journal man fin
silpac1850
BUS650_Chapter_07.pdf
Learning Objectives
After studying this chapter, you should be able to:
• Explain the significance of required return and its components.
• Describe the relationship between risk and return and how to measure for both.
• Identify how to use required return to determine valuation.
Associated Press7
Finding the Required Rate of Return for an Investment
byr80601_07_c07_201-224.indd 201 1/24/13 4:00 PM
CHAPTER 7Introduction
Introduction
Figure 7.0: Chapter 7 in focus
Customers Products FundsAsset
inputs Investors
The Financial Balance Sheet
Cash generated from operations
$
$
The discount rate used in valuation depends on the riskiness of the investment. Chapter 7 develops the method for measuring risk and finding the correct discount rate given that risk.
Investors come in many forms. They may be individuals who invest in corporate stocks, retirement accounts that invest in bonds, partnerships that invest in apartment buildings, or corporations that invest in productive projects. One thing all these investors have in common is their desire to increase their wealth, which is done by identifying projects whose value is expected to exceed their cost. If we invest $100 today in a project that pro- duces cash flows worth $125 in today’s terms, then we increase our wealth by $25. Equa- tion (7.1) is the basic formula for estimating the value of an investment, which is found by discounting the expected future cash flows back to today’s equivalent value at a rate of return that is appropriate given the investment’s risk. This fundamental formula for assessing value was first introduced in Chapter 2 and further developed in Chapters 4 and 5, while Chapter 3 explored cash flows in some detail.
(7.1) V0 5 aNt 5 1 CFt
11 1 R1r2 2 t
One part of the formula that hasn’t been covered is how to estimate the required return that is appropriate to use as the discount rate in the valuation calculation. Finding the required rate of return is the topic of this chapter (and is expanded upon in Chapter 8).
byr80601_07_c07_201-224.indd 202 1/24/13 4:00 PM
CHAPTER 7Section 7.1 The Building Blocks of the Required Return
Pre-Test
1. The two fundamental building blocks of the required return for an investment are the risk-free return and a risk premium.
a. True b. False
2. For simplicity’s sake expected returns are used to measure risk because historical returns only reflect past information.
a. True b. False
3. Required returns are used as the discount rate in valuation formulas. a. True b. False
Answers 1. a. True. The answer can be found in Section 7.1. 2. b. False. The answer can be found in Section 7.2. 3. a. True. The answer can be found in Section 7.3.
7.1 The Building Blocks of the Required Return
In Chapter 2, we introduced the idea that investors are assumed to be rational and risk averse. Because they are (mostly!) rational, investors will give up control of their money for a period of time by investing only if they expect to increase their wealth. Therefore, inves- tors have an almost instinc- tual return requirement as they invest. For example, a rational investor would always want to earn at least the risk-free rate of return when investing in some security or project. Other- wise, they would be settling for a return lower than what they could be assured of by simply depositing the funds in a sav- ings account that is guaranteed by both the bank and the government through the Federal Deposit Insurance Corporation (FDIC). The FDIC guarantees the first $250,000 of funds deposited to an individual’s bank account. So we establish that the first building block for assessing a required return is the risk-free interest rate.
Like children, who need to be bribed with the promise of a reward for their good behavior, investors require a worthwhile incentive before they will commit to an investment.
Beyond/SuperStock
byr80601_07_c07_201-224.indd 203 1/24/13 4:00 PM
CHAPTER 7Section 7.1 The Building Blocks of the Required Return
Different Types of Returns
It’s useful to do some thinking about different kinds of returns that investors might discuss when they are considering investment performance. One type of return is the historical return, also known as an actual or realized return. If you buy a share of stock for $20 and a year later you sell it for $22, you have earned a historical or realized return equal to 10% per year ($2 gain on a $20 investment). The actual return you earned is 10%. This may be the same or it may be quite different than the expected return that you were hoping for when you bought the stock. Perhaps your friend who is a stock broker told you that she had calculated a target selling price of $30 for the stock. If you believed her forecast, then you were expecting a 50% return when you decided to buy the stock. Clearly, if you were expect- ing a 50% return but the actual return was only 10%, then it’s likely that you were disappointed in result. But were you satisfied with the 10% that you earned? To answer that, we need to know your required return for the stock. The estimation of the required return for an investment is the subject of this chapter, but it is generally acknowledged that risk contributes to one’s required return. So if this was a super risky stock, you may have had a required return equal to 25%. In this case, you would have been pretty unhappy with the result. On the other hand, if the stock was considered a low risk invest- ment, then you might have had a return requirement of only 8%, and you were probably very satisfied with the 10% actual return, given the stock’s low risk.
For most investments, however, the risk-free rate is only the first component of the required return. Virtually all investments have some risk associated with them, so investors also require what is known as a risk premium to compensate them for this risk exposure. Recall that we assume that investors are risk averse, which implies that to bear risk they require compensation in order to subject themselves to distasteful uncertainty. This is a little like one of the authors of this text who used to pay his children five cents if they would eat all of their broccoli because his kids were “broccoli averse.”
Now we have the two fundamental building blocks of the required return for an invest- ment: the risk-free return and a risk premium.
R(r) 5 Risk-free rate of return 1 Risk premium
Given these intuitive building blocks, we will now take a closer look at returns, risk, and their relationship to one another in order to fully develop the methods for more precisely estimating the required rate of return for an investment.
byr80601_07_c07_201-224.indd 204 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
7.2 Risk and Return
The trade-off between risk and return is second nature to us: We understand that if we are going to invest in a bond issued by United Airlines, we would do so only if we expected to receive a rate of return greater than we would receive if we invested in a bond issued by the U.S. Treasury. Why? United Airlines is generally considered riskier than the US government. One of the great intellectual challenges of finance over the past fifty years was to find a method for measuring risk, and then find a formula that quan- tifies the relationship between risk and return. Using our example, we need to find a method for quantifying how much risk United Airlines has and then discover a method for estimating the return that investors should require given that level of risk.
Measuring Return But before delving into how to measure risk, let’s look at how to measure returns. For sim- plicity’s sake, we will use stocks to illustrate returns and risk. A single period’s historical return is given by the formula
(7.2) Return over a period 5 Rt 5 (Pricet 2 Pricet 2 1 1 Dividendt)/Pricet21
Example: If you buy a share of stock for $40, hold it for one year during which you collect a dividend of $2 a share, and then sell the stock for $40.50, what was your return?
The answer is ($40.50 2 $40 1 $2)/$40 5 2.50/40 5 0.0625 5 6.25%.
This stock formula can be generalized for any investment’s return:
(7.3) Return over a period 5 Rt 5 (Valuet – Valuet 2 1 1 Cash flowt)/Valuet 2 1
In words, the return for the period is equal to the change in value of the asset during the period, plus any cash flows paid by the asset during the period, divided by the value of the asset at the beginning of the period.
It would be really useful to predict returns (for one thing, you would get rich if you could consistently forecast returns!). Unfortunately, in order to predict returns, you would like to know what price changes will be in the future so these future prices can be plugged into the return formula. But, as you learned in Chapter 2, market efficiency implies that competitive market prices reflect all available information. Therefore, we cannot say what future price changes will be and therefore what returns will be. This is because price changes will only reflect new information, and it’s anybody’s guess whether that infor- mation will be good news or bad news for the company or for the economy. Because it is nearly impossible to predict returns, we often use the historical average return as our best estimate of the expected future return. Take caution with this approach. When using an average to predict the future, one should use a relatively long run average since almost anything can happen in the short term. For example, between 1950 and 2010, the average annual return for the stock market (as proxied by the S&P 500 index) has been about 11% per year. This is considered a better estimate than, say, the five-year average stock market return between 2007 and 2012, which averaged about zero!
byr80601_07_c07_201-224.indd 205 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Measuring Risk We begin our discussion of risk by considering uncertainty. We are not certain what return we will receive in the future when we invest. With some investments, we feel a greater level of uncertainty than we do with others. For example, if an investor chooses to buy a five-year certificate of deposit at an FDIC-insured bank, most investors would feel there is very little uncertainty about how much their deposit will be worth after the five-year period. However, if the funds were invested in Facebook common stock, there is a wide range of potential values that the stock could have five years after the investment is made. One might wonder, “How much riskier is Facebook stock than a certificate of deposit? Is it twice as risky? Ten times as risky? Twenty times as risky?”
In order to answer that question, we need a metric for measuring risk. We begin by intro- ducing the concept of an investment’s total risk. We will define total risk as the variability of returns, measured by their standard deviation. For simplicity’s sake we will be using historical returns to measure risk because, as previously discussed, future returns are dif- ficult to predict. Note that we are assuming in this case that past risk is a good predictor of future risk, which may be OK, but as you become a more sophisticated analyst, this estimate may be adjusted up or down depending on what you know about the prospects of the firm or the investment that you’re analyzing.
(7.4) Total risk 5 Standard deviation 5 Å a N
1 1Rt 2 E1R2 2/N2
Standard deviation measures the typical distance (or deviation) of a return from the aver- age (or expected) return. So a stock that has a standard deviation of 15% has more uncer- tainty regarding its returns than a stock with a standard deviation of only 10%. To see this, look at Figure 7.1, which illustrates the distribution of returns for two stocks, Pea- body Coal and Pacific Gas and Electric (PG&E). These histograms show the frequency of weekly returns from March 2010 until March 2012. Notice that PG&E’s returns are much more tightly clustered, whereas Peabody’s have long tails, particularly a long tail to the left of its center. Both of these distributions have about the same average return (0.00), but there is much more uncertainty about the return of Peabody because the standard devia- tion of its returns is 0.068 per week while Pacific Gas and Electric’s standard deviation is only 0.023. Therefore, judging by this historical data, risk-averse investors would be much more concerned about owning Peabody because of the uncertainty surrounding its returns.
byr80601_07_c07_201-224.indd 206 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Figure 7.1: Historical distribution of returns for Peabody Coal and PG&E
30
25
20
15
10
5
0 −0.08 0.08−0.04 0.040−0.12 0.12−0.16 0.16
60
50
40
30
20
10
0 −0.08 0.08−0.04 0.040−0.12 0.12−0.16 0.16
Peabody Coal
Pacific Gas and Electric
Returns are based on returns from 3/2010 to 3/2012.
byr80601_07_c07_201-224.indd 207 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
It is important to keep in mind where the uncertainty illustrated in Figure 7.1 actually comes from: Risk is measured by the variability of returns, and returns are generated by price changes as we saw in Equation (7.4). Recall that price changes are caused by the arrival to the marketplace of new information, which investors and analysts anxiously await in order to adjust their view of the company’s or investment’s worth. Risk, there- fore, has at its foundation information and the investment’s sensitivity to that information. As an example, consider what might happen to a company’s stock value, and therefore its returns, if the United States announced that it will impose a significant tax on car- bon emissions. The prices of oil companies would likely fall dramatically as one would imagine gasoline costs increasing and demand decreasing, lowering oil company profits. However, a hydroelectric-based utility company might see little change in its value since it does not produce carbon so its cost and pricing structure would remain unchanged—its value might actually increase as demand for clean energy would likely rise.
The risk of adverse price movements can be decreased by diversification. For example, in the previous example, consider what would happen to an investor’s portfolio (collection of investment assets) if the investor held both oil company stocks and hydroelectric utility stocks. The oil stock values would fall because of the carbon tax, but this risk would be mitigated by the positive response to the tax by hydroelectric firms. In this case, the fall in gas stock prices is offset by the positive response of the utility stocks. Risk is decreased in this case because of the different reactions by the two industries to the same information. When one has investments in a variety of companies, there is a good chance that what affects one company negatively may actually have little impact, or perhaps a positive impact, on the value of another stock in the portfolio.
Total risk can, therefore, be broken down into risk that may be diversified away (called diversifiable risk) and risk that cannot be avoided or mitigated (called systematic or nondiversifiable risk). Diversifiable risk is often characterized as “firm-specific” risk and “industry-specific” risk. Nondiversifiable risk is often referred to as market risk. Just so you know all the terms you might run into, diversifiable risk is also referred to as unsystematic risk, whereas market risk is also called systematic risk. Investors are primarily concerned with nondiversifiable risk because they can eliminate a great deal of the diversifiable risk by simply holding a large number of different stocks. Table 7.1 breaks down diversifiable and nondiversifiable risk.
(7.5) Total risk 5 Diversifiable risk 1 Nondiversifiable risk
(7.6) Diversifiable risk 5 Firm- and industry-specific risk 5 Unsystematic risk
(7.7) Nondiversifiable risk 5 Market risk 5 Systematic risk
Table 7.1: Classifying risk
Names for risk that can be diversified away Names for risk that cannot be diversified away
Industry- and firm-specific risk Market risk
Diversifiable risk Nondiversifiable risk
Idiosyncratic risk Systematic risk
Unsystematic risk Economy-wide risk
Example: CEO quits Example: Recession
byr80601_07_c07_201-224.indd 208 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Firm-specific risk is associated with events such as a company making a poor product decision, being sued, having a CEO get indicted or die, having a big fire at a factory, or having a competitor develop a new product. All of these would adversely affect the value of the company, but if an investor is well-diversified, the impact will be minimal to the overall portfolio because such an event impacts only a single firm. Also, with enough firms in a portfolio, there is a good chance that when a firm-specific bad event happens to company A, you may have another company that experiences firm-specific good news. For example, suppose that on the same day that Firm A losses a lawsuit, Firm B discovers oil, so these events would tend to offset one another in your portfolio. Sometimes, a news event for one company ripples through the industry. If Apple announces a new, more powerful but less expensive iPad, that will almost certainly affect the prospects of other companies making tablet computers. If one airline company has several planes grounded for safety inspections, other airlines might benefit as passengers switch their flight plans.
Industry-specific risks are also largely avoidable via diversification because events that harm a particular type of industry will not necessarily have a negative effect on other stocks in a portfolio that represent firms in other industries. For example, low interest rates may hurt the profits in the banking industry, yet they actually help the housing- building industry. Therefore, holding a portfolio of stocks (in other words, being diversi- fied) enables the negative impact of low interest rates on one industry to be offset by the positive effect these rates have on other industries within the investor’s portfolio.
Nondiversifiable risks are difficult to avoid regardless of how many stocks you own, or how diversified your investment portfolio becomes. Some events have negative effects that pervade the entire economy. For example, unemployment hurts almost all companies as consumer demand falls lowering sales and profits, and savings fall making capital scarce. These kinds of far-reaching events are referred to as nondiversifiable or market risks. High inflation, war, economic recessions, and oil embargos all have a negative impact on almost all of the firms in one’s portfolio, regardless of how many stocks you own!
Because much of the risk of investing may be avoided simply by diversifying one’s portfo- lio, it is argued that we need not concern ourselves with these diversifiable risks. It is, for example, just as easy to buy a mutual fund that holds shares of 500 different companies as it is to load up on a single firm’s stock. Clearly, the mutual fund strategy avoids much of the risk that the investor in a single security faces. In fact, the standard deviation (the vari- ability) of a diversified portfolio’s returns can easily be reduced by about half compared to the average standard deviation of the individual stocks in the portfolio. The diversi- fication effect of lowering risk is shown in Figure 7.2 where we can see that increasing the number of even randomly selected stocks in a portfolio can dramatically reduce the portfolio’s standard deviation of returns.
byr80601_07_c07_201-224.indd 209 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Figure 7.2: The diversification effect
Number of stocks 14 15 16 17 18 19 2013121110987654321
35%
0%
5%
10%
15%
20%
25%
30%
P o
rt fo
li o
s ta
n d
a rd
d e v ia
ti o
n
Unique risk
Market risk
The portfolio standard deviation of returns decreases as the number of randomly selected stocks in the portfolio increases.
Since investors can easily and inexpensively eliminate most diversifiable risk from their portfolios, we assume that everyone does so. Thus, the risk that is relevant to the investor is the nondiversifiable risk of an investment. The question becomes, how can we measure this risk? To measure market risk, we utilize a metric called beta. Beta measures a firm’s typi- cal responsiveness to information that impacts the entire market—like information about economic growth, political news, inflationary expectations, the balance of trade, natural disasters, and so on. By definition, the average sensitivity to this kind of information would be measured by the responsiveness of the market portfolio. The market portfolio theoreti- cally would be totally diversified and would include virtually all investment instruments including all of the stocks and bonds that are traded. In practice, there is no such thing as a true market portfolio so a proxy is used as an approximation. Typically, the S&P 500 Index is used as that proxy. The beta of the market portfolio is defined as being equal to positive one.
A firm may be more sensitive than the average to economic information, in which case the firm’s beta would be greater than one. A company that is twice as sensitive as the average firm to economic events will have a beta of 2.00, whereas a firm that is less sensitive than average will have a beta below one. Here is an example. Take a firm that sells luxury goods, like a Porsche automobile dealership. We might assume that when the economy is boom- ing, this business does really well, but when the economy is doing poorly, luxury sports car sales suffer drastically. Let’s suppose that Porsche dealership’s beta is 1.70, meaning
byr80601_07_c07_201-224.indd 210 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
that it is 1.7 times as sensitive as the overall market to “mac- roeconomic” type events. So, if the government announces that economic growth is very strong, we might hear that the S&P 500 portfolio had a return of 5% that day in response to this good economic news. But because a Porsche dealership is more sensitive than average to such information, its stock would likely return around 8.5% on the same day (found by taking the product of 1.7 3 5% 5 8.5%). If, on the other hand, the market portfolio declines by 10% one month because of bad economic news, then the dealership’s stock would be expected to fall by around 17%.
Of course, these are the expected returns for the Porsche dealership and may not be equal to the firm’s actual returns on those days because there are always firm-specific factors that may affect a single stock’s return. For example, on the day that the government announces strong economic growth (good news and we expect the 8.5% return), it may be the dealer- ship also learns that the company is being sued, so the firm’s stock could actually fall in value on the date because of this negative firm-specific announcement.
Some businesses are less sensitive to market-level information than the average firm is. An example might be an electric utility company, say Pacific Gas and Electric (PG&E). When the economy is doing well, Pacific Gas and Electric does well because there is more demand for electricity. When times are bad, demand for power falls, but it doesn’t fall too far because, unlike Porsche sports cars, electricity is close to being a necessity. So with this relatively low sensitivity, Pacific Gas and Electric has lower than average market risk, and its beta is less than one. In June 2012, Yahoo! Finance reported PG&E’s beta as 0.29. If the country goes into a recession and the market as proxied by the S&P 500 declines by 10%, PG&E, with its beta of 0.29, would see its stock price drop by only about 3% on average.
Betas are typically estimated using historical returns and linear regression estimation. Linear regression is a statistical technique for estimating a best-fit line through points plotted in an x-y coordinate system like the graphs typically used in algebra. The idea is that the slope of this line will capture the average relationship between the x- and the y-variables. So if the slope is 1.5 for a regression line, then for each unit increase in the x-value, the y-value will (on average) increase by one and a half units. Regression is used to estimate a variety of relation- ships, like the effect that the time spent studying has on the grade point average of students. For our purposes, we use returns for the S&P 500 as our x-values, and corresponding returns for the stock that we are interested in as our y-values. The regression’s slope, therefore, is an estimate of the stock’s average responsiveness to market-wide returns, or its beta.
Luxury markets like Porsche dealerships are highly susceptible to the rise and fall of the economy. Do you tend to feel more or less inclined to invest in these companies?
Associated Press
byr80601_07_c07_201-224.indd 211 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Since betas are statistical estimates, they can vary depending on the sample of data being used for the estimate. Figure 7.3 estimates the beta for PG&E by plotting the corporation’s returns against those of the S&P 500. As you can see, the beta we estimate (0.43) differs from the beta reported by Yahoo! in June 2012 (0.29). The difference can be attributed to different data sets; Yahoo! based their report on 36 monthly returns, whereas we have based our estimate on 24 weekly returns.
Figure 7.3: Estimating beta for PG&E
S&P 500 returns
PG&E return = 0.433 × S&P 500 return + 0.0024
P G
& E
r e tu
rn s
5%−5% −4% −2% −1% 1%
1%
2%
3%
4%
−4%
−3%
−2%
−1%
2% 3% 4% 0%
A stock’s beta is the slope of the line-of-best fit through the scatterplot of market returns (S&P500) and the company’s returns.
The Capital Asset Pricing Model Now we know how to measure returns and how to measure nondiversifiable risk (by using beta). Next we need to learn how to utilize these metrics to estimate the required rate of return for an investment. Recall from the beginning of the chapter that the “build- ing blocks” of a required return include the risk-free rate and a risk premium. These two elements are present in an equation called the capital asset pricing model (CAPM). We need this model to quantify the relationship between investor’s required rate of return and the risk of an investment. Here is the CAPM as it was originally developed:
(7.8) Required return for an investment 5 Rf 1 Beta[E(Rmkt) 2 Rf]
byr80601_07_c07_201-224.indd 212 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
where
Rf 5 the risk-free rate of return
E(Rmkt) 5 the expected return on the market portfolio
Beta 5 the stock’s beta
This theoretical relationship between risk and return was one of the path breaking achieve- ments in economics in the 1960s, for which several academics were awarded the Nobel Prize. Like many theories, however, there are challenges when using the CAPM in prac- tice. For example, no one knows what the expected return on the market, E(Rmkt), is equal to. The model also assumes there is a single, observable risk-free rate, when in reality there is no investment free of risk and there is more than one possible rate that can be used as a close proxy for risk-free. Because of these problems, most practitioners use a different form of the model which is given here:
(7.9) Required return for an investment 5 Rf 1 Beta(Market risk premium)
Rf can be thought of as the rate that links the CAPM to current market conditions. This is important because interest rates are constantly changing due to changes in inflation, eco- nomic activity, or government policies. We use yields on outstanding debt issued by the U.S. government as a proxy for the risk-free rate, choosing the Treasury bill or bond that best matches the life of the asset we are evaluating. So, for stocks that have an almost per- petual life, long-term U.S. Treasury bond yields are often used for the risk-free rate. The market risk premium (MRP) is the amount of return yielded by the market portfolio over and above the treasury yield. It can be thought of as the return required for each addi- tional unit of risk as measured by beta. Often, the MRP is assumed to equal its historical average, which is about 5% to 7%, depending on whose data you use.
Here is an example of using the CAPM. Let’s estimate the required return for Nordstrom’s (Ticker: JWN) stock given that Nordstrom’s beta is 1.58, as reported on Yahoo! Finance in June 2012 (http://finance.yahoo.com/q/ks?s5JWN1Key1Statistics). Nordstrom’s has a fairly high beta because it is considered a high-end or almost luxury retailer, not dealing in necessity goods. Consequently, when times are tough, some people may discontinue shopping at Nordstrom’s and may buy their shoes and clothing at a more moderately priced retailer. Let’s also assume that T-bonds are yielding 4.5% per year, and that the historical average market risk premium (the average return of the market portfolio over and above the risk-free return) is about 6%. Using this information, we may estimate the required return for Nordstrom’s stock using the CAPM.
RNordstroms 5 Rf 1 BNordstroms(Market risk premium) 5 0.045 1 1.58(0.06) 5 0.1398 5 13.98%
A second example would be required rate of return for PG&E’s stock. Using the published beta of 0.29 and the risk-free rate and market risk premium above we would compute PG&E’s required rate of return as:
RPG&E 5 Rf 1 BPG&E (Market risk premium) 5 0.045 1 0.29(0.06) 5 0.0624 5 6.24%
Notice that the much lower beta of PG&E results in a much lower required rate of return compared to Nordstrom.
byr80601_07_c07_201-224.indd 213 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Applying Finance: Finding Beta Using Excel
Finding an asset’s beta using Excel is a two-step process: first, compute returns from prices; second, use the LINEST function to compute the beta (slope of a regression line).
We downloaded stock prices for Dow Chemical (Ticker: DOW) from Yahoo! Finance using its histori- cal price feature. We then downloaded the index data for the S&P 500 (Yahoo! Ticker: ^GSPC). We use the adjusted close price to make sure dividends are included in the price. Our data are weekly and run from Friday, February 3, 2012, through Friday, June 22, 2012. We compute returns using the formula from the text:
(Change in price)/Beginning price
Since we are using adjusted prices we don’t need to explicitly include dividends in the returns equa- tion. Figure 7.4 shows the spreadsheet of prices showing the price series, the returns formulas and the LINEST formula.
Figure 7.4: DOW Chemical spreadsheet, LINEST
June 22, 2012
June 15, 2012
June 8, 2012
June 1, 2012
May 25, 2012
May 18, 2012
May 11, 2012
May 4, 2012
April 27, 2012
April 20, 2012
April 13, 2012
April 6, 2012
March 30, 2012
March 23, 2012
March 16, 2012
March 9, 2012
March 2, 2012
February 25, 2012
February 17, 2012
February 10, 2012
February 3, 2012
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
32.82
32.89
32.11
30.36
31.30
29.45
32.15
32.33
34.73
35.31
33.20
33.42
34.64
34.77
35.05
33.82
33.96
33.58
34.75
33.76
33.94
1335.02
1342.84
1325.66
1278.04
1317.82
1295.22
1353.39
1369.10
1403.36
1378.53
1370.26
1398.08
1408.47
1397.11
1404.17
1370.87
1369.63
1365.74
1361.23
1342.64
1344.90
C
S&P 500 Close
=(B2−B3)/B3 =(B3−B4)/B4 =(B4−B5)/B5 =(B5−B6)/B6 =(B6−B7)/B7 =(B7−B8)/B8 =(B8−B9)/B9 =(B9−B10)/B10 =(B10−B11)/B11 =(B11−B12)/B12 =(B12−B13)/B13 =(B13−B14)/B14 =(B14−B15)/B15 =(B15−B16)/B16 =(B16−B17)/B17 =(B17−B18)/B18 =(B18−B19)/B19 =(B19−B20)/B20 =(B20−B21)/B21 =(B21−B22)/B22
E
Dow Returns
D
=(C2−C3)/C3 =(C3−C4)/C4 =(C4−C5)/C5 =(C5−C6)/C6 =(C6−C7)/C7 =(C7−C8)/C8 =(C8−C9)/C9 =(C9−C10)/C10 =(C10−C11)/C11 =(C11−C12)/C12 =(C12−C13)/C13 =(C13−C14)/C14 =(C14−C15)/C15 =(C15−C16)/C16 =(C16−C17)/C17 =(C17−C18)/C18 =(C18−C19)/C19 =(C19−C20)/C20 =(C20−C21)/C21 =(C21−C22)/C22
F
S&P Returns
G
Beta
=LINEST(E2:E21, F2:F21)
B
Dow Close
A
Date
Figure 7.5 shows the same spreadsheet with the numerical results shown. Using this small sample of data, Dow’s beta estimate is 1.63. (continued)
byr80601_07_c07_201-224.indd 214 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Determining an Asset’s Beta During the discussions of the Porsche dealership, Nordstrom’s, and PG&E, we said that it is the nature of the products and services that are sold by a company that determine the company’s risk. Luxury goods, like sports cars, tend to have more market risk than do necessities like electricity. Demand for durable goods, items that are long-lived and can be repaired like cars and appliances, will fluctuate more as the economy rises and falls than demand for food or medicine. If a company has invested in productive assets to make luxury or durable goods, then it is likely to have a high beta (higher than 1 or the market average beta). Similarly, if the factories and equipment make food or electricity or things that are necessary (or that have steady demand), the company will have a lower beta (less than one). Thus, it is the assets of a company and the products those assets make that determine the company’s beta. Companies that produce similar goods that are sold in similar markets will have similar betas because those companies will be impacted simi- larly by the kind of macroeconomic news that creates market risk. Assess your expecta- tions of beta by completing the exercise in the Fieldtrip: Expectations of Beta feature.
Applying Finance: Finding Beta Using Excel (continued)
Figure 7.5: DOW Chemical spreadsheet, numerical
June 22, 2012
June 15, 2012
June 8, 2012
June 1, 2012
May 25, 2012
May 18, 2012
May 11, 2012
May 4, 2012
April 27, 2012
April 20, 2012
April 13, 2012
April 6, 2012
March 30, 2012
March 23, 2012
March 16, 2012
March 9, 2012
March 2, 2012
February 25, 2012
February 17, 2012
February 10, 2012
February 3, 2012
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
32.82
32.89
32.11
30.36
31.30
29.45
32.15
32.33
34.73
35.31
33.20
33.42
34.64
34.77
35.05
33.82
33.96
33.58
34.75
33.76
33.94
1335.02
1342.84
1325.66
1278.04
1317.82
1295.22
1353.39
1369.10
1403.36
1378.53
1370.26
1398.08
1408.47
1397.11
1404.17
1370.87
1369.63
1365.74
1361.23
1342.64
1344.90
C
S&P 500 Close
−0.213% 2.429%
5.764%
−3.003% 6.282%
−8.398% −0.557% −6.910% −1.643%
6.355%
−0.658% −3.522% −0.374% −0.799%
3.637%
−0.412% 1.132%
−3.367% 2.932%
−0.530%
E
Dow Returns
D
−0.582% 1.296%
3.726%
−3.019% 1.745%
−4.298% −1.147% −2.441%
1.801%
0.604%
−1.990% −0.738%
0.813%
−0.503% 2.429%
0.091%
0.285%
0.331%
1.385%
−0.168%
F
S&P Returns
G
Beta
1.628
B
Dow Close
A
Date
byr80601_07_c07_201-224.indd 215 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Field Trip: Expectations of Beta
Pick three firms that you think may have low betas and three that you think may have high betas. Visit Yahoo! Finance or Google Finance to look up their betas.
Visit Yahoo finance: http://finance.yahoo.com/
Google finance: http://www.google.com/finance
Are there any surprises? Can you think of some reasons that these betas are different from what you expected?
In theory, the asset beta of a Porsche dealership should be very nearly the same as the asset beta of, say, a BMW dealership. This is because they are similar businesses offering similar products. If both the Porsche and the BMW dealerships had no debt financing, then both of their asset betas would be identical to the betas of their stock. This is because the stock would represent the only claim against the assets, so the risk of the assets would translate directly to the risk of the stock. In this case, both dealerships’ stock, being in the same business, would probably have almost identical betas and both would also have almost identical required rates of return.
However, most companies use debt financing in addition to equity financing. This use of debt is also known as leverage. The use of leverage increases the risk of equity because debt, with its priority claim, forces equity holders to bear the risk that there will be lower cash flows available for them after debt payments are made. For this reason, the betas of stock differ even among firms in the same industry because of the varying amount of debt that the companies borrow. Asset betas, therefore, depend primarily on the nature of a company’s business, whereas equity betas—the betas of investing in just a company’s stock—depend on both a firm’s asset beta and on its use of leverage. A specific technique used for estimating an asset beta, called the pure-play approach, is covered in the next chapter.
Portfolio Betas There are times when investors may want to estimate the required return for a portfolio or stocks or other investment assets. For example, we may want to compare the actual, realized return on a portfolio to the required return on that portfolio in order to assess the performance of the manager who is in charge of the portfolio’s investments. If the realized return exceeds the required return given the portfolio’s risk, then the manager is performing at or above expectations. If, on the other hand, the realized return is below the required return for the portfolio, then the manager is performing below expectations, and may find his or her position in jeopardy.
Portfolio betas are found by taking the weighted average of the betas of the assets held in the portfolio, where the weights are determined by the amount invested in each asset. For example, consider the portfolio in Table 7.2.
byr80601_07_c07_201-224.indd 216 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
Table 7.2: Sample portfolio
Stock Stock’s beta Amount invested Weight
Acme, Inc. 1.20 $100,000 .10
XYZ Corp. 1.50 $150,000 .15
ABC Corp. 0.70 $500,000 .50
Delphi, Inc. 1.00 $250,000 .25
The weights represent the proportion of total investment that is invested in each asset. For example, the total investment in this portfolio is $1,000,000, so the investment of $150,000 in XYZ’s stock represents 15% of the total, making the weight for XYZ .15. In this case, the portfolio’s beta is the sum:
Beta portfolio 5 (1.20)(.10) 1 (1.50)(.15) 1 (.70)(.50) 1 (1.00)(.25) 5 .945
To illustrate the usefulness of this number, it could be used to estimate the risk of this port- folio versus another portfolio or a mutual fund. It could also be plugged into the CAPM to give an estimate of the required return for this portfolio.
One warning: beta is not a good measure of risk unless the investor is what is known as “well diversified.” Usually, if you own more than 20 stocks, you are considered well- diversified. However, if these stocks are concentrated in only a couple of industries, then you are probably not effectively diversified. Diversification is a subjective and relative term, so, as a rule, it’s better to be more diversified than to be less diversified. Next, we will look at why it is prudent to invest in several stocks and other assets (like bonds and real estate) that are not concentrated in only a few industries (or geographic locations).
Correlation and Diversification In a more advanced mathematical presentation of diversification’s effect, you would learn that diversification depends on asset returns having imperfect correlation with one another. In other words, if all stocks in a portfolio went up and down together, then they would be perfectly correlated, and there would be no point in diversifying. For example, if a disaster happened to one stock, it would also happen to all the other stocks because they are perfectly positively correlated to one another. As a result, because they would likely have high positive correlations with one another, it is not a good idea to concentrate your portfolio in only one industry or even just a few industries.
On the other hand, stocks with lower correlations make great choices for forming a well- diversified portfolio. In fact, the most efficient diversification happens when we mix nega- tively correlated assets in our portfolios because their risks will offset one another. To illustrate, consider this example. Suppose you owned stock A whose returns were per- fectly negatively correlated with another, stock B. Whenever A’s return went up, B’s went down and vice versa. Imagine that they both varied around an average return of 10%. If you were lucky enough to locate these two stocks, and you put your money in each one to form a special two-stock portfolio, your portfolio would earn exactly 10% but you would
byr80601_07_c07_201-224.indd 217 1/24/13 4:00 PM
CHAPTER 7Section 7.2 Risk and Return
experience zero variability. That is because every time A had a return below 10%, B would have a return above 10% because of its perfect negative correlation. In other words, you could have a risk-free portfolio with a 10% return. Of course, it is not easy (perhaps impos- sible) to find two stocks with perfect negative correlation. Figure 7.6 shows a graphic representation of two stocks with perfect negative correlation.
Figure 7.6: Returns with perfect negative correlation
10 12 1486420
−0.06
0.06
−0.04
0.04
−0.02
0.02
0
Stock A Stock B
This graph shows what perfect negative correlation between two stocks (A and B) might look like.
The good news is that you can always reduce risk by mixing assets whose returns are imperfectly correlated, and you do this without lowering their average return. Further- more, since almost all investment assets are imperfectly correlated, you can get the risk- reducing benefits of diversification by simply mixing together even a randomly selected bunch of stocks (as was shown in Figure 7.2). Of course, with a little insight, you can improve the benefits of diversification by being sure to not focus on one industry group and by mixing in, for example, a few international stocks (can you figure out why, in terms of correlation?).
byr80601_07_c07_201-224.indd 218 1/24/13 4:00 PM
CHAPTER 7Section 7.3 Required Returns and Valuation
7.3 Required Returns and Valuation
Now that we know how to estimate required returns, we want to consider once again the time value of money problems and security valuation. This is because required returns are used as the discount rates in these valuation formulas. To illustrate, suppose that PG&E just paid an annual dividend of $1.82 per share and that we believe dividends will grow at a 2% annual rate in the future. In this case, we can use the constant growth stock valuation formula to estimate the value of PG&E’s stock (and we will use the form of the model with D0 in the numerator because we were given the last dividend paid). Recalling that PG&E’s required return was 6.24%,
Value of PG&E stock 5 ($1.82)(1.02)/(0.0624 2 0.02) 5 $1.8564/.0424 5 $43.78
Suppose we did this estimation of value and looked up an actual quote for PG&E’s stock on the Internet. If the price is currently $43.00, this would mean that the stock appears to be under- priced on the market, which would indicate that it is a bargain according to our estimates. How- ever, before we run out to buy PG&E stock, which we think may be worth $1.64 more per share than its price, we need to consider market efficiency. Remember that market efficiency says that the market price (the $43.00) is the best available esti- mate of value. Now, we must decide whose esti- mate we put more faith in: our estimate ($44.64) or the market’s ($43.00)? If we believe in mar- ket efficiency, we would probably not make the investment.
There are times, however, when we need to value an asset or a closely held stock for which no mar- ket price exists. In this case, we have little choice but to rely on our own estimates. In these cases, the ability to estimate the required return is essen- tial. For example, before Facebook went public in 2012, there was no existing market price for the stock, yet the firm’s ownership had to place an initial price on the shares. If the price they chose was too high, no one would buy the stock, and the offer would be unsuccessful. If the offer price was too low, then the original owners would be selling a stake in their company for too little. To get the price correct, Facebook’s management, ownership, and financial advisors had to estimate the firm’s value, which depended on an accurate estimate of its risk and the required return of investors given that risk level.
Knowing the market price of a stock is beneficial, but it can often be more advantageous to know how to make your own estimate of a required return.
Stockbyte/Getty Images
byr80601_07_c07_201-224.indd 219 1/24/13 4:00 PM
CHAPTER 7Post-Test
Conclusion
In this chapter, the building blocks of required returns were introduced. Most of the chapter used stock to illustrate and explore the relationships between risk and inves-tors’ return requirements. The calculation of returns, of total risk (standard deviation of returns), and of market risk (beta) were covered. The benefit of diversification by elimi- nating certain types of risk was discussed as was the effectiveness of how diversification is linked to the correlation between investments’ returns. The capital asset pricing model, used to estimate the required return for an investment, was also covered and illustrated. The concept of an asset beta was also introduced. Chapter 8 extensively uses the CAPM along with the asset beta as a means to discover the overall required return for the entire firm rather than just the return requirement for its equity, which we focused on in this chapter. The theories and techniques explored in Chapter 7 will be vitally important for those of you who one day will enter a career in the investments field, but the insights will also be important for everyone who becomes an investor whether they are investing for retirement or for their child’s college fund.
Post-Test
1. The two fundamental building blocks of the required return for an investment are the risk-free return and a risk premium.
a. True b. False
2. For simplicity’s sake expected returns are used to measure risk because historical returns only reflect past information.
a. True b. False
3. Required returns are used as the discount rate in valuation formulas. a. True b. False
4. A rational investor in XYZ stock will require a. at least the risk-free rate of return when investing in some security or project. b. a return lower than what they could earn by depositing the funds in a savings
account. c. a return at least as high as the overall market return d. a guarantee from the FDIC.
5. ______________ are difficult to avoid because they impact the entire economy. a. Firm-specific risks b. Large capital losses c. Large capital gains d. Market risks
6. Valuation formulas, like time value of money problems, use__________________ as the discount rate.
a. required returns b. expected returns
byr80601_07_c07_201-224.indd 220 1/24/13 4:00 PM
CHAPTER 7Key Ideas
c. historical returns d. after-tax historical returns
Answers 1. a. True. The answer can be found in Section 7.1. 2. b. False. The answer can be found in Section 7.2. 3. a. True. The answer can be found in Section 7.3. 4. a. at least the risk-free rate of return when investing in some security or project. The answer can be found in
Section 7.1. 5. d. Market risks. The answer can be found in Section 7.2. 6. a. required returns. The answer can be found in Section 7.3.
Key Ideas
• A rational investor will always want to earn at least the risk-free rate of return when investing in some security or project. Otherwise, they would be settling for a return lower than what they could be assured of by simply depositing the funds in a savings account.
• Virtually all investments have some risk associated with them, so investors also require what is known as a risk premium to compensate them for this risk exposure.
• The two fundamental building blocks of the required return for an investment are the risk-free return and a risk premium. The required return for an investor 5 (Risk-free rate of return) 1 (Risk premium).
• An investment’s total risk is the variability of returns and is measured by their standard deviation. For simplicity’s sake, we will be using historical returns to measure risk because expected returns are difficult to predict.
• Returns are generated by price changes caused by the arrival to the marketplace of new information, which investors and analysts anxiously await in order to adjust their view of the company’s or investment’s worth.
• Total risk can be broken down into risk that may be diversified away and risk that cannot be avoided or mitigated.
• Firm-specific risk is associated with events specific to the firm that adversely affect the value of the company, but if an investor is well-diversified, the impact will be minimal to the overall portfolio because such an event impacts only a single firm.
• Industry-specific risks are largely avoidable via diversification because events that harm a particular type of industry will not necessarily have a negative effect on other stocks in a portfolio that represent firms in other industries.
• Nondiversifiable or market risks are difficult to avoid regardless of how many stocks you own or how diversified your investment portfolio becomes. Some events have negative effects that pervade the entire economy.
• To measure market risk, we utilize a metric called beta. Beta measures a firm’s typical responsiveness to information that impacts the entire market.
• The market risk premium (MRP) is the amount of return yielded by the market portfolio over and above the Treasury yield. It can be thought of as the return required for each additional unit of risk as measured by beta.
• Companies that produce similar goods, sold in similar markets, will have similar betas because those companies will be affected similarly by the kind of macroeco- nomic news that creates market risk.
byr80601_07_c07_201-224.indd 221 1/24/13 4:00 PM
CHAPTER 7Critical Thinking Questions
• Portfolio betas are found by taking the weighted average of the betas of the assets held in the portfolio, where the weights are determined by the amount invested in each asset.
• Diversification depends on asset returns having imperfect correlation with one another. In other words, if all stocks in a portfolio went up and down together, then they would be perfectly correlated, and there would be no point in diversifying.
• Stocks with lower correlations make great choices for forming a well-diversified portfolio. In fact, the most efficient diversification happens when we mix nega- tively correlated assets in our portfolios because then their risks will offset one another.
• Required returns are used as the discount rates in valuation formulas such as time value of money problems and security valuation.
Critical Thinking Questions
1. Total risk is measured by the standard deviation of returns. Jot down the formula for the standard deviation and then comment on what part of the formula has to do with deviations and what part is related to calculating the standard of these deviations. (Hint: deviation may be thought of as departure from what is typical and standard may be thought of as the average or what is expected).
2. The theoretical development of the CAPM calls for use of the risk-free rate. Swiss government bonds have typically had a lower risk rating than any other gov- ernment bond. Why isn’t the Swiss bond, therefore, the standard for use in the CAPM worldwide?
3. The average return on the S&P 500 has been in the neighborhood of 11%, and in 1980 U.S. Treasury bonds were yielding about 15%. Imagine you were an inves- tor in 1980. How do the circumstances at that time help explain why it is better to use the market risk premium (of around 6%) rather than [Rmkt 2 Rf] when esti- mating the required return with the CAPM?
4. Beta is the measure of market risk. Look at the businesses listed below and see if you can identify one that could very likely have a relatively high total risk but a low beta. Explain your reasoning.
a. The manufacturer of diamond-encrusted dog collars. b. A company that specializes in finding and salvaging old shipwrecks from the
Age of Discovery (the 1500s and 1600s). c. A casino
5. When you estimate betas using historical data and linear regression, you must make some of the following choices: what index to use as a proxy for the market portfolio (the S&P 500, the Wilshire 5000, and the NYSE Composite Index are a few of the possibilities); the length of the return period (daily returns, weekly returns, and monthly returns are all used); the length of the historical record (two, three, or five years are candidates). Each combination of these choices will yield a slight (or maybe even a major) difference in the estimated beta. How many different betas for a single firm could you and your classmates get on the same day by making different choices among these options?
6. Security A has a standard deviation of returns equal to 20% and a beta of 1.50. Security B has a standard deviation of 16% and a beta of 1.80. Which security probably has the higher required return? Explain.
byr80601_07_c07_201-224.indd 222 1/24/13 4:00 PM
CHAPTER 7Key Terms
beta A measure of an asset’s systematic risk, also known as its market risk. The average stock has a beta of one, while stocks with greater than average market risk will have betas greater than one and those with less risk will have betas less than one. Beta is used to find the required return for an asset using the CAPM.
capital asset pricing model (CAPM) A formula that quantifies the connection between an investment’s market risk and its required rate of return, specifically the required return on an asset equals the risk- free rate plus a risk premium. The risk pre- mium is the asset’s beta times the market risk premium. The CAPM is the equation of the security market line.
correlation A statistical measure of the co-movement of asset returns. Correla- tion varies between the negative return and the positive one, while a correlation of zero means that the two assets are “uncor- related” and move independently. Perfect positive correlation means that the two assets’ values move together in the same direction. Negatively correlated assets tend to move in opposite directions.
diversifiable risk Risk that can be avoided through diversification.
diversification The mixing of invest- ments in a single portfolio that can reduce risk exposure. Diversification’s benefits are most dramatic when the correlations between assets in the portfolio are low or even negative.
diversification effect The reduction in risk (standard deviation) that occurs through the blending of stocks into a portfolio.
historical return The past performance of a security or index.
leverage A description of the proportion of debt used in a firm’s capital structure.
market portfolio A theoretical bundle of investments that includes every kind of asset available in the financial market. Because a market portfolio is completely diversified, it is subject only to systematic risk.
market risk premium (MRP) The differ- ence between the rate of return on the mar- ket (e.g., S&P 500) and the risk-free return (e.g., Treasury bonds).
portfolio A collection of assets or invest- ments. Investing in a portfolio can reduce risk exposure compared to investing in a single asset.
portfolio betas The weighted average of the betas of the assets held in the portfolio, where the weights are determined by the amount invested in each asset.
required rate of return The minimum return investors must expect in order to be interested in investing in an asset.
risk averse Characteristic in which people focus more on losses than on equivalent gains. Risk aversion implies that investors must be paid to bear risk.
risk-free rate of return The return an investor earns on a risk-free asset.
risk premium The added return necessary to compensate investors for taking added risk.
S&P 500 Index (Standard & Poor’s 500) A price index of 500 stocks representing a broad cross section of industries often used to represent the entire stock market’s activity.
Key Terms
byr80601_07_c07_201-224.indd 223 1/24/13 4:00 PM
CHAPTER 7Web Resources
systematic or nondiversifiable risk Risk that cannot be avoided through diversification.
total risk The overall potential for finan- cial loss. The variability of returns, mea- sured by their standard deviation.
unsystematic risk Risk that affects pri- marily one company or industry. Unique risk may be mitigated by diversifying one’s portfolio.
Key Formulas
Basic formula for estimating value of an investment
(7.1) V0 5 a N
t 5 1
CFt 11 1 R1r2 2 t
(7.2) Return over a period 5 Rt 5 (Pricet 2 Pricet 2 1 1 Dividendt)/Pricet 2 1
(7.3) Return over a period 5 Rt 5 (Valuet 2 Valuet 2 1 1 Cash flowt)/Valuet 2 1
(7.4) Total risk 5 Standard deviation 5 Å a N
1 1Rt 2 E1R2 b
2
/N
(7.8) Required return for an investment 5 Rf 1 Beta[E(Rmkt) 2 Rf]
(7.9) Required return for an investment 5 Rf 1 Beta(Market risk premium)
Web Resources
This chapter has introduced some measures of risk. Follow this link to take a quiz assess- ing your own risk tolerance: http://njaes.rutgers.edu/money/riskquiz/
Professor Aswath Damodaran of NYU maintains a list of betas for different industries. These may be viewed and the sectors compared at the following website. It might be interesting to compare the average betas in two sectors, like gambling versus natural gas utilities to see if the betas conform with your intuition. http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html
byr80601_07_c07_201-224.indd 224 1/24/13 4:00 PM
