Textbook Questions

Traditional Versus Modern Portfolio Management

1. LG 5

2. LG 6

Individual and institutional investors currently use two approaches to plan and construct their portfolios. The traditional approach refers to the less quantitative methods that investors have been using since the evolution of the public securities markets. Modern portfolio theory (MPT) is a more mathematical approach that relies on quantitative analysis to guide investment decisions.

The Traditional Approach

Traditional portfolio management  emphasizes balancing the portfolio by assembling a wide variety of stocks and/or bonds. The typical emphasis is interindustry diversification. This produces a portfolio with securities of companies from a broad range of industries. Investors construct traditional portfolios using security analysis techniques that we will discuss later.

Table 5.5  presents some of the industry groupings and the percentages invested in them by a typical mutual fund that is managed by professionals using the traditional approach. This fund, American Funds’ Growth Fund of America (AGTHX), is an open-end mutual fund with a net asset value of $145.2 billion as of December 31, 2014. Its objective is to invest in a wide range of companies that appear to offer superior opportunities for growth of capital. The Growth Fund of America holds shares of more than 280 different companies and short-term securities issued from a wide range of industries. The AGTHX fund is most heavily invested in information technology, representing 21.7% of the portfolio. The consumer discretionary and health care industries represent 17.9% and 17.8% of the fund’s investment, respectively.

Table 5.5 The Growth Fund Of America (Agthx) Investments In Select Industry Groups As Of December 31, 2014

(Source: Data from The Growth Fund of America, Class A Shares, Quarterly Fund Fact Sheet, December 31, 2014.)

The Growth Fund of America appears to adhere to the traditional approach to portfolio management. Its total portfolio value is $145.2 billion, of which 80.8% ($117.3 billion) is U.S. equities, 10.2% ($14.8 billion) is non-U.S. equities, 0.2% ($290.4 million) is U.S. bonds, and 8.8% ($12.8 billion) is cash & equivalents.

Sector Breakdown	Percentage
Information technology	21.7%
Consumer discretionary	17.9%
Health care	17.8%
Industrials	9.6%
Financials	8.2%
Energy	7.7%
Consumer staples	4.6%
Materials	2.8%
Telecommunication services	0.6%
Utilities	0.1%

Analyzing the stock position of the Growth Fund of America, which accounts for 91% of the fund’s assets, we observe the traditional approach to portfolio management at work. This fund holds numerous stocks from a broad cross-section of the universe of available stocks. The stocks are a mix of large and small companies. The fund’s largest individual holding is Amazon.com Inc., which accounts for 3.7% of the portfolio. Google Inc., the world’s do-everything search engine, ranks second, at 3.3%. The third largest holding, 2.3%, is Gilead Sciences. Although many of the fund’s stocks are those of large, recognizable companies, its portfolio does include stocks of smaller, less recognizable firms.

Those who manage traditional portfolios tend to invest in well-known companies for three reasons. First, fund managers and investors may believe that investing in well-known companies is less risky than investing in lesser-known firms. Second, the securities of large firms are more liquid and are available in large quantities. Third, institutional investors prefer successful, well-known companies because it is easier to convince clients to invest in them. Called window dressing, this practice of loading up a portfolio with successful, well-known stocks makes it easier for institutional investors to sell their services.

Investor Facts

Watch Thy Neighbor’s Portfolio A new study finds that the portfolios held by mutual fund managers who live near each other (e.g., in the same zip code) are more similar than portfolios held by managers whose residences are farther apart (e.g., in the same city but not in the same zip code).

(Source: Veronica K. Pool, Noah Stoffman, and Scott E. Yonker, “The People in Your Neighborhood: Social Interactions and Mutual Fund Portfolios,” Journal of Finance, forthcoming.)

One tendency often attributed to institutional investors during recent years is that of “herding”—investing in securities similar to those held by their competitors. These institutional investors effectively mimic the actions of their competitors. In the case of The Growth Fund of America, for example, its managers would buy stocks in companies that are held by other large, growth-oriented mutual funds. While we don’t know for certain why The Growth Fund of America’s managers bought specific stocks, it is clear that most funds with similar objectives hold many of the same well-known stocks.

Modern Portfolio Theory

During the 1950s, Harry Markowitz, a trained mathematician, first developed the theories that form the basis of modern portfolio theory. In the years since Markowitz’s pioneering work, many other scholars and investment experts have contributed to the theory.  Modern portfolio theory (MPT)  uses several basic statistical measures to develop a portfolio plan. Portfolios formed using MPT principles estimate the average returns, standard deviations, and correlations among many combinations of investments to find an optimal portfolio. According to MPT, the maximum benefits of diversification occur when investors find securities that are relatively uncorrelated and put those securities together in a portfolio. Two important aspects of MPT are the efficient frontier and portfolio betas.

Watch Your Behavior

Don’t Be Underdiversified Many research studies have found that investors tend to be underdiversified, holding too few stocks in their portfolios. Investors tend to invest too heavily in companies that are familiar to them, such as local companies. Underdiversification results in inefficient portfolios that perform worse, earning lower returns (by as much as 3% annually according to one study) and experiencing higher volatility compared to well-diversified portfolios.

The Efficient Frontier

At any point in time, you are faced with hundreds of investments from which to choose. You can form any number of possible portfolios. In fact, using only a few different assets, you could create an unlimited number of portfolios by changing the proportion of each asset in the portfolio.

If we were to create all possible portfolios, calculate the return and risk of each, and plot each risk-return combination on a graph, we would have the feasible, or attainable, set of possible portfolios. This set is represented by the shaded area in  Figure 5.7 . It is the area bounded by ABYOZCDEF. As defined earlier, an efficient portfolio is a portfolio that provides the highest return for

Figure 5.7 The Feasible, or Attainable, Set and the Efficient Frontier

The feasible, or attainable, set (shaded area) represents the risk-return combinations attainable with all possible portfolios; the efficient frontier is the locus of all efficient portfolios. The point O, where the investor’s highest possible indifference curve is tangent to the efficient frontier, is the optimal portfolio. It represents the highest level of satisfaction the investor can achieve given the available set of portfolios.

a given level of risk. For example, let’s compare portfolio T to portfolios B and Y shown in  Figure 5.7 . Portfolio Y appears preferable to portfolio T because it has a higher return for the same level of risk. Portfolio B also “dominates” portfolio T because it has lower risk for the same level of return.

The boundary BYOZC of the feasible set of portfolios represents all efficient portfolios—those portfolios that provide the best tradeoff between risk and return. This boundary is the  efficient frontier . All portfolios on the efficient frontier are preferable to all other portfolios in the feasible set. Any portfolios that would fall to the left of the efficient frontier are not available for investment because they fall outside of the attainable set. For example, anyone would love to buy an investment with an extremely high return and no risk at all, but no such investment exists. Portfolios that fall to the right of the efficient frontier are not desirable because their risk-return tradeoffs are inferior to those of portfolios on the efficient frontier.

We can, in theory, use the efficient frontier to find the highest level of satisfaction the investor can achieve given the available set of portfolios. To do this, we would plot on the graph an investor’s indifference curves. These curves indicate, for a given level of utility (satisfaction), the set of risk-return combinations about which an investor would be indifferent. These curves, labeled I1, I2, and I3 in  Figure 5.7 , reflect increasing satisfaction as we move from I1 to I2 to I3. The optimal portfolio, O, is the point at which indifference curve I2 meets the efficient frontier. The investor cannot achieve the higher utility provided by I3 because there is no investment available that offers a combination of risk and return falling on the curve I3.

If we introduced a risk-free investment-paying return rf into  Figure 5.7 , we could eventually derive the equation for the capital asset pricing model introduced previously. Rather than focus further on theory, let’s shift our attention to the more practical aspects of the efficient frontier and its extensions.

Portfolio Betas

As we have noted, investors strive to diversify their portfolios by including a variety of noncomplementary investments that allow investors to reduce risk while meeting their return objectives. Remember that investments embody two basic types of risk: (1) diversifiable risk, the risk unique to a particular investment, and (2) undiversifiable risk, the risk possessed, at least to some degree, by every investment.

A great deal of research has been conducted on the topic of risk as it relates to security investments. The results show that, in general, to earn a higher return, you must bear more risk. Just as important, however, are research results showing that the positive relation between risk and return holds only for undiversifiable risk. High levels of diversifiable risk do not result in correspondingly high levels of return. Because there is no reward for bearing diversifiable risk, investors should minimize this form of risk by diversifying the portfolio so that only undiversifiable risk remains.

Risk Diversification

As we’ve seen, diversification minimizes diversifiable risk by offsetting the below-average return on one investment with the above-average return on another. Minimizing diversifiable risk through careful selection of investments requires that the investments chosen for the portfolio come from a wide range of industries.

To better understand how diversification benefits investors, let’s examine what happens when we begin with a single asset (security) in a portfolio and then expand the portfolio by randomly selecting additional securities. Using the standard deviation, sp, to measure the portfolio’s total risk, we can depict the behavior of the total portfolio risk as more securities are added in  Figure 5.8 . As we add securities to the portfolio (x-axis), the total portfolio risk (y-axis) declines because of the effects of diversification, but there is a limit to how much risk reduction investors can achieve.

Figure 5.8 Portfolio Risk and Diversification

As more securities are combined to create a portfolio, the total risk of the portfolio (measured by its standard deviation, sp) declines. The portion of the risk eliminated is the diversifiable risk; the remaining portion is the undiversifiable, or relevant, risk.

On average, most of the risk-reduction benefits of diversification can be gained by forming portfolios containing two or three dozen carefully selected securities, but our recommendation is to hold 40 or more securities to achieve efficient diversification. This suggestion tends to support the popularity of investment in mutual funds.

Because any investor can create a portfolio of assets that will eliminate virtually all diversifiable risk, the only  relevant risk  is that which is undiversifiable. You must therefore be concerned solely with undiversifiable risk. The measurement of undiversifiable risk is thus of primary importance.

Calculating Portfolio Betas

As we saw earlier, beta measures the undiversifiable, or relevant, risk of a security. The beta for the market is equal to 1.0. Securities with betas greater than 1.0 are more risky than the market, and those with betas less than 1.0 are less risky than the market. The beta for the risk-free asset is 0.

The  portfolio beta, bp , is merely the weighted average of the betas of the individual assets in the portfolio. You can easily calculate a portfolio’s beta by using the betas of the component assets. To find the portfolio beta, bp, calculate a weighted average of the betas of the individual stocks in the portfolio, where the weights represent the percentage of the portfolio’s value invested in each security, as shown in  Equation 5.4 .

Portfolio beta=(Proportion of portfolio's totaldollar valuein asset 1×Betaforasset 1)+(Proportion of portfolio'stotal dollar value in asset 2×Beta for asset 2)+...+(Proportion of portfolio's total dollar value in assetn×Beta for assetn)=n∑j=1(Proportion ofportfolio's totaldollar valuein assetj×Beta for assetj)Portfolio beta =(Proportion of portfolio's total dollar value in asset 1×Beta for asset 1)+(Proportion of portfolio's total dollar value in asset 2×Beta for asset 2)+...+(Proportion of portfolio's total dollar value in asset n×Beta for asset n)=∑j=1n(Proportion of portfolio's total dollar value in asset j×Beta for asset j)Equation5.4

bp=(w1×b1)+(w2×b2)+...+(wn×bn)=n∑j=1(wj×bj)bp=(w1×b1)+(w2×b2)+...+(wn×bn)=∑j=1n(wj×bj)Equation5.4a

Of course, n∑j=1wj=1,∑j=1nwj=1, which means that 100% of the portfolio’s assets must be included in this computation.

Portfolio betas are interpreted in exactly the same way as individual asset betas. They indicate the degree of responsiveness of the portfolio’s return to changes in the market return. For example, when the market return increases by 10%, a portfolio with a beta of 0.75 will experience a 7.5% increase in its return (0.75 × 10%). A portfolio with a beta of 1.25 will experience a 12.5% increase in its return (1.25 × 10%). Low-beta portfolios are less responsive, and therefore less risky, than high-beta portfolios.

To demonstrate, consider the Austin Fund, a large investment company that wishes to assess the risk of two portfolios, V and W. Both portfolios contain five assets, with the proportions and betas shown in  Table 5.6 . We can calculate the betas for portfolios V and W, bv and bw, by substituting the appropriate data from the table into  Equation 5.4 , as follows.

Table 5.6 Austin Fund’S Portfolios V And W

	Portfolio V	Portfolio W
Asset	Proportion	Beta	Proportion	Beta
1	0.10	1.65	0.10	0.80
2	0.30	1.00	0.10	1.00
3	0.20	1.30	0.20	0.65
4	0.20	1.10	0.10	0.75
5	0.20	1.25	0.50	1.05
Total	1.00		1.00

bv=(0.10×1.65)+(0.30×1.00)+(0.20×1.30)+(0.20×1.10)+(0.20×1.25)=0.165+0.300+0.260+0.220+0.250=1.195≈1.20––––––––––bw=(0.10×0.80)+(0.10×1.00)+(0.20×0.65)+(0.10×0.75)+(0.50×1.05)=0.080+0.100+0.130+0.075+0.525=0.91––––––––––bv=(0.10×1.65)+(0.30×1.00)+(0.20×1.30)+(0.20×1.10)+(0.20×1.25)=0.165+0.300+0.260+0.220+0.250=1.195≈1.20__bw=(0.10×0.80)+(0.10×1.00)+(0.20×0.65)+(0.10×0.75)+(0.50×1.05)=0.080+0.100+0.130+0.075+0.525=0.91__

Portfolio V’s beta is 1.20, and portfolio W’s is 0.91. These values make sense because portfolio V contains relatively high-beta assets and portfolio W contains relatively low-beta assets. Clearly, portfolio V’s returns are more responsive to changes in market returns—and therefore more risky—than portfolio W’s.

Interpreting Portfolio Betas

If a portfolio has a beta of 1.0, the portfolio experiences changes in its rate of return equal to changes in the market’s rate of return. The 1.0 beta portfolio would tend to experience a 10% increase in return if the stock market as a whole experienced a 10% increase in return. Conversely, if the market return fell by 6%, the return on the 1.0 beta portfolio would also fall by 6%.

Table 5.7  lists the expected returns for three portfolio betas in two situations: an increase in market return of 10% and a decrease in market return of 10%. The portfolio with a beta of 2.0 moves twice as much (on average) as the market does. When the market return increases by 10%, the portfolio return increases by 20%. When the market return declines by 10%, the portfolio’s return will fall by 20%. This portfolio would be considered a high-risk, high-return portfolio.

The middle, 0.5 beta portfolio is considered a low-risk, low-return portfolio. This would be a conservative portfolio for investors who wish to maintain a low-risk investment posture. The 0.5 beta portfolio is half as volatile as the market.

A portfolio with a beta of -1.0 moves in the opposite direction from the market. A bearish investor would probably want to own a negative-beta portfolio because this

Table 5.7 Portfolio Betas And Associated Changes In Returns

Portfolio Beta	Changes in Market Return (%)	Change in Expected Portfolio Return (%)
+ 2.0	+ 10.0%	+ 20.0%
	− 10.0%	− 20.0%
+ 0.5	+ 10.0%	+ 5.0%
	− 10.0%	− 5.0%
− 1.0	+ 10.0%	− 10.0%
	− 10.0%	+ 10.0%

Figure 5.9 The Portfolio Risk-Return Tradeoff

As the risk of an investment portfolio increases from 0, the return provided should increase above the risk-free rate, rf. Portfolios A and B offer returns commensurate with their risk, portfolio C provides a high return at a low-risk level, and portfolio D provides a low return for high risk. Portfolio C is highly desirable; portfolio D should be avoided.

type of investment tends to rise in value when the stock market declines, and vice versa. Finding securities with negative betas is difficult, however. Most securities have positive betas because they tend to experience return movements in the same direction as changes in the stock market.

The Risk-Return Tradeoff: Some Closing Comments

Another valuable outgrowth of modern portfolio theory is the specific link between undiversifiable risk and investment returns. The basic premise is that an investor must have a portfolio of relatively risky investments to earn a relatively high rate of return. That relationship is illustrated in  Figure 5.9 . The upward-sloping line shows the  risk-return tradeoff . The point where the risk-return line crosses the return axis is called the  risk-free rate, rf . This is the return an investor can earn on a risk-free investment such as a U.S. Treasury bill or an insured money market deposit account.

As we proceed upward along the risk-return tradeoff line, portfolios of risky investments appear, as depicted by four investment portfolios, A through D. Portfolios A and B are investment opportunities that provide a level of return commensurate with their respective risk levels. Portfolio C provides a high return at a relatively low risk level—and therefore would be an excellent investment. Portfolio D, in contrast, offers high risk but low return—an investment to avoid.

Reconciling the Traditional Approach and MPT

We have reviewed two fairly different approaches to portfolio management: the traditional approach and MPT. The question that naturally arises is which technique should you use? There is no definite answer; the question must be resolved by the judgment of each investor. However, we can offer a few useful ideas.

The average individual investor does not have the resources and the mathematical acumen to implement a total MPT portfolio strategy. But most individual investors can extract and use ideas from both the traditional and MPT approaches. The traditional approach stresses security selection, which we will discuss later in this text. It also emphasizes diversification of the portfolio across industry lines. MPT stresses reducing correlations between securities within the portfolio. This approach calls for diversification to minimize diversifiable risk. Thus, diversification must be accomplished to ensure satisfactory performance with either strategy. Also, beta is a useful tool for determining the level of a portfolio’s undiversifiable risk and should be part of the decision-making process.

We recommend the following portfolio management policy, which uses aspects of both approaches:

· Determine how much risk you are willing to bear.

· Seek diversification among types of securities and across industry lines, and pay attention to how the return from one security is related to that from another.

· Consider how a security responds to the market, and use beta in diversifying your portfolio to keep the portfolio in line with your acceptable risk level.

· Evaluate alternative portfolios to make sure that the portfolio selected provides the highest return for the acceptable level of risk.

Concepts in Review

Answers available at  http://www.pearsonhighered.com/smart

1. 5.12 Describe traditional portfolio management. Give three reasons why traditional portfolio managers like to invest in well-established companies.

2. 5.13 What is modern portfolio theory (MPT)? What is the feasible or attainable set of all possible portfolios? How is it derived for a given group of investments?

3. 5.14 What is the efficient frontier? How is it related to the attainable set of all possible portfolios? How can it be used with an investor’s utility function to find the optimal portfolio?

4. 5.15 Define and differentiate among the diversifiable, undiversifiable, and total risk of a portfolio. Which is considered the relevant risk? How is it measured?

5. 5.16 Define beta. How can you find the beta of a portfolio when you know the beta for each of the assets included within it?

6. 5.17 Explain how you can reconcile the traditional and modern portfolio approaches.

Constructing a Portfolio Using an Asset Allocation Scheme

1. LG 1

We begin by examining the criteria for constructing a portfolio and then use them to develop a plan for allocating assets in various investment categories. This plan provides a basic, useful framework for selecting individual investments for the portfolio. In attempting to weave the concepts of risk and diversification into a solid portfolio policy, we will rely on both traditional and modern approaches.

Investor Characteristics and Objectives

You should consider a wide variety of issues as you make plans to manage your own portfolio. Of course these factors include the risk and return characteristics of specific investments that you might include in your portfolio, but they also include personal issues. For example, the size of your income and the certainty of your employment are important. If you hold a secure, well-paying job, you can afford to take more risk in your investment portfolio. Also, as you earn more income over time, you will probably face higher marginal tax rates, so the tax ramifications of your investment program become more important. Your marital status is important, and certainly having children changes your savings and investment objectives. Finally, your investment experience also influences your investment strategy. It normally is best to “get your feet wet” in the investment market by slipping into it gradually rather than leaping in head first. A cautiously developed investment program is likely to provide more favorable long-run results than an impulsive one.

Now you should ask yourself, what do I want from my portfolio? You must generally choose between high current income and significant capital appreciation. It is difficult to have both. The price of having high appreciation potential is often low potential for current income.

Your needs may determine which avenue you choose. A retired person whose income depends on his or her portfolio will probably choose a lower-risk, current-income-oriented approach. A young investor may be much more willing to take on risky investments in the hope of accumulating wealth at a more rapid pace. Thus, a portfolio must be built around your needs, which depend on your income, your age, the size of your family, and your risk preferences.

Watch your Behavior

Marriage Is Good for Your Portfolio A fascinating research study found that single women earned higher returns on their investments than single men did, partly because single men were too confident about their investment prowess, traded too frequently, and generated excessive transactions costs. But the investment performance achieved by married men was much closer to that exhibited by married women. In other words, at least if you are a man, marriage seems to be good for your portfolio.

(Source: Brad M. Barber and Terrance Odean, “Boys Will Be Boys: Gender, Overconfidence, and Common Stock Investment,” Quarterly Journal of Economics, 2001, Vol. 16, Issue 1, pp. 261–292.)

An Advisor’s Perspective

James Johnson President, All Mark Insurance Services

“When you are young, you can risk your money.”

MyFinanceLab

Portfolio Objectives and Policies

Constructing a portfolio is a logical process that is best done after you have analyzed your needs and investment options. When planning and constructing a portfolio, you should consider these objectives:

· Generating current income

· Preserving capital

· Growing capital

· Reducing taxes

· Managing risk

All of these factors may play an influential role in defining the portfolio that is best for you. The first two items, current income and capital preservation, are consistent with a low-risk, conservative investment strategy. Normally, a portfolio with this orientation contains low-beta (low-risk) securities. The third item, a capital growth objective, implies increased risk and a reduced level of current income. Higher-risk growth stocks, options, futures, and other more speculative investments may be suitable for you if you place a high value on the capital growth objective. The fourth item, your tax bracket, will also influence your investment strategy. If you are in a high tax bracket, you have a great incentive to defer taxes and earn investment returns in the form of capital gains. This implies a strategy of higher-risk investments and a longer holding period. If you are in a lower bracket, you will be less concerned with the form that your investment income takes, so you may be more willing to invest in higher-current-income securities. The most important item, finally, is risk. Investors should consider the risk-return tradeoff in all investment decisions.

How to Choose Your Asset Allocation

Developing an Asset Allocation Scheme

Once you have translated your needs into specific portfolio objectives, you can construct a portfolio designed to achieve these goals. Before buying any investments, however, you must develop an asset allocation scheme.  Asset allocation  involves dividing your portfolio into various asset classes, such as U.S. stocks and bonds, foreign securities, short-term securities, and other assets like tangibles (e.g., gold) and real estate. Asset allocation and diversification are related but different ideas. Asset allocation focuses on investment in various asset classes. Spreading your wealth across different types of assets does help to diversify your portfolio, but then beyond that, you can diversify within an asset class by selecting individual securities that are not highly correlated with each other. For example, by allocating your assets between stocks and bonds you reap some diversification benefit, but within the stock portfolio, you want to select stocks that do not move together so that the stock portfolio itself is well diversified. The same could be said of the bonds in your portfolio. The second step in this process is called  security selection —selecting the specific securities to be held within an asset class.

Asset allocation is based on the belief that the total return of a portfolio is influenced more by the division of investments into asset classes than by the actual investments within each asset class. In fact, studies have shown that as much as 90% of a portfolio’s return comes from asset allocation. Therefore, less than 10% can be attributed to the actual security selection. Furthermore, researchers have found that asset allocation has a much greater impact on reducing total risk than does selecting the best investment in any single asset category.

Approaches to Asset Allocation

The basic approaches to asset allocation are (1) fixed weightings, (2) flexible weightings, and (3) tactical asset allocation. The first and second differ with respect to the proportions of each asset category maintained in the portfolio. The third is a more exotic technique used by institutional portfolio managers.

Fixed Weightings

The  fixed-weightings approach  allocates a fixed percentage of the portfolio to each of the asset categories (most individuals invest in three to five asset classes). Assuming four categories—common stock, bonds, foreign securities, and short-term securities—a fixed allocation might be as follows.

Category	Allocation
Common stock	30%
Bonds	50%
Foreign securities	15%
Short-term securities	5%
Total Portfolio	100%

Generally, the fixed weightings do not change over time. Because market values shift, you may have to adjust the portfolio annually or after major market moves to maintain the desired fixed-percentage allocations. For example, if the stock market booms, the percentage of the portfolio in stocks will rise, even without any new investments, so to maintain the fixed weightings, you would sell stocks and buy securities in the other asset classes.

Watch Your Behavior

Weighting the Choices It is surprising how many investors’ asset allocation decisions in their retirement accounts are influenced by the menu of choices available to them. One study found that if a firm’s menu of investment options included more stock funds, employees of that firm invested significantly more in stocks, even though it is not necessary to have a large number of stock funds on the menu to achieve a high allocation to stocks. For example, this study would predict that employees working for a company that offered two stock funds and one bond fund would allocate less money to stocks than would employees whose firms allowed them to allocate their retirement savings among three stock funds and one bond fund.

(Source: Jeffrey R. Brown, Nellie Liang, and Scott Weisbenner, “Individual account investment options and portfolio choice: Behavioral lessons from 401 (k) plans,” Journal of Public Economics, 2007, Vol. 91, Issue 10, pp. 1992–2013.)

Fixed weights may or may not represent equal percentage allocations to each category. One could, for example, allocate 25% to each of the four categories above. Research has shown that many investors choose to spread their money evenly across the investment options presented to them, a phenomenon called the “1/N heuristic.” This behavior appears to be especially common in retirement accounts. For example, if a firm’s retirement plan allows employees to allocate the retirement contributions among five mutual funds, many investors will choose to invest 1/5th (i.e., 1/N where N equals the number of choices) of their money to each fund. While this simple rule of thumb will probably result in a portfolio with a reasonable balance between risk and return, there is no guarantee that spreading assets equally among the available asset classes represents an optimal strategy.

Flexible Weightings

The  flexible-weightings approach  involves periodic adjustment of the weights for each asset category on the basis of market analysis. The use of a flexible-weighting scheme is often called strategic asset allocation. For example, the initial and new allocation based on a flexible-weighting scheme may be as follows.

Category	Initial Allocation	New Allocation
Common stock	30%	45%
Bonds	40%	40%
Foreign securities	15%	10%
Short-term securities	15%	5%
Total portfolio	100%	100%

A change from the initial to the new allocation would be triggered by shifts in market conditions or expectations. For example, the new allocation shown above may have resulted from an anticipated improvement in domestic economic conditions. That improvement should result in increased domestic stock prices, producing higher returns on that asset class relative to foreign and short-term securities. The weightings were therefore changed to capture greater returns in a changing market.

Tactical Asset Allocation

The third approach,  tactical asset allocation , is a form of market timing that uses stock-index futures and bond futures, which we will discuss later, to change a portfolio’s asset allocation. When investors expect lower returns on stocks than on bonds, this strategy would direct them to sell stock-index futures and buy bond futures. Conversely, when bonds are forecast to be less attractive than stocks, the strategy results in buying stock-index futures and selling bond futures. Because this sophisticated technique relies on a large portfolio and the use of quantitative models for market timing, it is generally appropriate only for large institutional investors.

Asset Allocation Alternatives

Assuming the use of a fixed-weight asset allocation plan and using, just as an example, four asset categories, we can demonstrate three

Test Your Risk Tolerance

Table 13.1 Alternative Asset Allocations

Allocation Alternative
Category	Conservative (low return/low risk)	Moderate (average return/average risk)	Aggressive (high return/high risk)
Common stock	15%	30%	40%
Bonds	45%	40%	30%
Foreign securities	5%	15%	25%
Short-term securities	35%	15%	5%
Total portfolio	100%	100%	100%

asset allocations.  Table 13.1  shows allocations in each of four categories for conservative (low return/low risk), moderate (average return/average risk), and aggressive (high return/high risk) portfolios. The conservative allocation relies heavily on bonds and short-term securities to provide predictable returns. The moderate allocation consists largely of common stock and bonds and includes more foreign securities and fewer short-term securities than the conservative allocation. Its moderate risk-return behavior reflects a move away from safe, short-term securities to a larger dose of common stock and foreign securities. Finally, in the aggressive allocation, more dollars are invested in common stock, fewer in bonds, and more in foreign securities, thereby generally increasing the expected portfolio return and risk.

Applying Asset Allocation

An asset allocation plan should consider the economic outlook, your savings and spending patterns, your tax situation, the returns expected from different asset classes, and your risk tolerance. You also must periodically revise the plan to reflect changing investment goals. Generally, to decide on the appropriate asset mix, you must evaluate each asset category in terms of current return, growth potential, safety, liquidity, transaction costs (brokerage fees), and potential tax savings.

Many investors use mutual funds as part of their asset allocation activities, to diversify within each asset category. Or, as an alternative to constructing your own portfolio, you can buy shares in an asset allocation fund—a mutual fund that seeks to reduce variability of returns by investing in the right assets at the right time. These funds, like all asset allocation schemes, emphasize diversification. They perform at a relatively consistent level by passing up the potential for spectacular gains in favor of predictability. Some asset allocation funds use fixed weightings, whereas others have flexible weights that change within prescribed limits. As a rule, investors with more than about $100,000 to invest and adequate time can justify do-it-yourself asset allocation. Those with between $25,000 and $100,000 and adequate time can use mutual funds to create a workable asset allocation. Those with less than $25,000 or with limited time may find asset allocation funds most attractive.

Most important, you should recognize that to be effective, an asset allocation scheme must be designed for the long haul. Develop an asset allocation scheme you can live with for at least seven years, and perhaps longer. Once you have it set, stick with it. The key to success is remaining faithful to your asset allocation and fighting the temptation to deviate from your plan.

Concepts in Review

Answers available at  http://www.pearsonhighered.com/smart

1. 13.1 What role, if any, do an investor’s personal characteristics play in determining portfolio policy? Explain.

2. 13.2 What role do an investor’s portfolio objectives play in constructing a portfolio?

3. 13.3 What is asset allocation? How does it differ from diversification? What role does asset allocation play in constructing an investment portfolio?

4. 13.4 Briefly describe the basic approaches to asset allocation: (a) fixed weightings, (b) flexible weightings, and (c) tactical asset allocation.

5. 13.5 What role could an asset allocation fund play? What makes an asset allocation scheme effective?

Evaluating the Performance of Individual Investments

1. LG 2

Imagine that one of your most important personal goals is to have accumulated enough savings three years from now in order to make the down payment on your first house. You project that the desired house will cost $200,000 and that the $33,000 will be sufficient to make a 15% down payment and pay the associated closing costs. Your calculations indicate that you can achieve this goal by investing existing savings plus an additional $200 per month over the next three years in an investment earning 10% per year. Projections of your income and expenses over the three-year period indicate that you should just be able to set aside the needed $200 per month. You consult with an investment advisor, Cliff Orbit, who leads you to believe that under his management, the 10% return can be achieved.

It seems simple. Give Cliff your existing savings, send him $200 each month for the next 36 months, and at the end of that period, you will have the $33,000 needed to purchase the house. Unfortunately, there are many uncertainties involved. What if you don’t set aside $200 each month? What if Cliff fails to earn the 10% annual return? What if in three years the desired house costs more than $200,000? Clearly, you must do more than simply devise what appears to be a feasible plan for achieving a goal. Rarely are there guarantees that your planned investment and portfolio outcomes will actually occur. Therefore, it is important to assess your progress toward your investment goals periodically.

As actual outcomes occur, you must compare them to the planned outcomes and make any necessary alterations in your plans—or in your goals. Knowing how to measure investment performance is therefore crucial. Here we will emphasize measures suitable for analyzing investment performance. We begin with sources of data.

Obtaining Data

The first step in analyzing investment returns is gathering data that reflect the actual performance of each investment. Many sources of investment information are available, both online and in print. The Wall Street Journal,  WSJ.com , and Yahoo! Finance, for example, contain numerous items of information useful in assessing the performance of securities. You use the same type of information to evaluate investment performance that you use to make an investment decision. Two key areas to stay informed about are (1) returns on investments and (2) economic and market activity.

Return Data

The basic ingredient in analyzing investment returns is current market information, such as daily price quotations for stocks and bonds. Investors often maintain logs or spreadsheets that contain the cost of each investment, as well as dividends, interest, and other sources of income received. By regularly recording price and return data, you can create an ongoing record of price fluctuations and cumulative returns. You should also monitor corporate earnings and dividends, which affect a company’s stock price. These sources of investment return—current income and capital gains—must of course be combined to determine total return.

Economic and Market Activity

Changes in the economy and market affect returns—both the level of current income and the market value of an investment. The astute investor keeps abreast of international, national, and local economic and market developments. By following economic and market changes, you should be able to assess their potential impact on returns. As economic and market conditions change, you must be prepared to make revisions in the portfolio. In essence, being a knowledgeable investor will improve your chances of generating a profit (or avoiding a loss).

Indexes of Investment Performance

In measuring investment performance, it is often worthwhile to compare your returns with broad-based market measures. Indexes useful for the analysis of common stock include the Dow Jones Industrial Average (DJIA), the Standard & Poor’s 500 Stock Composite Index (S&P 500), and the Nasdaq Composite Index. Although the DJIA is widely cited by the news media, it is not the most appropriate comparative gauge of stock price movement because of its narrow coverage and because it is a price-weighted index. If your portfolio is composed of a broad range of common stocks, the S&P 500 Index is probably a more appropriate tool.

A number of indicators are also available for assessing the general behavior of the bond markets. These indicators consider either bond yield or bond price behavior. Bond yield data reflect the rate of return one would earn on a bond purchased today and held to maturity. Popular sources of these data include the Wall Street Journal, Barron’s, Standard & Poor’s, Mergent, Yahoo! Finance, and the Federal Reserve. The Dow Jones Corporate Bond Index, based on the closing prices of 32 industrial, 32 financial, and 32 utility/telecom bonds, is a popular measure of bond price behavior. It reflects the mathematical average of the closing prices of the bonds.

Indexes of bond prices and information about bond yields can be obtained for specific types of bonds (industrial, utility, and municipal), as well as on a composite basis. In addition, indexes reported in terms of total returns are available for both stocks and bonds. They combine dividend/interest income with price behavior (capital gain or loss) to reflect total return.

Investors frequently use the Lipper indexes to assess the general behavior of mutual funds. These indexes are available for various types of equity and bond funds. Unfortunately, for most other types of funds, no widely published index or average is available. A few other indexes cover listed options and futures.

Measuring the Performance of Investments

To monitor an investment portfolio, investors need reliable techniques for consistently measuring the performance of each investment in the portfolio. In particular, the holding period return (HPR) measure that we studied earlier can be used to determine actual return performance. HPR is an excellent way to assess actual return behavior because it captures total return performance. It is most appropriate for holding or assessment periods of one year or less. Total return, in this context, includes the periodic cash income from the investment as well as price appreciation (or loss), whether realized or unrealized. To calculate returns for periods of more than a year, you can use the internal rate of return, which recognizes the time value of money. Because the following discussions center on the annual assessment of return, we will use HPR as the measure of return.

The formula for HPR is restated in  Equation 13.1 .

Holding period return=Current income during period+Capital gain (or loss) during periodBeginning investment valueHolding period return=Current income during period + Capital gain (or loss) during periodBeginning investment valueEquation13.1

HPR=C+CGV0HPR=C+CGV0Equation13.1a

where

Capital gain (or loss)during period=Ending investment value−Beginninginvestment valueCapital gain (or loss) during period = Ending investment value − Beginning investment valueEquation13.2

CG=Vn−V0CG=Vn−V0Equation13.2a

Stocks and Bonds

There are several measures of investment return for stocks and bonds. Dividend yield, measures the current yearly dividend return earned from a stock investment. It is calculated by dividing a stock’s yearly cash dividend by its price. The current yield and yield to maturity (promised yield) for bonds capture various components of return but do not always reflect actual total return. The holding period return method measures the total return (income plus change in value) actually earned on an investment over a given investment period. We will use HPR, with a holding period of approximately one year, in the illustrations that follow.

Stocks

The HPR for common and preferred stocks includes both cash dividends received and any price change in the security during the period of ownership.  Table 13.2  illustrates the HPR calculation as applied to the actual performance of a common stock. Assume you purchased 1,000 shares of Dallas National Corporation in May 2016 at a cost of $27,312 (including commissions). After holding the stock for just over one year, you sold it, reaping proceeds of $32,040. In addition to the $4,728 capital gain on the sale, you also received $2,000 in cash dividends. Thus, the calculated HPR is 24.63%.

This HPR was calculated without consideration for income taxes paid on the dividends and capital gain. Because many investors are concerned with both pretax and after-tax rates of return, it is useful to calculate an after-tax HPR. We assume, for simplicity, that you are in the 30% ordinary tax bracket (federal and state combined). We also assume that, for federal and state tax purposes, dividends and capital gains for holding periods of more than 12 months are taxed at a 15% rate. Thus, both your dividend and capital gain income are taxed at a 15% rate. Income taxes reduce the after-tax dividend income to $1,700[i.e., (1 − 0.15) × $2,000]$1,700 [i.e., (1 − 0.15) × $2,000] and the after-tax capital gain to $4,019 [i.e, (1 − 0.15) × ($32,040 − $27,312)]$4,019 [i.e, (1 − 0.15) × ($32,040 − $27,312)]. The after-tax HPR is therefore 20.94% or ($1,700 + $4,019) ÷ $27,312 = 0.2094($1,700 + $4,019) ÷ $27,312 = 0.2094, a reduction of 3.69 percentage points. It should be clear that both pretax HPR and after-tax HPR are useful gauges of return.

Table 13.2 Calculation of Pretax HPR on a Common Stock

Security: Dallas National Corporation common stock

Date of purchase: May 1, 2016

Purchase cost: $27,312

Date of sale: May 7, 2017

Sale proceeds: $32,040

Dividends received (May 2016 to May 2017): $2,000

Holding period return=$2,000 + $32,040 − $27,312$27,312=24.63%––––––––––––––––Holding period return = $2,000 + $32,040 − $27,312$27,312= 24.63%__

Bonds

The HPR for a bond investment is similar to that for stocks. The calculation holds for both straight debt and convertible issues. It includes the two components of a bond investor’s return: interest income and capital gain or loss.

Calculation of the HPR on a bond investment is illustrated in  Table 13.3  . Assume you purchased Phoenix Brewing Company bonds for $10,000, held them for just over one year, and then realized $9,704 at their sale. In addition, you earned $1,000 in interest during the year. The HPR of this investment is 7.04%. The HPR is lower than the bond’s current yield of 10% (i.e., $1,000 interest ÷ $10,000 purchase price) because the bonds were sold at a capital loss. Assuming a 30% ordinary tax bracket and a 15% capital gains tax rate (because the bond has been held more than 12 months), the after-tax HPR is 4.48%: {[(1−0.30)×$1,000]+[(1−0.15)×($9,704−$10,000)]}÷$10,000{[(1−0.30)×$1,000]+[(1−0.15)×($9,704−$10,000)]}÷$10,000. This is 2.56% less than the pretax HPR.

Table 13.3 Calculation of Pretax HPR on a Bond

Security: Phoenix Brewing Company 10% bonds

Date of purchase: June 2, 2016

Purchase cost: $10,000

Date of sale: June 5, 2017

Sale proceeds: $9,704

Interest earned (June 2016 to June 2017): $1,000

Holding period return=$1,000 + ($9,704 − $10,000)$10,000=7.04%–––––––Holding period return= $1,000 + ($9,704 − $10,000)$10,000=7.04%_

Mutual Funds

The basic components of return from a mutual fund investment are dividend income (including any capital gains distribution) and change in value. The basic HPR equation for mutual funds is identical to that for stocks.

Table 13.4  presents a holding period return calculation for a no-load mutual fund. Assume you purchased 1,000 shares of the fund in July 2016 at a net asset value (NAV) of $10.40 per share. Because it is a no-load fund, no commission was charged, so your cost was $10,400. During the one-year period of ownership, the Pebble Falls Mutual Fund distributed investment income dividends totaling $270 and capital gains dividends of $320. You redeemed (sold) this fund at an NAV of $10.79 per share, thereby realizing $10,790. As seen in  Table 13.4  , the pretax holding period return on this investment is 9.42%. Assuming a 30% ordinary tax bracket and a 15% dividend and capital gains tax rate (because the fund has been held for more than 12 months),

Table 13.4 CALCULATION OF PRETAX HPR ON A MUTUAL FUND

Security: Pebble Falls Mutual Fund

Date of purchase: July 1, 2016

Purchase cost: $10,400

Date of redemption: July 3, 2017

Sale proceeds: $10,790

Distributions received (July 2016 to July 2017)

Investment income dividends: $270

Capital gains dividends: $320

Holding period return=($270 + $320) + ($10,790 − $10,400)$10,400=9.42%––––––––––––––Holding period return = ($270 + $320) + ($10,790 − $10,400)$10,400= 9.42%__

the after-tax HPR for the fund is 8.01%: {[(1−0.15)×($270+$320)]+[(1−0.15)×($10,790−$10,400)]}÷$10,400{[(1−0.15)×($270+$320)]+[(1−0.15)×($10,790−$10,400)]}÷$10,400. This is 1.41% below the pretax return.

Options and Futures

The only source of return on options and futures is capital gains. To calculate a holding period return for an investment in a call option, for instance, you use the basic HPR formula, but you would set current income equal to zero. If you purchased a call on 100 shares of Facebook for $325 and sold the contract for $385 after holding it for just over 12 months, the pretax holding period return would be 18.46%. This calculation simply takes the sales proceeds of $385, subtracts the initial cost of $325, and divides by the initial cost. Assuming the 15% capital gains tax rate applies, the after-tax HPR would be 15.69%, which is the after-tax gain of $51[i.e.,(1−0.15)×$60]$51[i.e., (1−0.15)×$60] divided by the initial cost of $325.

The HPRs of futures are calculated in a similar fashion. Because the return is in the form of capital gains only, the HPR analysis can be applied to any investment on a pretax or an after-tax basis. (The same basic procedure is used for securities that are sold short.)

Comparing Performance to Investment Goals

After computing an HPR (or yield) on an investment, you should compare it to your investment goal. Keeping track of an investment’s performance will help you decide which investments you should continue to hold and which you might want to sell. Clearly, an investment would be a candidate for sale under any one of the following conditions: (1) The investment failed to perform up to expectations and no real change in performance is anticipated. (2) It has fulfilled the original investment objective. (3) Better investment outlets are currently available.

Balancing Risk and Return

We have frequently discussed the basic tradeoff between investment risk and return. To earn more return, you must take more risk. In analyzing an investment, the key question is, am I getting the proper return for the amount of investment risk I am taking?

Nongovernment security investments are by nature riskier than U.S. government bonds or insured money market deposit accounts. This implies that a rational investor should invest in these riskier assets only when the expected rate of return exceeds what could have been earned from a low-risk investment. Thus, one benchmark against which to compare investment returns is the rate of return on low-risk investments. If one’s risky investments are outperforming low-risk investments, they are obtaining extra return for taking extra risk. If they are not outperforming low-risk investments, you should carefully reexamine your investment strategy.

Isolating Problem Investments

It is best to analyze each investment in a portfolio periodically. For each, you should consider two questions. First, has it performed in a manner that could reasonably be expected? Second, if you didn’t currently own it, would you buy it today? If the answers to both are negative, then the investment probably should be sold. A negative answer to one of the questions qualifies the investment for the “problem list.” A problem investment is one that has not lived up to expectations. It may be a loss situation or an investment that has provided a return less than you expected. Many investors try to forget about problem investments, hoping the problem will go away or the investment will turn itself around. This is a mistake. Problem investments require immediate attention, not neglect. In studying a problem investment, the key question is, “Should I take my loss and get out, or should I hang on and hope it turns around?”

Concepts in Review

Answers available at  http://www.pearsonhighered.com/smart

1. 13.6 Why is it important to continuously manage and control your portfolio?

2. 13.7 What role does current market information play in analyzing investment returns? How do changes in economic and market activity affect investment returns? Explain.

3. 13.8 Which indexes can you use to compare your investment performance to general market returns? Briefly explain each of these indexes.

4. 13.9 What are indicators of bond market behavior, and how are they different from stock market indicators? Name three sources of bond yield data.

5. 13.10 Briefly discuss holding period return (HPR) and yield as measures of investment return. Are they equivalent? Explain.

6. 13.11 Distinguish between the types of dividend distributions that mutual funds make. Are these dividends the only source of return for a mutual fund investor? Explain.

7. 13.12 Under what three conditions would an investment holding be a candidate for sale? What must be true about the expected return on a risky investment, when compared with the return on a low-risk investment, to cause a rational investor to acquire the risky investment? Explain.

8. 13.13 What is a problem investment? What questions should one consider when analyzing each investment in a portfolio?

Assessing Portfolio Performance

1. LG 3

2. LG 4

A portfolio can be passively or actively managed. A passive portfolio results from buying and holding a well-diversified portfolio over the given investment horizon. An active portfolio is built using the traditional and modern approaches presented earlier and is managed and controlled to achieve its stated objectives. Passive portfolios may at times outperform equally risky active portfolios. But  active portfolio management  can help you adjust your portfolio as your investment objectives change. Many of the ideas presented in this text are consistent with the belief that active portfolio management will help you achieve your investment goals.

Once you have built a portfolio, the first step in active portfolio management is to assess performance, perhaps after a few quarters or a year. Based on the information from your assessment, you may revise the portfolio, continuing to assess and revise the portfolio periodically as needed. Calculating the portfolio return can be tricky. The procedures used to assess portfolio performance are based on many of the concepts presented earlier in this chapter. Here we will demonstrate how to assess portfolio performance, using a hypothetical securities portfolio over a one-year holding period. We will examine three measures that you can use to compare a portfolio’s return with a risk-adjusted, market-adjusted rate of return.

Measuring Portfolio Return

Table 13.5  presents the investment portfolio, as of January 1, 2017, of Bob Hathaway. He is a 50-year-old widower, whose children are married. His income is $60,000 per year. His primary investment objective is long-term growth with a moderate dividend return. He selects stocks with two criteria in mind: quality and growth potential. On January 1, 2017, his portfolio consisted of 10 stocks, all of good quality. Hathaway has been fortunate in his selection process. He has approximately $74,000 in unrealized price appreciation in his portfolio. During 2017 he decided to make a change in the portfolio. On May 7 he sold 1,000 shares of Dallas National Corporation for $32,040. The holding period return for that issue was discussed earlier (see  Table 13.2  ). Using proceeds from the Dallas National sale, he acquired an additional 1,000 shares of Florida Southcoast Banks on May 10 because he liked the prospects for the Florida bank. Florida Southcoast is based in one of the fastest growing counties in the country.

Measuring the Amount Invested

Every investor would be well advised to list his or her holdings periodically, as is done in  Table 13.5  . The table shows number of shares, acquisition date, cost, and current value for each issue. These data aid in continually formulating strategy decisions. The cost data, for example, are used to determine the amount invested. Hathaway’s portfolio does not use the leverage of a margin account. Were leverage present, all return calculations would be based on the investor’s equity in

Table 13.5 Bob Hathaway’s Portfolio (January 1, 2017)

Number of Shares	Company	Date Acquired	Total Cost (including commission)	Cost per Share	Current Price per Share	Current Value
1,000	Bancorp West, Inc.	1/16/12	$ 21,610	$21.61	$30	$ 30,000
1,000	Dallas National Corporation	5/01/13	$  27,312	$27.31	$29	$ 29,000
1,000	Dator Companies, Inc.	4/13/08	$ 13,704	$13.70	$27	$ 27,000
500	Excelsior Industries	8/16/11	$ 40,571	$81.14	$54	$ 27,000
1,000	Florida Southcoast Banks	12/16/11	$  17,460	$17.46	$30	$ 30,000
1,000	Maryland-Pacific	9/27/11	$ 22,540	$22.54	$26	$ 26,000
1,000	Moronson	2/27/11	$ 19,100	$19.10	$47	$ 47,000
500	Northwest Mining and Mfg.	4/17/12	$ 25,504	$51.00	$62	$ 31,000
1,000	Rawland Petroleum	3/12/12	$ 24,903	$24.90	$30	$ 30,000
1,000	Vornox	4/16/12	$  37,120	$37.12	$47	$ 47,000
	Total		$249,824			$324,000

Investor Facts

Dividends Count! Historically, dividends have made a significant contribution to investor returns and have helped investors beat inflation. Consider an investment in the S&P 500 Stock Index. For the 20-year period ending in June 2015, the average annual return on the S&P500 Index was 8.93%. Ignoring dividends, the average annual return would have been just 6.98%, so dividends accounted for nearly one-quarter of the annual total return on the index. High-dividend stocks may not outperform the market, but they continue to reward investors year after year, regardless of stock prices. Income-seeking investors look to dividends to “guarantee” some measure of return.

(Source: S&P500 Return Calculator,  http://dqydj.net/sp-500-return- calculator/ , accessed July 6, 2015.)

the account. Recall that an investor’s equity in a margin account equals the total value of all the securities in the account minus any margin debt.

To measure Hathaway’s return on his invested capital, we need to calculate the one-year holding period return. His invested capital as of January 1, 2017, is $324,000. He made no new additions of capital in the portfolio during 2017, although he sold one stock, Dallas National, and used the proceeds to buy another, Florida Southcoast Banks.

Measuring Income

There are two sources of return from a portfolio of common stocks: income and capital gains. Current income is realized from dividends or, for bonds, is earned in the form of interest. Investors must report taxable dividends and interest on federal and state income tax returns. Companies are required to furnish income reports (Form 1099-DIV for dividends and Form 1099-INT for interest) to stockholders and bondholders. Many investors maintain logs to keep track of dividend and interest income as it is received.

Table 13.6  lists Hathaway’s dividends for 2017. He received two quarterly dividends of $0.45 per share before he sold the Dallas National stock. He also received two $0.32-per-share quarterly dividends on the additional Florida Southcoast Banks shares he acquired. His total dividend income for 2017 was $10,935.

Measuring Capital Gains

Table 13.7  shows the unrealized gains in value for each of the issues in the Hathaway portfolio. The January 1, 2017, and December 31, 2017, values are listed for each issue except the additional shares of Florida Southcoast Banks. The amounts listed for Florida Southcoast Banks reflect the fact that 1,000 additional shares of the stock were acquired on May 10, 2017, at a cost of $32,040. Hathaway’s current holdings had beginning-of-the-year values of $327,040 (including the additional Florida Southcoast Banks shares at the date of purchase) and are worth $356,000 at year-end.

Table 13.6 Dividend Income on Hathaway’s Portfolio (Calendar Year 2017)

Number of Shares	Company	Annual Dividend per Share	Dividends Received
* Sold May 7, 2017.
** 1,000 additional shares acquired on May 10, 2017.
1,000	Bancorp West, Inc.	$1.20	$  1,200
1,000	Dallas National Corporation *	$1.80	$  900
1,000	Dator Companies, Inc.	$1.12	$ 1,120
500	Excelsior Industries	$2.00	$  1,000
2,000	Florida Southcoast Banks **	$1.28	$   1,920
1,000	Maryland-Pacific	$1.10	$   1,100
1,000	Moronson	—	—
500	Northwest Mining and Mfg.	$2.05	$   1,025
1,000	Rawland Petroleum	$1.20	$   1,200
1,000	Vornox	$1.47	$   1,470
	Total		$10,935

Table 13.7 Unrealized Gains in Value of Hathaway’s Portfolio (January 1, 2017, to December 31, 2017)

Number of Shares	Company	Market Value (1/1/17)	Market Price (12/31/17)	Market Value (12/31/17)	Unrealized Gain (Loss)	Percentage Change
* 1,000 additional shares acquired on May 10, 2017, at a cost of $32,040. The value listed is the cost plus the market value of the previously owned shares as of January 1, 2017.
** This total includes the $324,000 market value of the portfolio on January 1, 2017 (from  Table 13.5  ) plus the $3,040 realized gain on the sale of the Dallas National Corporation stock on May 7, 2017. The inclusion of the realized gain in this total is necessary to calculate the unrealized gain on the portfolio during 2017.
1,000	Bancorp West, Inc.	$            30,000	$27	$    27,000	($           3,000)	–10.0%
1,000	Dator Companies, Inc.	$            27,000	$36	$  36,000	$    9,000	33.3%
500	Excelsior Industries	$           27,000	$66	$  33,000	$    6,000	22.2%
2,000	Florida Southcoast Banks *	$         62,040	$35	$  70,000	$    7,960	12.8%
1,000	Maryland-Pacific	$       26,000	$26	$  26,000	—	—
1,000	Moronson	$           47,000	$55	$  55,000	$          8,000	17.0%
500	Northwest Mining and Mfg.	$       31,000	$60	$  30,000	($           1,000)	–3.2%
1,000	Rawland Petroleum	$       30,000	$36	$  36,000	$    6,000	20.0%
1,000	Vornox	$           47,000	$43	$  43,000	($     4,000)	–8.5%
	Total	$327,040 **		$356,000	$28,960	8.9%

During 2017 the portfolio increased in value by 8.9%, or $28,960, in unrealized capital gains. In addition, Hathaway realized a capital gain in 2017 by selling his Dallas National holding. From January 1, 2017, until its sale on May 7, 2017, the Dallas National holding rose in value from $29,000 to $32,040. This was the only sale in 2017, so the total realized gain was $3,040. During 2017 the portfolio had both a realized gain of $3,040 and an unrealized gain of $28,960. The total gain in value equals the sum of the two: $32,000. Put another way, Hathaway neither added nor withdrew capital over the year. Therefore, the total capital gain is simply the difference between the year-end market value (of $356,000, from  Table 13.7  ) and the value on January 1 (of $324,000, from  Table 13.5  ). This, of course, amounts to $32,000. Of that amount, for tax purposes, only $3,040 is considered realized.

Measuring the Portfolio’s Holding Period Return

We use the holding period return to measure the total return on the Hathaway portfolio during 2017. The basic one-year HPR formula for portfolios appears below.

Holding period return for a portfolio=Dividends and interest received+Realized gain+Unrealized gainInitial equity investment+(New funds×Number of months in portfolio12)−(Withdrawn funds×Number of months Withdrawn form portfolio12)Holding period return for a portfolio = Dividends and interest received + Realized gain + Unrealized gainInitial equity investment + (New funds × Number of months in portfolio12)−(Withdrawn funds× Number of months Withdrawn form portfolio12)Equation13.3

HPRp=C+RG+UGE0+(NF×ip12)−(WF×wp12)HPRp=C+RG+UGE0+(NF×ip12)−(WF×wp12)Equation13.3a

Table 13.8 Holding Period Return Calculation on Hathaway’s Portfolio (January 1, 2017, to December 31, 2017)

Data	Value
Portfolio value (1/1/17)	$324,000
Portfolio value (12/31/17)	$356,000
Realized appreciation (1/1/17 to 5/7/17 when Dallas National Corporation was sold)	$ 3,040
Unrealized appreciation (1/1/17 to 12/31/17)	$ 28,960
Dividends received	$  10,935
New funds invested or withdrawn	None
Portfolio HPR Calculation
HPRp=$10,935+$3,040+$28,960$324,000+$0+$0=13.25%––––––––HPRp=$10,935+$3,040+$28,960$324,000+$0+$0=13.25%_

This formula includes both the realized gains (income plus capital gains) and the unrealized yearly gains of the portfolio. Portfolio additions and deletions are time-weighted for the number of months they are in the portfolio.

Table 13.7  lays out in detail the portfolio’s change in value: It lists all the stocks that are in the portfolio as of December 31, 2017, and calculates the unrealized gain during the year. The beginning and year-end values are included for comparison purposes. The crux of the analysis is the HPR calculation for the year, presented in  Table 13.8  . All the elements of a portfolio’s return are included. Dividends total $10,935 (from  Table 13.6  ). The realized gain of $3,040 represents the increment in value of the Dallas National holding from January 1, 2017, until its sale. During 2017 the portfolio had a $28,960 unrealized gain (from  Table 13.7  ). There were no additions of funds, and no funds were withdrawn. Using  Equation 13.3  for HPR, we find that the portfolio had a total return of 13.25% in 2017.

Comparison of Return with Overall Market Measures

Bob Hathaway can compare the HPR figure for his portfolio with market measures such as stock indexes. This comparison will show how his portfolio is doing in relation to the stock market as a whole. The S&P 500 Stock Composite Index and the Nasdaq Composite Index are acceptable indexes to represent the stock market as a whole. Assume that during 2017 the return on the S&P 500 Index was 10.75% (including both dividends and capital gains). The return from Hathaway’s portfolio was 13.25%, which compares very favorably with the broadly based index. The Hathaway portfolio performed about 23% better than the broad indicator of stock market return.

Such a comparison factors out general market movements, but it fails to consider whether Hathaway’s portfolio is more or less risky than the broad stock market indexes. That requires further analysis. A number of risk-adjusted, market-adjusted rate-of-return measures are available for use in assessing portfolio performance. Here we’ll discuss the most popular—Sharpe’s measure, Treynor’s measure, and Jensen’s measure—and demonstrate their application to Hathaway’s portfolio.

Sharpe’s Measure

Sharpe’s measure  of portfolio performance, developed by William F. Sharpe, compares the risk premium on a portfolio to the portfolio’s standard deviation of return. The risk premium on a portfolio is the total portfolio return minus the risk-free rate. Sharpe’s measure can be expressed as the following formula:

Sharpe's measure=Total portfolio return−Risk-free rateStandard deviation of portfolio returnSharpe's measure = Total portfolio return− Risk-free rateStandard deviation of portfolio returnEquation13.4

SM=rp−rfspSM = rp−rfspEquation13.4a

This measure allows the investor to assess the risk premium per unit of total risk, which is measured by the portfolio standard deviation of return.

Assume the risk-free rate, rf, is 7.50% and the standard deviation of return on Hathaway’s portfolio, sp, is 16%. The total portfolio return, rp, which is the HPR for Hathaway’s portfolio calculated in  Table 13.8  , is 13.25%. Substituting those values into  Equation 13.4 , we get Sharpe’s measure, SMp.

SMp=13.25%−7.50%16%=5.75%16%=0.36––––––––––SMp=13.25%−7.50%16%=5.75%16%=0.36__

Sharpe’s measure is meaningful when compared either to other portfolios or to the market. In general, the higher the value of Sharpe’s measure, the better—the higher the risk premium per unit of risk. If we assume that the market return, rm, is currently 10.75% and the standard deviation of return for the market portfolio, spm, is 11.25%, Sharpe’s measure for the market, SMm, is

SMm=10.75%−7.50%11.25%=3.75%11.25%=0.29––––––––––SMm=10.75%−7.50%11.25%=3.75%11.25%=0.29__

Because Sharpe’s measure of 0.36 for Hathaway’s portfolio is greater than the measure of 0.29 for the market portfolio, Hathaway’s portfolio exhibits superior performance. Its risk premium per unit of risk is above that of the market. Had Sharpe’s measure for Hathaway’s portfolio been below that of the market (below 0.29), the portfolio’s performance would be considered inferior to the market performance.

Treynor’s Measure

Jack L. Treynor developed a portfolio performance measure similar to Sharpe’s measure.  Treynor’s measure  uses the portfolio beta to measure the portfolio’s risk. Treynor therefore focuses only on nondiversifiable risk, assuming that the portfolio has been built in a manner that diversifies away all diversifiable risk. (In contrast, Sharpe focuses on total risk.) Treynor’s measure is calculated as shown in  Equation 13.5 .

Treynor's measure=Total portfolio return−Risk-free ratePortfolio betaTreynor's measure = Total portfolio return− Risk-free ratePortfolio betaEquation13.5

TM=rp−rfbpTM = rp−rfbpEquation13.5a

This measure gives the risk premium per unit of nondiversifiable risk, which is measured by the portfolio beta.

Using the data for the Hathaway portfolio presented earlier and assuming that the beta for Hathaway’s portfolio, bp, is 1.20, we can substitute into  Equation 13.5  to get Treynor’s measure, TMp, for Hathaway’s portfolio.

TMp=13.25%−7.50%1.20=5.75%1.20=4.79%––––––––––––––TMp=13.25%−7.50%1.20=5.75%1.20=4.79%__

Treynor’s measure, like Sharpe’s measure, is useful when compared either to other portfolios or to the market. Generally, the higher the value of Treynor’s measure, the better—the greater the risk premium per unit of nondiversifiable risk. Again assuming that the market return, rm, is 10.75% and recognizing that, by definition, the beta for the market portfolio, bm, is 1.00, we can use  Equation 13.5  to find Treynor’s measure for the market, TMm.

TMm=10.75%−7.50%1.00=3.25%1.00=3.25%––––––––––––––TMm=10.75%−7.50%1.00=3.25%1.00=3.25%__

The fact that Treynor’s measure of 4.79% for Hathaway’s portfolio is greater than the market portfolio measure of 3.25% indicates that Hathaway’s portfolio exhibits superior performance. Its risk premium per unit of nondiversifiable risk is above that of the market. Had Treynor’s measure for Hathaway’s portfolio been below that of the market (below 3.25%), the portfolio’s performance would be viewed as inferior to that of the market.

Jensen’s Measure (Jensen’s Alpha)

Michael C. Jensen developed a portfolio performance measure that seems quite different from the measures of Sharpe and Treynor, yet is theoretically consistent with Treynor’s measure.  Jensen’s measure , also called  Jensen’s alpha , is based on the capital asset pricing model (CAPM). It calculates the portfolio’s excess return. Excess return is the amount by which the portfolio’s actual return deviates from its required (or expected) return, which is determined using its beta and the CAPM. The value of the excess return may be positive, zero, or negative. Like Treynor’s measure, Jensen’s measure focuses only on the nondiversifiable, or relevant, risk by using beta and CAPM. It assumes that the portfolio has been adequately diversified. Jensen’s measure is calculated as shown in  Equation 13.6 .

Jensen's measure=(Total portfolio return−Risk-free rate)−[Portfolio beta×(Market return−Risk-free rate)]Jensen's measure = (Total portfolio return− Risk-free rate)−[Portfolio beta × (Market return− Risk-free rate)]Equation13.6

JM=(rp−rf)−[bp×(rm−rf)]JM = (rp−rf)−[bp×(rm−rf)]Equation13.6a

Jensen’s measure indicates the difference between the portfolio’s actual return and its required return. Positive values indicate superior performance. They indicate that the portfolio earned a return in excess of its risk-adjusted, market-adjusted required return. A value of zero indicates that the portfolio earned exactly its required return. Negative values indicate the portfolio failed to earn its required return.

Using the data for Hathaway’s portfolio presented earlier, we can substitute into  Equation 13.6  to get Jensen’s measure, JMp, for Hathaway’s portfolio.

JMp=(13.25%−7.50)−[1.20×(10.75%−7.50)]=5.75%−(1.20×3.25)=5.75%−3.90%=1.85%––––––––––––––JMp= (13.25%−7.50)−[1.20 ×(10.75%−7.50)]=5.75%−(1.20 × 3.25)=5.75%−3.90%=1.85%__

The 1.85% value for Jensen’s measure indicates that Hathaway’s portfolio earned an excess return that was 1.85 percentage points above its required return, given its nondiversifiable risk as measured by beta. Clearly, Hathaway’s portfolio has outperformed the market on a risk-adjusted basis.

Note that unlike the Sharpe and Treynor measures, Jensen’s measure, through its use of CAPM, automatically adjusts for the market return. Therefore, there is no need to make a separate market comparison. In general, the higher the value of Jensen’s measure, the better the portfolio has performed. Only those portfolios with positive Jensen measures have outperformed the market on a risk-adjusted basis. Because of its computational simplicity, its reliance only on nondiversifiable risk, and its inclusion of both risk and market adjustments, Jensen’s measure (alpha) tends to be preferred over those of Sharpe and Treynor for assessing portfolio performance.

Investor Facts

Time to Revise Your Portfolio? Over time, you will need to review your portfolio to ensure that it reflects the right risk-return characteristics for your goals and needs. Here are four good reasons to perform this task:

· A major life event—marriage, birth of a child, job loss, illness, loss of a spouse, a child’s finishing college—changes your investment objectives.

· The proportion of one asset increases or decreases substantially.

· You expect to reach a specific goal within two years.

· The percentage in an asset class varies from your original allocation by 10% or more.

Portfolio Revision

In the Hathaway portfolio we have been discussing, one transaction occurred during 2017. The reason for this transaction was that Hathaway believed the Florida Southcoast Banks stock had more return potential than the Dallas National stock. You should periodically analyze your portfolio with one basic question in mind. Does this portfolio continue to meet my needs? In other words, does the portfolio contain those issues that are best suited to your risk-return needs? Investors who systematically study the issues in their portfolios occasionally find a need to sell certain issues and purchase new securities to replace them. This process is commonly called  portfolio revision . As the economy evolves, certain industries and stocks become either less or more attractive as investments, prompting investors to make adjustments to their portfolios.

Given the dynamics of the investment world, periodic reallocation and rebalancing of the portfolio are a necessity. Many circumstances require such changes. For example, as an investor nears retirement, the portfolio’s emphasis normally evolves from a strategy that stresses growth and capital appreciation to one that seeks to preserve capital. Changing a portfolio’s emphasis normally occurs as an evolutionary process rather than an overnight switch. Individual issues in the portfolio often change in risk-return characteristics. As this occurs, you would be wise to eliminate those issues that do not meet your objectives. In addition, the need for diversification is constant. As investments rise or fall in value, their diversification effect may be lessened. Thus, you may need portfolio revision to maintain diversification.

Concepts in Review

Answers available at  http://www.pearsonhighered .com/smart

1. 13.14 What is active portfolio management? Will it result in superior returns? Explain.

2. 13.15 Describe the steps involved in measuring portfolio return. Explain the role of the portfolio’s HPR in this process and explain why one must differentiate between realized and unrealized gains.

3. 13.16 Why is comparing a portfolio’s return to the return on a broad market index generally inadequate? Explain.

4. 13.17 Briefly describe each of the following measures for assessing portfolio performance and explain how they are used.

a. Sharpe’s measure

b. Treynor’s measure

c. Jensen’s measure (Jensen’s alpha)

5. 13.18 Why is Jensen’s measure (alpha) generally preferred over the measures of Sharpe and Treynor for assessing portfolio performance? Explain.

6. 13.19 Explain the role of portfolio revision in the process of managing a portfolio.

Timing Transactions

1. LG 5

2. LG 6

The essence of timing is to “buy low and sell high.” This is the dream of all investors. Although there is no tried-and-true way to achieve such a goal, there are several methods you can use to time purchases and sales. First, there are formula plans, which we discuss next. Investors can also use limit and stop-loss orders as a timing aid. They can follow procedures for warehousing liquidity, and they can also take into consideration other aspects of timing when selling their investments.

Formula Plans

Formula plans  are mechanical methods of portfolio management that try to take advantage of price changes that result from cyclical price movements. Formula plans are not set up to provide unusually high returns. Rather, they are conservative strategies employed by investors who do not wish to bear a high level of risk. We discuss four popular formula plans: dollar-cost averaging, the constant-dollar plan, the constant-ratio plan, and the variable-ratio plan.

Dollar-Cost Averaging

Dollar-cost averaging  is a formula plan in which a fixed dollar amount is invested in a security at fixed time intervals. In this passive buy-and-hold strategy, the periodic dollar investment is held constant. To make the plan work, you must invest on a regular basis. The goal of a dollar-cost averaging program is growth in the value of the security to which the funds are allocated. The price of the investment security will probably fluctuate over time. If the price were to decline, you would purchase more shares per period. Conversely, if the price were to rise, you would purchase fewer shares per period.

Look at the example of dollar-cost averaging in  Table 13.9  . The table shows investment of $500 per month in the Wolverine Mutual Fund, a growth-oriented, no-load mutual fund. Assume that during one year’s time you have placed $6,000 in the mutual fund shares. (Because this is a no-load fund, shares are purchased at net asset value.) You made purchases at NAVs ranging from a low of $24.16 to a high of $30.19. At year-end, the value of your holdings in the fund was slightly less than $6,900. Dollar-cost averaging is a passive strategy; other formula plans are more active.

Constant-Dollar Plan

A  constant-dollar plan  consists of a portfolio that is divided into two parts, speculative and conservative. The speculative portion consists of securities that have high promise of capital gains. The conservative portion consists of low-risk investments such as bonds or a money market account. The target dollar amount for the speculative portion is constant. You establish trigger points (upward or downward movement in the speculative portion) at which funds are removed from or added to that portion. The constant-dollar plan basically skims off profits from the speculative portion of the portfolio if it rises a certain percentage or amount in value and adds these funds to the conservative portion of the portfolio. If the speculative portion of the portfolio declines by a specific percentage or amount, you add funds to it from the conservative portion.

Assume that you have established the constant-dollar plan shown in  Table 13.10  . The beginning $20,000 portfolio consists of $10,000 invested in a high-beta, no-load mutual fund and $10,000 deposited in a money market account. You have decided to rebalance the portfolio every time the speculative portion is worth $2,000 more or $2,000 less than its initial value of $10,000. If the speculative portion of the portfolio

Excel@Investing

Table 13.9 Dollar-Cost Averaging ($500 Per Month, Wolverine Mutual Fund Shares)

Transactions
Month	Net Asset Value (NAV) Month-End	Number of Shares Purchased
January	$26.00	19.23
February	$27.46	18.21
March	$27.02	18.50
April	$24.19	20.67
May	$26.99	18.53
June	$25.63	19.51
July	$24.70	20.24
August	$24.16	20.70
September	$25.27	19.79
October	$26.15	19.12
November	$29.60	16.89
December	$30.19	16.56
Annual Summary
Total investment: $6,000.00
Total number of shares purchased: 227.95
Average cost per share: $26.32
Year-end portfolio value: $6,881.81

equals or exceeds $12,000, you sell sufficient shares of the fund to bring its value down to $10,000 and add the proceeds from the sale to the conservative portion. If the speculative portion declines in value to $8,000 or less, you use funds from the conservative portion to purchase sufficient shares to raise the value of the speculative portion to $10,000.

Two portfolio-rebalancing actions are taken in the time sequence illustrated in  Table 13.10  . Initially, $10,000 was allocated to each portion of the portfolio. When the mutual fund’s net asset value rose to $12, the speculative portion was worth $12,000. At that point, you sold 166.67 shares valued at $2,000 and added the proceeds to the money market account. Later, the mutual fund’s NAV declined to $9.50 per share, causing the value of the speculative portion to drop below $8,000. This change triggered the purchase of sufficient shares to raise the value of the speculative portion to $10,000. Over the long run, if the speculative investment of the constant-dollar plan rises in value, the conservative component of the portfolio will increase in dollar value as profits are transferred into it.

Constant-Ratio Plan

The  constant-ratio plan  is similar to the constant-dollar plan except that it establishes a desired fixed ratio of the speculative portion to the conservative portion of the portfolio. When the actual ratio of the two differs by a predetermined amount from the desired ratio, rebalancing occurs. At that point, you make transactions to bring the actual ratio back to the desired ratio. To use the constant-ratio plan, you must decide on the appropriate apportionment of the portfolio between speculative and conservative investments. You must also choose the ratio trigger point at which transactions occur.

Table 13.10 Constant-Dollar Plan

Mutual Fund NAV	Value of Speculative Portion	Value of Conservative Portion	Total Portfolio Value	Transactions	Number of Shares in Speculative Portion
$10.00	$10,000.00	$10,000.00	$20,000.00		1,000.00
$11.00	$11,000.00	$10,000.00	$21,000.00		1,000.00
$12.00	$12,000.00	$10,000.00	$22,000.00		1,000.00
→ $12.00	$10,000.00	$12,000.00	$22,000.00	Sold 166.67 shares	833.33
$11.00	$ 9,166.63	$12,000.00	$21,166.63		833.33
$ 9.50	$     7,916.64	$12,000.00	$19,916.64		833.33
→ $   9.50	$10,000.00	$ 9,916.64	$19,916.64	Purchased 219.30 shares	1,052.63
$10.00	$10,526.30	$ 9,916.64	$20,442.94		1,052.63

To see how this works, assume that the constant-ratio plan illustrated in  Table 13.11  is yours. The initial portfolio value is $20,000. You have decided to allocate 50% of the portfolio to the speculative, high-beta mutual fund and 50% to a money market account. You will rebalance the portfolio when the ratio of the speculative portion to the conservative portion is greater than or equal to 1.20 or less than or equal to 0.80. A sequence of changes in net asset value is listed in  Table 13.11  . Initially, $10,000 is allocated to each portion of the portfolio. When the fund NAV reaches $12, the 1.20 ratio triggers the sale of 83.33 shares. Then the portfolio is back to its desired 50:50 ratio. Later, the fund NAV declines to $9, lowering the value of the speculative portion to $8,250. The ratio of the speculative portion to the conservative portion is then 0.75, which is below the 0.80 trigger point. You purchase 152.78 shares to bring the desired ratio back up to the 50:50 level.

The long-run expectation under a constant-ratio plan is that the speculative securities will rise in value. When this occurs, you will sell securities to reapportion the

Table 13.11 Constant-Ratio Plan

Mutual Fund NAV	Value of Speculative Portion	Value of Conservative Portion	Total Portfolio Value	Ratio of Speculative Portion to Conservative Portion	Transactions	Number of Shares in Speculative Portion
$10.00	$10,000.00	$10,000.00	$20,000.00	1.000		1,000.00
$     11.00	$11,000.00	$10,000.00	$21,000.00	1.100		1,000.00
$12.00	$12,000.00	$10,000.00	$22,000.00	1.200		1,000.00
→ $12.00	$  11,000.00	$11,000.00	$22,000.00	1.000	Sold 83.33 shares	916.67
$     11.00	$  10,083.00	$11,000.00	$21,083.00	0.917		916.67
$10.00	$   9,166.70	$11,000.00	$20,166.70	0.833		916.67
$             9.00	$   8,250.00	$11,000.00	$19,250.00	0.750		916.67
→ $             9.00	$   9,625.00	$             9,625.00	$19,250.00	1.000	Purchased 152.78 shares	1,069.44
$10.00	$   10,694.40	$              9,625.00	$20,319.40	1.110		1,069.44

portfolio and increase the value of the conservative portion. This philosophy is similar to the constant-dollar plan, except that it uses a ratio as a trigger point.

Variable-Ratio Plan

The  variable-ratio plan  is the most aggressive of these four fairly passive formula plans. It attempts to turn stock market movements to the investor’s advantage by timing the market. That is, it tries to “buy low and sell high.” The ratio of the speculative portion to the total portfolio value varies depending on the movement in value of the speculative securities. When the ratio rises a certain predetermined amount, the amount committed to the speculative portion of the portfolio is reduced. Conversely, if the value of the speculative portion declines so that it drops significantly in proportion to the total portfolio value, the amount committed to the speculative portion of the portfolio is increased.

When implementing the variable-ratio plan, you have several decisions to make. First, you must determine the initial allocation between the speculative and conservative portions of the portfolio. Next, you must choose trigger points to initiate buy or sell activity. These points are a function of the ratio between the value of the speculative portion and the value of the total portfolio. Finally, you must set adjustments in that ratio at each trigger point.

Assume that you use the variable-ratio plan shown in  Table 13.12  . Initially, you divide the portfolio equally between the speculative and the conservative portions. The speculative portion consists of a high-beta (around 2.0) mutual fund. The conservative portion is a money market account. You decide that when the speculative portion reaches 60% of the total portfolio, you will reduce its proportion to 45%. If the speculative portion of the portfolio drops to 40% of the total portfolio, then you will raise its proportion to 55%. The logic behind this strategy is an attempt to time the cyclical movements in the mutual fund’s value. When the fund moves up in value, you take profits, and you increase the proportion invested in the no-risk money market account. When the fund declines markedly in value, you increase the proportion of capital committed to the speculative portion.

A sequence of transactions is depicted in  Table 13.12  . When the fund net asset value climbs to $15, the 60% ratio trigger point is reached, and you sell 250 shares of the fund. You place the proceeds in the money market account, which causes the speculative portion then to represent 45% of the value of the portfolio. Later, the fund NAV declines to $10, causing the speculative portion of the portfolio to drop to 35%. This triggers a portfolio rebalancing, and you purchase 418.75 shares, moving the speculative portion to 55%. When the fund NAV then moves to $12, the total portfolio is

Table 13.12 Variable-Ratio Plan

Mutual Fund NAV	Value of Speculative Portion	Value of Conservative Portion	Total Portfolio Value	Ratio of Speculative Portion to Total Portfolio Value	Transactions	Number of Shares in Speculative Portions
$10.00	$10,000.00	$10,000.00	$20,000.00	0.50		1,000.00
$15.00	$15,000.00	$10,000.00	$25,000.00	0.60		1,000.00
→ $15.00	$ 11,250.00	$13,750.00	$25,000.00	0.45	Sold 250 shares	750.00
$10.00	$                  7,500.00	$13,750.00	$21,250.00	0.35		750.00
→ $10.00	$         11,687.50	$             9,562.50	$21,250.00	0.55	Purchased 418.75 shares	1,168.75
$12.00	$ 14,025.00	$             9,562.50	$ 23,587.50	0.59		1,168.75

worth in excess of $23,500. In comparison, had the initial investment of $20,000 been allocated equally and had no rebalancing been done between the mutual fund and the money market account, the total portfolio value at this time would have been only $22,000 (i.e., $12×1,000=$12,000$12 × 1,000=$12,000 in the speculative portion plus $10,000 in the money market account).

Using Limit and Stop-Loss Orders

Earlier in this text we discussed the market order, the limit order, and the stop-loss order. Here we will see how you can use the limit and stop-loss orders to rebalance a portfolio. These types of security orders, if properly used, can increase return by lowering transaction costs.

Limit Orders

There are many ways investors can use limit orders when they buy or sell securities. For instance, if you have decided to add a stock to the portfolio, a limit order to buy will ensure that you buy only at or below the desired purchase price. A limit good-’til-canceled (GTC) order to buy instructs the broker to buy stock until the entire order is filled. The primary risk in using limit instead of market orders is that the order may not be executed. For example, if you placed a GTC order to buy 100 shares of State Oil of California at $27 per share and the stock never traded at $27 per share or less, the order would never be executed. Thus, you must weigh the need for immediate execution (market order) against the possibility of a better price with a limit order.

Limit orders, of course, can increase your return if they enable you to buy a security at a lower cost or sell it at a higher price. During a typical trading day, a stock’s price will fluctuate up and down over a normal trading range. For example, suppose the common shares of Jama Motor traded 10 times in the following sequence: $36.00, $35.88, $35.75, $35.94, $35.50, $35.63, $35.82, $36.00, $36.13, and $36.00. A market order to sell could have been executed at somewhere between 35.50 (the low) and 36.13 (the high). A limit order to sell at 36.00 would have been executed at 36.00. Thus, $0.50 per share might have been gained by using a limit order.

Stop-Loss Orders

Stop-loss orders can be used to limit the downside loss exposure of an investment. For example, assume you purchase 500 shares of Easy Work at $26.00 and have set a specific goal to sell the stock if it reaches $32.00 or drops to $23.00. To implement this goal, you would enter a GTC stop order to sell with a price limit of $32.00 and another stop order at a price of $23.00. If the issue trades at $23.00 or less, the stop-loss order becomes a market order, and the broker sells the stock at the best price available. Or, if the issue trades at $32.00 or higher, the broker will sell the stock. In the first situation, you are trying to reduce your losses; in the second, you are attempting to protect a profit.

The principal risk in using stop-loss orders is  whipsawing —a situation where a stock temporarily drops in price and then bounces back upward. If Easy Work dropped to $23.00, then $22.57, and then rallied back to $26.00, you would have been sold out at a price between $23.00 and $22.57. For this reason, limit orders, including stop-loss orders, require careful analysis before they are placed. You must consider the stock’s probable fluctuations as well as the need to purchase or sell the stock when choosing among market, limit, and stop-loss orders.

Warehousing Liquidity

Investing in risky stocks or in options or futures offers probable returns in excess of those available with money market deposit accounts or bonds. However, stocks and options and futures are risky investments. One recommendation for an efficient portfolio is to keep a portion of it in a low-risk, highly liquid investment to protect against total loss. The low-risk asset acts as a buffer against possible investment losses. A second reason for maintaining funds in a low-risk asset is the possibility of future opportunities. When opportunity strikes, an investor who has extra cash available will be able to take advantage of the situation. If you have set aside funds in a highly liquid investment, you need not disturb the existing portfolio.

The primary media for warehousing liquidity are money market deposit accounts at financial institutions and money market mutual funds. The money market accounts at savings institutions provide relatively easy access to funds and furnish returns competitive with (but somewhat lower than) money market mutual funds. The products offered by financial institutions are becoming more competitive with those offered by mutual funds and stock brokerage firms.

Watch Your Behavior

Leaving Money on the Table One of the easiest ways to build wealth is to take advantage of a program in which your employer matches contributions you make to a retirement plan such as a 401 (k) account. When your employer matches your contribution, that’s almost like getting an instant 100% rate of return on your investment. It’s true that younger workers face a tax penalty if they withdraw these funds early, but one study found that even investors old enough to withdraw the money at any time often failed to take advantage of the employer match. They were simply leaving money on the table because if they had contributed money to the plan, they could’ve received the employer match and immediately withdrawn those funds.

(Source: James J. Choi, David Laibson, and Brigitte C. Madrian, “$100 Bills on the Sidewalk: Suboptimal Investment in 401(k) Plans,” Review of Economics and Statistics, 2011, Vol. 93, No. 3, pp. 748–763.)

Timing Investment Sales

Knowing when to sell a stock is as important as choosing which stock to buy. You should review your portfolio periodically and consider possible sales and new purchases. Here we discuss two issues relevant to the sale decision: tax consequences and achieving investment goals.

Tax Consequences

Taxes affect nearly all investment actions. All investors can and should understand certain basics. The treatment of capital losses is important: A maximum of $3,000 of losses in excess of capital gains can be written off against other income in any one year. If you have a loss position in an investment and have concluded that it would be wise to sell it, the best time to sell is when you have a capital gain against which you can apply the loss. Clearly, one should carefully consider the tax consequences of investment sales prior to taking action.

Achieving Investment Goals

Every investor would enjoy buying an investment at its lowest price and selling it at its top price. At a more realistic level, you should sell an investment when it no longer meets your needs. In particular, if an investment has become either more or less risky than is desired or if it has not met its return objective, it should be sold. The tax consequences mentioned above help to determine the appropriate time to sell. However, taxes are not the foremost consideration in a sale decision. The dual concepts of risk and return should be the overriding concerns.

Be sure to take the time periodically to examine each investment in light of its return performance and relative risk. You should sell any investment that no longer belongs in the portfolio and should buy investments that are more suitable. Finally, you should not hold out for every nickel of profit. Very often, those who hold out for the top price watch the value of their holdings plummet. If an investment looks ripe to sell, sell it, take the profit, reinvest it in an appropriate asset, and enjoy your good fortune.

Concepts in Review

Answers available at  http://www.pearsonhighered.com/smart

1. 13.20 Explain the role that formula plans can play in the timing of security transactions. Describe the logic underlying the use of these plans.

2. 13.21 Briefly describe each of the following plans and differentiate among them.

a. Dollar-cost averaging

b. Constant-dollar plan

c. Constant-ratio plan

d. Variable-ratio plan

3. 13.22 Describe how a limit order can be used when securities are bought or sold. How can a stop-loss order be used to reduce losses? To protect profit?

4. 13.23 Give two reasons why an investor might want to maintain funds in a low-risk, highly liquid investment.

5. 13.24 Describe the two items an investor should consider before reaching a decision to sell an investment.