numerical value of the five-year holding period return for

AG Index and the comparison indices. Bolded values indicate five-year periods where the AG

Index outperformed both of the market indices and asterisked values indicate five-year periods

where the AG Index outperformed only one of the market indices. With the exception of two 5-

-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

10%

15%

20%

25%

30%

35%

AG Index -Geometric Return

Dow Jones - Geometric Return

Figure 4: Annual Geometric Return, AG Index, S&P 500, and the Dow Jones Industrial Average

(1970-2008)

year periods (1990 to 1994 and 2000 to 2004), the three indices have identical signs. During the

2000-2004 period of divergence the AG Index, showed positive returns while the two

Table 3: Five-Year Geometric Returns, 1970-2008

comparison indices showed negative returns. The AG Index outperformed at least one of the

market indices three of the eight 5-year holding periods (1980-1984, 2000-2004, and 2005-

2008). Only in the 2000-2004 5-year holding period did the AG Index showed higher returns

than both of the comparison indices. For the period of 2005 to 2008, the AG Index showed less

-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

10%

15%

20%

25%

30%

35%

AG Index -Geometric Return

Dow Jones - Geometric Return

S&P 500 - Geometric Return

Return Periods AG Index S&P 500 Dow Jones

1970-1974 -10.16246% -5.82437% -5.40806%

1975-1979 0.91591% 9.05409% 5.94676%

1980-1984 9.67176%* 9.95148% 8.12703%

1985-1989 5.64102% 7.37845% 17.19192%

1990-1994 -2.84233% 5.30378% 6.50936%

1995-1999 2.12043% 26.02835% 24.07875%

2000-2004 0.86133% -3.72495% -1.40965%

2005-2008 -6.59831%* -6.90884% -4.80796%

negative returns than that of the S&P 500 index at -6.59 to -6.91 percent respectively. The largest

divergence observed was during the period of 1995 to 1999 where the spread between the AG

Index and the S&P 500 and the DOW was 23.91 percent and 21.96 percent respectively. The

period of 1995 to 1999 saw tremendous growth in the general market, yet the AG Index did not

experience the same growth. Recent results suggest that investor interest in the US Agriculture

sector is justifiable as the most recent 5-year periods show the AG Index outperforming the

market. The ten-year holding period returns for the AG Index and the two comparison indices

show similar characteristics and are given in Table 4. The AG Index failed to outperform the

comparison indices in all but one of the four ten-year periods. The most recent decade of data

showed the AG Index in negative growth (-2.53 percent) though, the market indices were down

further (S&P 500 at -5.15 percent and the DOW at -2.93 percent). Three of the four periods

showed negative returns for the AG Index while the comparison indices showed negative returns

Table 4: Ten-Year Geometric Returns, 1970-2008

in only one of the four periods. The only ten-year period of positive AG Index returns was 1980

to 1989 at 7.64 percent, though this trailed behind the returns of the S&P 500 and the DOW at

8.66 and 12.57 percent respectively. Graphs of the five and ten-year geometric returns are

provided in Appendix J, K, L, and M.

4.3 Risk Comparisons

Appendix N contains the annual standard deviation results for the AG Index and the comparison

indices for the period of 1970 to 2008. Peak annual AG Index price variability was recorded in

Return Periods AG Index S&P 500 Dow Jones

1970-1979 -4.784259% 1.34218% 0.108491%

1980-1989 7.637525% 8.65735% 12.568268%

1990-1999 -0.391852% 15.20096% 14.958898%

2000-2008 -2.524920% -5.15324% -2.934733%

2008 at 2.167 percent, though this was lower than the S&P 500 and the DOW indices, which

were 2.58 and 2.39 percent, respectively. The lowest annual AG Index price variability was

recorded in 2006 at 0.57 percent, while the standard deviation for the S&P 500 and DOW were

0.63 and 0.62 respectively. Both the peak and lowest price variability numbers show that the AG

Index carried less price variability than that of the comparison indices. However, Figure 5 shows

that this trend was not true for the entire 1970 to 2008 period. The solid series represents the

annual standard deviation for the AG Index while the large dashed and small dashed lines

represent the S&P 500 and the DOW, respectively. The graph shows that the price variability of

the AG Index closely follows that of the comparison indices during the 1970’s but deviated from

Figure 5: Annual Standard Deviation, AG Index, S&P 500, and the Dow Jones Industrial

Average (1970-2008)

them during the early 1980’s. From 1978 to 1985, the AG Index showed less price risk than both

of the comparison indices did. The sharp increase in price variability during the late 1980’s was

felt equally across all three indices though the persistence of the risk was longer for the AG

0.0000%

0.2250%

0.4500%

0.6750%

0.9000%

1.1250%

1.3500%

1.5750%

1.8000%

2.0250%

2.2500%

2.4750%

2.7000%

2.9250%

AG Index -Standard Deviation

S&P 500 - Standard Deviation

Dow Jones Industrial Average -Standard Deviation

Index. This trend of higher AG Index variability continued in to the late 1990’s. From 2001 to

the end of the data period in 2008, the AG Index has shown to carry less price variability

indicating that the AG Index may be a safer investment than a general market based index. To

get a closer look at the story of price risk among the three indices in question, standard deviation

measures were calculated for five and ten-year holding periods. Table 5 contains the standard

deviation calculations for the AG Index and the two comparison indices. Bolded values indicate

a five-year period in which the AG Index showed less price variability than both of the

comparison indices did and an asterisked value indicated a five-year period when the AG Index

showed less price variability than one of the comparison indices. The AG Index showed less

Table 5: Five-Year Standard Deviation 1970-2008

price variability than at least one of the comparison indices in five of the eight five-year periods

and less than both comparison indices in three of five of those periods. Table 6 contains the ten-

year period standard deviation measures for the three indices. Again, bolded values indicate a

ten-year period in which the AG Index showed less price variability than both of the comparison

indices and an asterisked value indicated a ten-year period when the AG Index showed less price

variability than one of the comparison indices. The AG Index showed to have less price

variability than at least one of the comparison indices in three of the four ten-year periods.

During the most recent period, 2000 through 2008, the AG Index showed less price variability

Periods AG Index S&P 500 Dow Jones

1970-1974 1.00025%* 0.95185% 1.01169%

1975-1979 0.75790%* 0.75410% 0.83770%

1980-1984 0.81340% 0.94395% 0.96045%

1985-1989 1.30862% 1.20152% 1.28085%

1990-1994 0.95213% 0.75036% 0.78071%

1995-1999 1.10918% 1.01207% 0.99278%

2000-2004 1.05832% 1.26754% 1.23033%

2005-2008 1.24574% 1.46630% 1.36315%

Table 6: Ten-Year Standard Deviation, 1970-2008

than both comparison indices. Five and ten-year standard deviation graphs are provided in

Appendices O, P, Q, and R.

Based on these preliminary results, it can be argued that the AG Index carried less price

variability risk during much of the 39 years of data than the market indices. However, further

analysis is needed to determine conclusively the price risk associated with investing in the US

Agricultural sector. Investors, in the hopes of getting large returns, are not always opposed to

price variability, (large standard deviation value). Rather, they are mainly concerned about

downside variability. Since the standard deviation, only reports variability in general with no

consideration of upward or downward variability, it only tells part of the story of the risk of a

security. “Risk adjusted return” measures, like the Sharpe Ratio, have gained popularity among

investors and analysts in recent years and are better measures of security performance.

4.4 Sharpe Ratio

A security’s Sharpe Ratio tells an investor how much excess return he/she is receiving per unit of

risk. Excess return is defined as the difference between the security’s return and the risk free rate.

The risk free rate proxy is dependent on the investment horizon. Annual Sharpe Ratio measures

are calculated using geometric returns on 1-year US Treasury Bills, five and ten-year Sharpe

Ratio measures are calculated using geometric returns on five and ten-year US Treasury Bills.

The risk measure used is standard deviation. Appendix S contains the annual Sharpe Ratio

calculations for the AG Index, S&P 500, and DOW for the period 1970 to 2008. Appendix T

Periods AG Index S&P 500 Dow Jones

1970-1979 0.88742%* 0.85890% 0.928756%

1980-1989 1.08912%* 1.08005% 1.131851%

1990-1999 1.033415% 0.89122% 0.893263%

2000-2008 1.144823% 1.35873% 1.290481%

contains a line graph of the Sharpe Ratio series for all three indices from 1970 to 2008. For 14

out of the 39 years in the study, the AG Index showed higher excess returns per unit of risk

(larger Sharpe Ratio value) than at least one of the comparison indices. To explain the long-term

risk adjusted risk associated with the AG Index better, measure was calculated for five and ten-

year hold periods. Table 7 contains the five-year Sharpe Ratio calculations for the AG Index,

S&P 500, and the DOW for the period 1970 through 2008. Bolded values indicate a five-year

period in which the AG Index had a higher Sharpe Ratio value than both of the comparison

indices and an asterisked value indicates a five-year period when the AG Index had a higher

Sharpe Ratio value than one of the two comparison indices. These results indicate that the AG

Index showed higher excess returns per unit of risk than a market index in only three of the eight

Table 7: Five-Year Sharpe Ratio, 1970-2008

five-year periods. Both comparison indices showed positive returns per unit of risk for the period

of 1990 to 1994, while the AG Index a showed negative Sharpe Ratio value. During the period of

1995 to 1999, the market indices experienced tremendous growth, while the AG Index did not

exhibit similar risk reward tradeoff. Table 8 contains the ten-year Sharpe Ratio calculations for

the three indices. Again, bolded values indicate a ten-year period in which the AG Index showed

a higher Sharpe Ratio value than both of the comparison indices did. These results indicate that

Period AG Index S&P 500 DOW

1970-1974 -7.73 -3.55 -2.92

1975-1979 -7.76 2.95 -1.04

1980-1984 10.34 9.23 7.15

1985-1989 9.70 12.01 18.94

1990-1994 -3.10 6.83 8.10

1995-1999 5.82 30.28 28.82

2000-2004 12.92 7.23 9.32

2005-2008 9.02* 7.45 9.56

the AG Index enjoyed more excess returns per unit of risk than the comparison indices in only

the most recent of the four ten-year periods, 2000 through 2008. The most obvious divergence

Table 8: Ten-Year Sharpe Ratio, 1970-2008

among the three indices was during the 1990’s. The S&P 500 and DOW during this period

enjoyed high-risk adjusted returns at 19.71 and 19.36, respectively, while the AG Index showed

only 1.85% return per unit of risk. The five and ten-year Sharpe Ratio calculations, relative to the

annual calculations, provide less evidence that an investment in the AG Index would carry less

risk than an investment in a market index. However, these results mirror those of the returns and

Standard Deviation calculations, as the most recent periods show the AG Index outperforming

the two comparison indices. These most recent results legitimize current investor interest in the

sector. Graphs illustrating the five and ten-year Sharpe Ratio measures are provided in

Appendices U and V.

4.5 Beta Values

A security’s beta tells an investor how its return co-varies with a market portfolio. Therefore, it is

especially valuable for investors looking to diversify the risk associated with investing in certain

assets. To determine how the US agricultural sector co-varies with the market, beta parameters

were estimated for all 39 years, each of the 8 five-year holding periods, each of the 4 ten-year

holding periods, and over the entire holding period from 1970 to 2008. Table 9 summarizes the

results. During the 39 years in study, the AG Index beta value was greater than one only 8 years.

Therefore, during 31 out of the 39 in the sample, a 1 percent move

Periods AG Index S&P 500 Dow Jones

1970-1979 -8.19 -1.32 -2.55

1980-1989 9.77 10.79 13.75

1990-1999 1.85 19.71 19.36

2000-2008 7.75 4.61 6.57

Table 9: Beta Value Estimation Summary, AG Index (1970-2008)

in the value of the market portfolio was followed by a less than 1 percent move in the AG Index.

Securities that share this characteristic are considered defensive in nature and are seen as good

investments when the general market sours. Appendix W contains the annual beta estimation for

the AG Index from 1970 to 2008. Refer to Figure 6 for an illustration of the annual beta value

estimation for the AG Index over the 39 years of study. This graph shows that the correlation of

the AG Index and the market portfolio (S&P 500) was not constant over time. Two large drops in

correlation were observed with the first in the late 70’s and second in the late 90’s. However, this

figure clearly shows that over most of the observed period, the AG Index had a beta value of less

Figure 6: Annual Beta Value Estimation, AG Index (1970-2008)

Holding Period Beta of < 1 Beta of > 1 Total Periods

1 year 31 839

Five-Year 7 1 8

Ten-Year 4 0 4

0.2

0.4

0.6

0.8

1.2

Annual Beta Value

than one. Five-year and ten-year beta estimations show identical results. They are provided in

Table 10 and Table 11. The AG Index had a beta value of greater than one in only one of the 8

five-year periods examined in this study. For the ten-year holding period beta estimations, all 4

Table 10: Five-year Average Beta Estimation

periods showed the AG Index to be defensive towards market movements. These results are

consistent with the a priori expectations of this study, the beta estimation of the US Food Sector

by NYU, and with the aforementioned investor sentiment regarding the US agricultural sector.

This information would be very valuable to investors seeking ways to diversify portfolio risk.

Table 11: Ten-year Average Beta Estimation

Five and ten-year estimated beta values are provided in graphical form in Appendix X and Y.

The beta value for the AG Index over the entire observed period was .793, indicating that the

long term reaction of the AG Index returns to the market was defensive.

Year AG Index Beta Estimation

1970-1974 0.952277005

1975-1979 0.874722411

1980-1984 0.774966197

1985-1989 0.96696327

1990-1994 1.042287329

1995-1999 0.811818249

2000-2004 0.471286473

2005-2008 0.757134992

Year AG Index Beta Estimation

1970-1979 0.921846822

1980-1989 0.89318051

1990-1999 0.894844709

2000-2008 0.617782228

CHAPTER 5: CONCLUSION

5.1 Discussion and Future Research

As expected, the AG Index has historically exhibited lower returns than the market indices;

however, data that is more recent has shown a shift in this paradigm. Preliminary evidence also

indicates that the sector carries less risk than the market as a whole. Over the past 39 years, the

US agriculture sector, as summarized by the AG Index, has shown to have a lower standard

deviation, higher excess return per unit of risk, and beta value of less than one. All of these

results indicate that the industry would be a wise investment during periods of high market

volatility. Additionally, in recent years the sector has outperformed the market indices.

Overall, the agricultural industry has undergone tremendous growth during the past 39

years. Refer to Table 12 for firm and market size statistics in 2009 dollars. The total market

value of the index, which represents only the top 70th percentile of firms in the sector, grew from

$24.675 billion in 1970 to $91.8 billion in 2008 in real terms, an increase of more than 270

percent. This increase in market value has occurred while the number of firms that make up the

top 70th percentile of the sector has decreased from an average of 53 firms throughout the 1970’s

Table 12: Average Firm Size and Average Real Market Value (1970-2008)

to 36.22 in the 2000’s. Refer to Appendix Z for a list of the number of firms included in the

index by year. In other words, an average of 36.22 firms in the 2000’s were, worth almost four

times what an average of 53 firms were worth in the 1970’s in real dollars (2009 dollars).

Moreover, the average real market value per firm increased over this period by more than 440

Decade Average # of Firms Average Real MKT Value Average Real MKT Value/Firm

1970's 53 24,675,675,000.00 465,578,773.58

1980's 54.7 30,180,185,000.00 551,740,127.97

1990's 43.6 71,827,484,000.00 1,647,419,357.80

2000's 36.22 91,620,218,000.00 2,529,547,708.45

percent. To summarize these results; the top 70th percentile of the US agriculture sector has

grown tremendously over the past 39 years, though the average market value per firm has grown

at almost twice the rate. It is quite clear that this trend is linked to the increasing concentration of

firms within the Agricultural sector. Consolidation and vertical integration can affect firm

profitability, therefore investors are likely to be interested in how these trends and how they

affect stock price value.

As noted in an earlier section, a limitation of many stock price indices is that dividend

payments are usually ignored. However, from an investor’s point of view, income from dividend

streams is often just as important as price growth. Furthermore, it can be argued that dividend

payments reduce retained earnings, which in turn imply lower future cash flows and

consequently, lower stock price return. Therefore, the lower stock price returns observed in the

AG Index over the past 39 year may be explained by higher dividend payments. This limitation

will be addressed in future research, however, some preliminary results suggest that the observed

lower returns of the AG Index, as compared to the market, may indeed be offset by the

comparably larger dividend yield associated with the agribusiness firms in the index. Current

dollar dividend payments per share were attained for all the firms included in the index in 2008.

Percent dividend, or “yield”, was calculated for each firm by dividing the share price of each

index by their respective dollar dividend payment. The average yield was calculated for the

entire index, by subsector, and by the top five and top ten firms in the AG Index. The same

calculations were completed for funds that follow the comparison indices and a fund that

represents the total market. Table 13 contains these preliminary dividend results. The top 5 and

10 firms included in the AG Index, as of 2008, had higher dividend yield than those top firms in

all three of the comparison indices. When all of firms included in the AG Index are considered,

the yield was somewhat lower than that of the market indices though a further segmentation of

Table 13: Average Dividend Yield, AG Index, S&P 500, Dow Jones Industrial Average, and the

Vanguard Total Market ETF (2009 Prices and Dividend Data)

the AG Index tells a more interesting story. When the average yield is calculated for each of the

three SIC code subcategories, it is clear that the “closely related to farming” category carries the

highest dividend yield among the three. These values are provided in Table 14. When compared

to the three market indices, the closely related to farming subsector shows higher or similar yield

potential. These results indicate that even though these three categories are involved to some

extent in satisfying the final demand for agricultural products, each one may have differing

characteristics. The results from the table below indicate that, from an investment standpoint, it

might be beneficial to drop the pure farming stocks and specify the index to represent the “first

Table 14: Average Dividend Yield by Subcategory, AG Index (2009 Prices and Dividend Data)

handlers” of raw agricultural products in the closely related to farming category. This includes

processors, marketers, and agricultural input firms. It is likely that each category has unique

performance and risk characteristics that can be exploited through different investment strategies.

Therefore, segmenting the larger US agriculture sector by specific characteristics such as firm

size or input versus output orientation could be very valuable to investors. Moreover, recent

literature suggests that farm owners looking to hedge some of their financial risk may be better

off investing in the larger Ag sector rather than just a market portfolio. Detre et al. (2007)

Average Yield AG Index

S&P 500 (Vanguard

500 "VFINX")

DOW (DIAMONDS

Trust "DIA")

Vanguard Total

Market (VTI)

Top 5 Firms 4.47% 2.13% 2.80% 2.13%

Top 10 Firms 3.30% 2.53% 2.84% 2.53%

All 2.16% 2.68% 3.06% 2.53%

Farming 0.55%

Closely Related to Farming 3.05%

Peripherally Related to Farming 2.43%

Average Yield

showed that an investment in both the AG sector and a market index could reduce downside risk

exposure as compared to an investment in only a market index. A possible application of this

research is the development of an investible Equity Traded Fund (ETF) or an agriculturally

related family of mutual funds. ETF’s are investible vehicles that are traded on a stock exchange

much like a normal stock. Investors purchase shares of an ETF, which replicates the performance

of an index of a basket of stocks, minus fees and expenses. Like stocks, commodities, or any

other tradable security, ETF’s can be shorted and their capital gains can be controlled. Therefore,

farm owners expecting poor farm returns can short a larger AG sector ETF to hedge on-farm

risk. Likewise, institutional investors looking to diversify portfolio risk could hold a portion of

investment capital in one of these tradable securities. Moreover, future projections of the AG

Index would be very useful to investors, as would projections of price risk. These estimations are

attainable through modern econometric methods such as autoregressive conditional

heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity

(GARCH) volatility models. Future extension of this research will consider these issues.

As previously discussed, the role of seasonality and agricultural planting and harvest

cycles can affect performance and risk conditions in the sector. The effect of seasonality can be

felt on the demand and supply side of any market. This effect is particular important when

studying commodities and agribusiness companies. This is because one of the biggest

determinants of supply is weather and climate. Business cycles, by definition, are fluctuations in

economic activity along the long-term growth trend. Having the ability to determine where

businesses are in their cycle is of great benefit to the potential investor. Further research is

needed to determine the impact of these factors, as they are likely to affect the accuracy of price

projections.

Another valuable extension of this research would be to determine the impact of

changing macroeconomic factors on agribusiness profitability and stock prices. Examples of

these factors could include, US Gross Domestic Product, the value of the US dollar, the price of

gold, the price of oil and other commodities, and inflation. The links between these factors can

examined through simple correlation calculations.

In any statistical or financial study, it is important to discuss the limitations of the

methods and therefore the accuracy of results. As with most indices, dividends were ignored in

this study. Over long holding periods, dividend income can influence investment returns greatly.

Because dividends are ignored, the return calculations are only measures of price change from

one period to another, not investment return with dividends reinvested. Future extensions of the

AG Index will examine the possibility of correcting for dividends to determine a true investment

holding period return. Another limitation is the frequency by which share counts were updated.

A more accurate tracking of the US agricultural sector would require immediate corrective action

for large changes in share counts and quarterly correction of all small changes in share counts.

Lastly, the fees and transactional costs of investing in the AG Index are not included in this

study. Potential investors should closely evaluate these costs before making investment

decisions.

5.2 Summary

The growing global demand for food, popularity of organic products, and increasing competition

among the alternative uses of feed crops, are a few observable trends that have made investing

US agricultural sector an area of interest among investors. The rising prices of commodity crops

and subsequent increase in firm profitability have signaled famers to increase production. The

accompanying increase in demand for agricultural inputs such as feed, seed, and equipment, has

affected the profitability of US agribusiness firms involved in their production. Despite these

trends, little literature exists that analyzes the historical risk and return associated with investing

in publicly traded US agricultural securities. This study has provided original research on the

returns and risks associated with an investment in publicly traded agribusiness companies. This

was accomplished through the development of a large-cap agribusiness stock price index. The

resulting index is a continuous series that represents the largest US agribusiness firms over a 39-

year period. The calculated risk and return measures associated with the agribusiness index were

compared to that of the market as a whole. The results indicate that although the returns

associated with investing in the US agricultural sector were less than what could be expected by

investing in a market index, preliminary evidence indicates that the sector is less susceptible to

price variability and is defensive in nature.

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APPENDIX A: DAX GLOBAL AGRIBUSINESS INDEX CONSTITUENTS (AS OF

DECEMBER 2009)

Company Name Country Trading Symbol Exchange

AGCO Corp United States AGCO NYSE

Agrium Inc Canada AGU NYSE

The Andersons Inc United States ANDE NasdaqGS

Astra Agro Lestari Indonesia AALI.JK JKT

AWB Ltd Australia AWB.AX ASX

BRF - Brasil Foods SA ADR Brazil

BRFS NYSE

Bunge Ltd (Bermuda) United States

BG NYSE

CF Industries Holdings United States

CF NYSE

China Agri Inds Hld Hong Kong CIDHF.PK Other OTC

Chiquita Brands Intl Inc United States

CQB NYSE

CNH Global NV Netherlands

CNH NYSE

Corn Products Intl United States

CNP NYSE

Cosan Ltd Brazil CZZ NYSE

Cresud SA Com Ind Argentina CRESY NasdaqGS

Darling Ing Intl Inc United States DAR NYSE

Del Monte Foods Co United States DLM NYSE

Glanbia Plc Ireland GL9.IR ISE

Golden Agri-Res Singapore 4G3A SES

Graincorp Ltd Australia GNC.AX ASX

Indofood Agri Res Singapore ZVF SES

Intrepid Potash United States IPI NYSE

IOI Corporation Ber Malaysia IOI MK KLS

Kuala L Kepong B Malaysia KLKB MK KLS

Lindsay Corp United States LNN NYSE

London Sumatr Ind Indonesia LSIP.JK JKT

Maple Leaf Foods Canada MFI.TO TOR

Nufarm Ltd Australia NUF.AX ASX

Nutreco Hldg Nv Netherlands NUO.AS AMS/AEX

Olam Intl Ltd Singapore O5I SES

Potash Corp. (US) Canada

POT NYSE

Smithfield Foods Inc United States

SFD NYSE

Soc Quimica Min ADR B Chile QYM NYSE

Tate & Lyle Britain 36IS.L LSE

Terra Industries Inc United States

TRA NYSE

Tyson Foods Inc A United States

TSN NYSE

Viterra Inc Canada VT.TO TOR

Wilmar Intl Ltd Singapore RTHA SES

Yara International Norway YAR.OL OSL

APPENDIX B: STANDARD AND POORS AGRIBUSINESS NORTH AMERICA INDEX

CONSTITUENTS (AS OF DECEMBER 2009)

Company Name Country Trading Symbol Exchange

AGCO Corp United States AGCO NYSE

Agrium Inc Canada AGU NYSE

Archer-Daniels-Midland Co United States ADM NYSE

BRF - Brasil Foods SA ADR Brazil BRFS NYSE

Bunge Ltd (Bermuda) United States BG NYSE

CF Industries Holdings United States CF NYSE

CNH Global NV Netherlands CNH NYSE

Cal Maine Foods Inc United States CALM NasdaqGS

Chiquita Brands Intl Inc United States CQB NYSE

Corn Products Intl United States CPO NYSE

Deere & Co United States DE NYSE

Fresh Del Monte Produce(Caymans) United States FDP NYSE

Hormel Foods Corp United States HRL NYSE

Kubota Corp ADR Japan KUB NYSE

Monsanto Co. United States MON NYSE

Mosaic Co United States MOS NYSE

Potash Corp. (US) Canada POT NYSE

Sanderson Farms United States SAFM NasdaqGS

Smithfield Foods Inc United States SFD NYSE

Sociedad Quimica y Minera de Chile -B (ADR) Chile SQM NYSE

Syngenta AG ADR Switzerland SYT NYSE

Terra Industries Inc United States TRA NYSE

Tyson Foods Inc A United States TSN NYSE

Viterra Inc Canada VT.TO Toronto

Industry

groups

and

components

1987

Standard

Industrial

Classification

(SIO)|

‘Farming.

[Farm

production

(farm

proprietors,

and

wage

and

salary

01-02

[1]

Closely

industries:

[Agricultural

services,

forestry,

and

fishing

(071

Soil

preparation

services|

072

Crop

services|

074

Veterinary

services

075

Animal

services,

except

veterinary|

076

Farm

labor

and

management

services

Forestry|

Fishing,

hunting.

and

trapping|

[Agricultural

input

industries

[Agricultural

chemicals

287

[Farm

machinery

and

equipment

3523

[Farm

supply

and

machinery

(wholesale

trade)

‘5083

Farm

and

garden

machinery

and

equipment

5191 Farm

supplies|

[Commodity

contract

brokers

and

dealers

62,

[Agricultural

processing

and

marketing

[Meat

products

201

[Dairy

products

202,

[Canned,

frozen,

and

preserved

fruits

and

vegetables

203;

[Grain

mill

products

204]

[Bakery

products

205]

Sugar

and

confectionery

products

206|

[Fats

and

oils

products

207

[Beverages

208|

[Miscellaneous

food

preparations

and

kindred

products

209]

[Tobacco

products

21]

[Apparel

and

textiles

221

Broadwoven

fabric

mills,

cotton]

222

Broadwoven

fabric

mills,

manmade

fiber

and

silk

223

Broadwaven

fahric

mills,

wool

(inchiding

dyeing

and

finishing)

224

Narrow

fabric

and

other

smallwares

mills:

cotton,

wool,

silk,

and

manmade

fiber|

2251

Women's

full-length

and

knee-length

hosiery,

except

socks

2252

Hosiery,

NEC|

2253

Knit

outerwear

mills|

2254

Knit

underwear and

nightwear

mills

2257

Weft

knit

fabric

mills|

2258

Lace

and

warp

knit

fabric

mills

1226

Dyeing and

finishing

textiles,

except

wool

fabrics

and|

knit

goods|

228

Yam

and

thread

mills|

231

Men's

and

boys’

suits,

coats,

and

overcoats|

232

Men's

and

boys'

furnishing,

work

clothing,

and

allied|

garments|

233

Women's,

misses’,

and

juniors'

outerwear|

234

Women's,

misses’,

children's,

and

infants|

undergarments|

235

Hats,

caps,

and

millinery|

236

Girls’,

children's,

and

infants’

outerwear

237

Fur

goods|

238

Miscellaneous

apparel

and

accessories

2397

Schifili

machine

embroideries|

3965

Fastemer,

buttons,

needles,

and

pins|

lLeather

products

and

footwear

302

Rubber

and

plastics

footwear|

Leather

and

leather

products

[Packaging

2441

Nailed

and

lock

corner

wood

boxes

and

shook|

2449

Wood

containers,

NEC|

3221

Glass

containers|

3411

Metal

cans|

3466

Crowns

and

closures|

[Farm-related

raw

materials

(Wholesale

trade)

515]

[Warehousing

4221 Farm

product

warehousing

and

storage|

4222

Refrigerated

warehousing

and

storage|

APPENDIX C: ECONOMIC RESEARCH SERVICE AGRIBUSINESS INDUSTRY GROUPS

BY STANDARD INDUSTRIAL CLASSIFICATION CODES

Peripherally

industries:

[Agricultural

wholesale

and

retail

trade

—

Wholesale

trade

‘513

Apparel,

piece

goods,

and

notions|

514

Groceries

and

products|

518

Beer,

wine,

and

distilled

alcoholic

beverages|

5194

Tobacco

and

tobacco

products|

[Retail

trade

‘54

Food

stores|

‘56

Apparel

and

accessory

stores|

‘58

Eating

and

drinking

places|

‘592

Liquor

stores

5948

Luggage

and

leather

goods

stores|

5949

Sewing,

needlework,

and

piece

goods

stores|

5993

Tobacco

stores

and

stands

[Indirect

‘business

—

[Chemical

and

fertilizer

mining

147|

[Miscellaneous

textile

products

2259

Knitting

mills,

NEC|

2298

Cordage and

twine|

2299

Textile

goods,

NEC|

2393

Textile

bags

2395

Pleating,

decorative

and

novelty

stitching,

andl

tucking

for

the

trade|

|Containers,

paper

products,

and

pulpwood

products

263

Paperboard

mils

265

Paperboard

containers

and

boxes|

2671

Packaging

paper

and

plastics

film,

coated

and|

laminated

2672

Coated and

laminated

paper,

NEC|

2673

Plastics,

foil

and

coated

paper

bags

2674

Uncoated

paper

and

mutiwall

bags

2679

Converted

paper

and

paperboard

products,

NEC|

[Food

products

machinery

3556|

Miscellaneous

manufacturing

2448

Wood

containers,

NEC|

3497

Metal

foil

and

leat

(APPENDIX C CONTINUED)

APPENDIX D: FIRMS DROPPED FROM THE INDEX BY CRSP PERMANENT NUMBER (1970-2008)*

* No firms were cut from the sample because of missing data for the following years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, or 2008.

APPENDIX E: AG INDEX CONSTITUENTS BY CRSP PERMANENT NUMBER (1970-1989)

(APPENDIX E CONTINUED)

APPENDIX F: AG INDEX CCONSTITUENTS BY CRSP PERMANENT NUMBER (1990-2008)

(APPENDIX F CONTINUED)

APPENDIX G: NUMBER OF TRADING DAYS BY YEAR (1970-2008)

Year # of Trading Days

1970 254

1971 253

1972 251

1973 252

1974 253

1975 253

1976 253

1977 252

1978 252

1979 253

1980 253

1981 253

1982 253

1983 253

1984 253

1985 252

1986 253

1987 253

1988 253

1989 252

1990 253

1991 253

1992 254

1993 253

1994 252

1995 252

1996 254

1997 253

1998 252

1999 252

2000 252

2001 248

2002 252

2003 252

2004 252

2005 252

2006 251

2007 251

2008 253

APPENDIX H: GRAPH - AG INDEX VALUE (1970-2008)

APPENDIX I: ANNUAL GEOMETRIC RETURN, AG INDEX, S&P 500, AND THE DOW

JONES INDUSTRIAL AVERAGE (1970-2008)

Period AG Index S&P 500 Dow Jones

1970 1.58935%* -0.91398% 3.67276%

1971 7.62254%* 12.00219% 7.17941%

1972 1.85683% 16.11095% 14.69920%

1973 -23.82525% -18.09404% -17.52675%

1974 -31.01787% -29.81163% -27.95211%

1975 29.02264%* 28.42090% 34.86646%

1976 5.30076% 18.21782% 16.99526%

1977 -19.23706% -11.12150% -16.86222%

1978 2.89380% 2.44084% -1.55673%

1979 -7.29580% 11.58896% 3.36694%

1980 14.28594% 28.36611% 16.90821%

1981 -3.72838% -10.11442% -10.05160%

1982 23.92878% 14.58367% 18.58541%

1983 10.52141% 19.22076% 22.55024%

1984 5.28449% 1.95074% -3.28640%

1985 18.68194% 27.76199% 29.01065%

1986 -7.87475% 15.54463% 23.29538%

1987 -7.36100% 0.25563% 0.59772%

1988 12.64345% -4.43463% 7.60799%

1989 15.31872%* 0.93106% 28.37586%

1990 -12.63256% -8.19317% -6.28045%

1991 29.62800% 27.76535% 21.38135%

1992 -11.97989% 4.42170% 4.05685%

1993 -8.54084% 7.13629% 13.44335%

1994 -5.04279% -1.32563% 2.07209%

1995 38.20239% 34.15739% 33.31110%

1996 -2.59837% 19.33369% 24.54529%

1997 2.90604% 31.67121% 22.75145%

1998 5.51871% 26.06970% 15.27161%

1999 -24.01794% 19.63602% 25.18273%

2000 13.38657% -9.27282% -5.01448%

2001 -12.48483% -10.53481% -5.86672%

2002 -9.45797% -23.80334% -17.19151%

2003 10.43562% 22.31940% 21.45101%

2004 5.20083%* 9.33170% 3.58468%

2005 2.17573%* 3.84417% -0.11119%

2006 6.68611% 11.78279% 14.89517%

2007 10.41616% 3.65382% 6.33531%

2008 -36.76891%* -37.58465% -32.71683%

APPENDIX J: GRAPH - FIVE-YEAR GEOMETRIC RETURN, AG INDEX AND THE S&P 500 (1970-2008)

-10%

-8%

-5%

-3%

10%

13%

15%

18%

20%

23%

25%

1970-1974

1975-1979

1980-1984

1985-1989

1990-1994

1995-1999

2000-2004

2005-2008

AG Index -Geometric Return

S&P 500 - Geometric Return

APPENDIX K: GRAPH - FIVE-YEAR GEOMETRIC RETURNS, AG INDEX AND THE DOW JONES INDUSTRIAL AVERAGE

(1970-2008)

-10%

-8%

-5%

-3%

10%

13%

15%

18%

20%

23%

25%

1970-1974

1975-1979

1980-1984

1985-1989

1990-1994

1995-1999

2000-2004

2005-2008

AG Index -Geometric Return

Dow Jones - Geometric Return

APPENDIX L: GRAPH - TEN-YEAR GEOMETRIC RETURN, AG INDEX AND THE S&P 500 (1970-2008)

-10%

-5%

10%

15%

20%

1970-1979

1980-1989

1990-1999

2000-2008

AG Index -Geometric Return

S&P 500 - Geometric Return

APPENDIX M: GRAPH - TEN-YEAR GEOMETRIC RETURN, AG INDEX AND THE DOW JONES INDUSTRIAL AVERAGE (1970-

2008)

-10%

-5%

10%

15%

20%

1970-1979

1980-1989

1990-1999

2000-2008

AG Index -Geometric Return

Dow Jones - Geometric Return

APPENDIX N: ANNUAL STANDARD DEVIATION, AG INDEX, S&P 500, AND THE

DOW JONES INDUSTRIAL AVERAGE (1970-2008)

Period AG Index S&P 500 DOW

1970 0.90105% 0.95275% 0.97498%

1971 0.63183% 0.64337% 0.69817%

1972 0.72247% 0.50143% 0.58341%

1973 1.054462%* 0.99686% 1.11397%

1974 1.44840% 1.37459% 1.42532%

1975 1.01992%* 0.97201% 1.06453%

1976 0.68944% 0.69961% 0.78396%

1977 0.6137%* 0.57171% 0.65196%

1978 0.73187% 0.79343% 0.89920%

1979 0.67311% 0.68321% 0.72922%

1980 0.88779% 1.03718% 0.98958%

1981 0.73533% 0.84738% 0.85165%

1982 0.99720% 1.15004% 1.17494%

1983 0.69442% 0.83913% 0.88138%

1984 0.72238% 0.80309% 0.87687%

1985 0.74251% 0.64026% 0.65332%

1986 1.22587% 0.92561% 0.96619%

1987 1.94011% 2.02469% 2.17207%

1988 1.16705% 1.07639% 1.14317%

1989 1.16294% 0.82257% 0.89521%

1990 1.23033% 1.00471% 1.02820%

1991 1.09214% 0.90074% 0.92297%

1992 0.90946% 0.60995% 0.65074%

1993 0.77174% 0.54182% 0.54651%

1994 0.67284%* 0.62012% 0.68747%

1995 0.69772% 0.49177% 0.54666%

1996 1.03093% 0.74210% 0.75439%

1997 1.36848% 1.14215% 1.17947%

1998 1.20128% 1.27802% 1.24968%

1999 1.07703%* 1.13838% 1.01829%

2000 1.44898% 1.39990% 1.30642%

2001 0.97118% 1.35793% 1.34533%

2002 1.17792% 1.63971% 1.60907%

2003 0.92359% 1.07516% 1.04479%

2004 0.65577% 0.69883% 0.68313%

2005 0.60236% 0.64780% 0.64881%

2006 0.56621% 0.63153% 0.62167%

2007 0.86385% 1.00700% 0.91558%

2008 2.16655% 2.58107% 2.38646%

APPENDIX O: GRAPH - FIVE-YEAR STANDARD DEVIATION, AG INDEX AND THE S&P 500 (1970-2008)

0.0000%

0.2250%

0.4500%

0.6750%

0.9000%

1.1250%

1.3500%

1.5750%

1970-1974

1975-1979

1980-1984

1985-1989

1990-1994

1995-1999

2000-2004

2005-2008

AG Index -Standard Deviation

S&P 500 - Standard Deviation

APPENDIX P: GRAPH - FIVE-YEAR STANDARD DEVIATION, AG INDEX AND THE DOW JONES INDUSTRIAL AVERAGE

(1970-2008)

0.0000%

0.2250%

0.4500%

0.6750%

0.9000%

1.1250%

1.3500%

1.5750%

1970-1974

1975-1979

1980-1984

1985-1989

1990-1994

1995-1999

2000-2004

2005-2008

AG Index -Standard Deviation

Dow Jones - Standard Deviation

APPENDIX Q: GRAPH - TEN-YEAR STANDARD DEVIATION, AG INDEX AND THE S&P 500 (1970-2008)

0.0000%

0.2250%

0.4500%

0.6750%

0.9000%

1.1250%

1.3500%

1.5750%

1970-1979

1980-1989

1990-1999

2000-2008

AG Index -Standard Deviation

S&P 500 - Standard Deviation

APPENDIX R: GRAPH - TEN-YEAR STANDARD DEVIATION, AG INDEX AND THE DOW JONES INDUSTRIAL AVERAGE

(1970-2008)

0.0000%

0.2250%

0.4500%

0.6750%

0.9000%

1.1250%

1.3500%

1.5750%

1970-1979

1980-1989

1990-1999

2000-2008

AG Index -Standard Deviation

Dow Jones - Standard Deviation

APPENDIX S: ANNUAL SHARPE RATIO, AG INDEX, S&P 500, AND THE DOW JONES

INDUSTRIAL AVERAGE (1970-2008)

Period AG Index S&P 500 DOW

1970 46.53 41.38 45.14

1971 26.86* 33.19 23.67

1972 -34.11 -20.73 -20.23

1973 -48.79 -45.86 -40.53

1974 -21.13* -21.39 -19.33

1975 43.43 44.95 47.10

1976 39.04 56.93 49.25

1977 -101.46 -94.72 -91.87

1978 -65.73 -61.20 -58.45

1979 -26.57 1.47 -9.90

1980 -2.57 11.37 0.34

1981 -4.88 -11.77 -11.64

1982 60.09 43.97 46.45

1983 -9.24 2.72 6.37

1984 19.50 13.39 6.29

1985 48.46 70.38 70.89

1986 11.62 40.69 47.01

1987 -14.70 -10.32 -9.47

1988 -11.58 -28.42 -16.22

1989 25.92* 19.15 48.25

1990 0.04 4.46 6.22

1991 62.72 73.98 65.28

1992 0.67 27.89 25.58

1993 -13.61 9.54 21.00

1994 -150.45* -157.25 -136.90

1995 95.39 127.12 112.80

1996 -8.90 17.19 23.82

1997 3.68 29.60 16.83

1998 18.77 33.73 25.85

1999 -50.68 -9.60 -5.29

2000 17.96 2.41 5.84

2001 46.39 34.61 38.40

2002 27.72 11.16 15.48

2003 23.50 31.24 31.32

2004 -159.69 -143.94 -155.66

2005 -91.00 -82.04 -88.01

2006 -13.19 -3.76 1.19

2007 50.18 36.33 42.89

2008 23.80 19.66 23.30

APPENDIX T: GRAPH - ANNUAL SHARPE RATIO, AG INDEX, S&P 500, AND THE DOW JONES INDUSTRIAL AVERAGE

(1970-2008)

-160.00

-134.50

-109.00

-83.50

-58.00

-32.50

-7.00

18.50

44.00

69.50

95.00

120.50

146.00

AG Index -Sharpe Ratio

Dow Jones - Sharpe Ratio

S&P 500 - Sharpe Ratio

APPENDIX U: GRAPH – FIVE-YEAR SHARPE RATIO, AG INDEX, S&P 500, AND THE DOW JONES INDUSTRIAL AVERAGE

(1970-2008)

-10.00

-7.50

-5.00

-2.50

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

22.50

25.00

27.50

30.00

32.50

1970-1974

1975-1979

1980-1984

1985-1989

1990-1994

1995-1999

2000-2004

2005-2008

AG Index -Sharpe Ratio

S&P 500 - Sharpe Ratio

Dow Jones - Sharpe Ratio

APPENDIX V: GRAPH – TEN-YEAR SHARPE RATIO, AG INDEX, S&P 500, AND THE DOW JONES INDUSTRIAL AVERAGE

(1970-2008)

-10.00

-7.50

-5.00

-2.50

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

22.50

1970-1979

1980-1989

1990-1999

2000-2008

AG Index -Sharpe Ratio

S&P 500 - Sharpe Ratio

Dow Jones - Sharpe Ratio

APPENDIX W: ANNUAL BETA VALUE ESTIMATION, AG INDEX (1970-2008)

Year AG Index

1970 0.8673522

1971 0.814655374

1972 0.957848146

1973 0.97733653

1974 1.010285371

1975 0.990376806

1976 0.92249389

1977 0.539339786

1978 0.875118904

1979 0.818083808

1980 0.751708057

1981 0.753252878

1982 0.806229279

1983 0.721237264

1984 0.836670553

1985 0.882333666

1986 1.076474714

1987 0.918651449

1988 1.030492438

1989 1.064008532

1990 1.068307286

1991 1.093708485

1992 1.07502552

1993 1.071220489

1994 0.807102592

1995 0.835797474

1996 0.852878645

1997 0.970509587

1998 0.794700964

1999 0.64788324

2000 0.314776233

2001 0.351949199

2002 0.527148295

2003 0.675452115

2004 0.754172555

2005 0.807023211

2006 0.692120307

2007 0.773707482

2008 0.754433291

APPENDIX X: GRAPH - FIVE-YEAR BETA VALUE ESTIMATION, AG INDEX (1970-2008)

0.2

0.4

0.6

0.8

1.2

1970-1974

1975-1979

1980-1984

1985-1989

1990-1994

1995-1999

2000-2004

2005-2008

Five-Year Beta Value

APPENDIX Y: GRAPH - TEN-YEAR BETA VALUE ESTIMATION, AG INDEX (1970-2008)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1970-1979

1980-1989

1990-1999

2000-2008

Ten-Year Beta Value

APPENDIX Z: NUMBER OF FIRMS INCLUDED IN THE AG INDEX BY YEAR (1970-

2008)

Year # of Firms

1970 48

1971 48

1972 50

1973 58

1974 51

1975 50

1976 53

1977 57

1978 59

1979 56

1980 58

1981 55

1982 57

1983 60

1984 61

1985 56

1986 54

1987 51

1988 46

1989 49

1990 47

1991 43

1992 44

1993 46

1994 48

1995 46

1996 42

1997 44

1998 41

1999 35

2000 35

2001 31

2002 33

2003 35

2004 36

2005 40

2006 40

2007 41

2008 35

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