1

276Gitman/JoehnkFundamentals of Investing, Ninth Edition

Chapter 14Managing Your Own Portfolio277

Chapter 14Managing Your Own Portfolio

(Outline

Learning Goals

I.Portfolio Planning in Action

A)Dara Yasakawa: Woman Wonder

B)Bon and Gail Weiss: Lottery Winners

C)Julio and Gina Vitello: Retirees

D)Lucille Hatch: Widow

Concepts in ReviewII.Evaluating The Performance of Individual Investments

A)Obtaining Needed Data

1.Return Data

2.Economic and Market Activity

B)Indexes of Investment Performance

C)Measuring the Performance of Investment Vehicles

1.Stocks and Bonds

a.Stocks

b.Bonds

2.Mutual Funds

3.Options and Futures

D)Comparing Performance to Investment Goals

1.Balancing Risk and Return

2.Isolating Problem Investments

Concepts in Review

III.Assessing Portfolio PerformanceA)Measuring Portfolio Return

1.Measuring the Amount Invested

2.Measuring Income

3.Measuring Capital Gains

4.Measuring the Portfolios Holding Period Return

B)Comparison of Return with Overall Market Measures

1.Sharpes Measure

2.Treynors Measure

3.Jensens Measure (Jensens Alpha)

C)Portfolio Revision

Concepts in Review

IV.Timing TransactionsA)Formula Plans

1.Dollar Cost Averaging

2.Constant-Dollar Plan

3.Constant-Ratio Plan

4.Variable-Ratio Plan

B)Using Limit and Stop-Loss Orders

1.Limit Orders

2.Stop-Loss Orders

C)Warehousing Liquidity

D)Timing Investment Sales

1.Tax Consequences

2.Achieving Investment Goals

Concepts in ReviewSummary

Putting Your Investment Know-How to the Test

Discussion Questions

Problems

Case Problems

14.1.Assessing the Stalchecks Portfolio Performance

14.2.Evaluating Formula Plans: Charles Spurges Approach

Excel with Spreadsheets

Trading Online with OTIS

(Key Concepts

1.The relationship between investor objectives and the risk-return profiles reflected in various types of portfolios.

2.Obtaining needed data, indexes of investment performance, and techniques for measuring the performance of investment vehicles.

3.The methods used to compare investment performance to investment goals.

4.The techniques used to measure the amount invested, current income, capital gains, and total portfolio return relative to the amount of money actually invested in the portfolio.

5.Statistical measures of portfolio returnSharpes, Treynors, and Jensens measuresand their uses, and the importance of portfolio revision.

6.The role of common types of formula plans in timing purchase and sale decisions.

7.The use of limit and stop-loss orders in investment timing, the warehousing of liquidity, and the key factors in timing investment sales in order to achieve maximum benefits.

(Overview

This chapter describes how investment portfolios are monitored, including procedures for evaluating investment performance and timing portfolio transactions.

1.The chapter begins with four model portfolios that demonstrate portfolio management in action. The asset allocation of each investor, along with a close look at their securities portfolios risk-return characteristics, is presented in light of his or her investment objectives

2.The evaluation of an individual investments performance is discussed. Such performance may be measured by comparing an investments return against a standard. Two such standards might involve comparing actual with anticipated returns, or comparing an actual return against the return of another vehicle of a similar type. The text stresses the need for a broad range of data to assess performance accurately.

3.Investment performance also may be measured by computing and comparing holding period returns (HPR) before and after tax. The instructor might work out HPRs for different investment vehicles such as stocks, bonds, mutual funds, or real estate. It should be emphasized that the comparison of HPRs must be accompanied by the consideration of the associated risk. Riskier investments should provide higher returns than low-risk investments to compensate for the greater risk involved.

4.Next, the assessment of portfolio performance is considered. The instructor should discuss procedures for computing the amount invested, income, and capital gains of a portfolio. Applying risk-adjusted, market-adjusted rate of return measuresSharpes, Treynors and Jensens measuresallows the investor to compare the base portfolio return figure to a risk-adjusted, market-adjusted rate of return. Depending upon its performance, an investor may want to revise or rebalance a portfolio in order to better attain his or her investment goals.

5.The final section of the chapter discusses the timing of portfolio transactions. The instructor may want to indicate that, even though buying low and selling high is theoretically a good strategy, it is often difficult for an investor to determine when the price is too high or too low. A price may dip lower or rise higher in one day, and the investor has no way of anticipating such a change until it happens.

6.Techniques investors use to time buy and sell decisions are formula plans, including dollar cost averaging, constant-dollar plans, and constant- or variable-ratio plans, and limit and stop-loss orders. Also emphasized are the role of liquidity in the portfolio and the importance of tax considerations when timing investment sales.

(Answers to Concepts in Review

1.It is generally recognized that given favorable levels of income a younger investor would seek growth-oriented, longer-term, capital-gains investments. As an investor ages, more secure investment returns are sought. Finally, at retirement the investor will want secure income-producing investments.

(a)The retired investor would probably hold secure, income-producing securities with low risk.

(b)The high-income, financially secure investor would hold a diversified, growth-oriented group of securities providing capital gains and favorable tax treatment.

(c)A young investor with a secure job and no dependents would probably hold a combination of diversified income-producing securities and would depend on the investors tax bracket and need for additional current income. If the investor needs little or no additional current income, the securities would be primarily growth-oriented offering expected capital gains.

2.It is important for an investor to continuously manage and control his or her portfolio to be sure that investment goals are being met. Over time, the securities in the portfolio may change their investment characteristics, thereby changing the character of the portfolio. If the portfolio performance is inconsistent with its goals, it should be adjusted and revised to remain consistent with the investors needs. The management and control process involves assessing actual performance, comparing it to planned performance, revising and making needed adjustments, and timing these adjustments to achieve maximum benefit.

3.Current market information, such as share price, dividend yield, and similar return data, are critical to performance evaluation. Regularly checking this data, as well as following a companys earnings, dividend payments, and general news, provides a way to monitor stock performance and decide whether the investment should be held. Changes in economic and market activity can affect the level of current income and the market value of each investment vehicle differently. For some investment vehicles, such as real estate, local economic activity is most important. Bonds may be most affected by nationwide economic conditions. Gold is most affected by international economic and political conditions. Sources of economic information include large regional banks, New York City banks, The Federal Reserve Banks, and investment services. All investments are affected by nondiversifiable risk which is tied to changes in market activity.

4.In evaluating the performance of his or her portfolio, an investor should compare it to some measure of general market returns. For stocks, one could use the Dow Jones Industrial Average. However, it is actually not considered the most appropriate gauge of stock price movement. Including only thirty stocks, it is not broad based. A better index is the Standard and Poors 500 Stock Composite Index or the New York Stock Exchange Composite Index. For bonds, the Dow Jones Corporate Bond Average or data from Standard & Poors, Mergent, and/or the Federal Reserve are appropriate. Real estate returns are more localized. Therefore, in real estate markets one would analyze local returns. This information may be available at local real estate boards and/or agencies. The investor should probably distinguish between income property and undeveloped property.

5.A bond market indicator is information and/or an index which reflects the general behavior of the bond markets. Where stock indexes are presented relative to an original base, bond indexes are stated relative to the bonds par, or face value, or as the yield to maturity. The Dow Jones Corporate Bond Index is a popular measure of bond price behavior. It is based on the closing prices of 32 industrial, 32 financial, and 32 utility/telecom bonds. This average is published daily in The Wall Street Journaland weekly in Barrons and reflects the mathematical average of the closing prices of these bonds. Bond yield data may also be obtained from Standard & Poors, Mergent, Yahoo.com, and the Federal Reserve, and is also published in The Wall Street Journal and Barrons.

6.The dividend yield measures the current yearly dividend return earned from a stock investment. It is calculated by dividing the stocks yearly cash dividend by its price. The holding period return (HPR), on the other hand, measures the total return (income plus change in value) earned on an investment over a given investment period. The change in value (capital gain or loss) need not be realized to be considered in HPR. The dividend yield and the HPR are not equivalent. They are equal only when the price of the stock is the same at the end of the period as it was at the beginning of the period.

7.Mutual funds pay investment income dividends and capital gains dividends. Income dividends are derived from the interest and dividends received by the fund, while capital gains dividends are a result of gains net of losses realized by the fund on its security purchase and sale transactions. These dividends are not the only source of return on a mutual fund investment; the other source of return is a change in the value of the mutual fund which is attributable to unrealized gains that exist in the portfolio.

8.An investment holding is a candidate for sale when:

(1)It fails to perform as expected and no major change in performance is anticipated.(2)It has met the original investment objective.(3)The investor now has better investment opportunities available for the funds.

A risky investment must provide a higher return than a low-risk investment to attract a rational investor, who must be compensated for taking the additional risk.9.A problem investment is one that has not lived up to expectations. Either the investment has experienced a loss, or has provided an actual return less than the investor expected.

When analyzing an investment, the investor should first ask: Has the investment performed reasonably in light of initial expectations? The second question is: Would the investment be included in the portfolio today if it were not already there? If the answer to both questions is no for a specific investment, it should probably be sold. A negative answer to one of the questions indicates that the investment is a problem investment and should be watched closely.

10.Active portfolio management is the process of building a portfolio using traditional and modern portfolio approaches and then managing and controlling it to meet investment objectives. Active management should improve the returns earned on the portfolio. This contradicts the efficient market hypothesis, which states that markets are so efficient that available information about a company and/or its securities is always fully reflected in the securitys price. If this were true, investors could not expect to consistently outperform the market by managing their portfolios.

11.Portfolio performance is measured by calculating the holding period return (HPR) for the portfolio. This involves (1) measuring the amount invested, (2) measuring income, (3) measuring capital gain, and (4) combining these components to find the portfolios HPR.

The HPR formula includes both realized returns (income plus realized capital gains) and the unrealized capital gains of the portfolio. Further, portfolio additions and deletions must be time-weighted for the number of months they are in the portfolio. Unrealized capital gains are those that have not yet been received. Realized capital gains, on the other hand, are the capital gains an investor has received from sale of particular securities. An unrealized capital gain can become a capital loss when economic conditions change drastically.

12.Once the HPR for the portfolio is calculated, the return figure should be utilized in a risk-adjusted, market-adjusted rate of return analysis. This type of comparative study can be very useful because it provides the investor with insight into how his or her portfolio is performing relative to the stock market as a whole. Comparing the return to a broad market index does not take risk into account.

13.(a)Sharpes measure compares a portfolios risk premium to its standard deviation of return to assess the risk premium per unit of total risk. The formula is:

Sharpes measure (SM)

Once calculated, Sharpes measure can be compared to the Sharpes measures of other portfolios or the market. If the portfolios SM is higher, it is performing better than the other portfolio or the market.

(b)Treynors measure also measures the risk premium per risk unit but uses beta rather than the standard deviation to do so. It focuses on nondiversifiable risk only and is calculated as follows:

Treynors measure (TM)

Using the TM, an investor can compare her or his portfolio to the market or to another portfolio. A higher TM indicates better performance.

(c)Jensens measure, also called alpha, uses portfolio beta and the capital asset pricing model (CAPM) to calculate the excess returnthe difference between the actual return and the required return. The excess return may be positive, negative, or zero and is calculated as follows:

Jensens measure (Total portfolio return Risk-free rate) [Portfolio beta

(alpha)(Market return Risk-free rate)]

JM (rp RF) [bp (rm RF)]

Positive JM values indicate the portfolio earned more than its risk-adjusted, market-adjusted required rate of return; a JM of zero means the portfolio earned its required return; negative values mean the portfolio fell short of its required return.

14.Jensens measure is similar to Treynors measure; both focus only on nondiversifiable risk by using beta. Jensens measure is preferred because it automatically adjusts for market return through its use of the CAPM. This eliminates the need to compute a measure for the market; no further comparison is necessary. As with the other two measures, the higher the JM value, the better the portfolio is performing.

15.When an investor decides to change the composition of a portfolio by selling some securities and replacing them with others, he or she is engaging in portfolio revision. Periodically, the investor must check to see if the portfolio continues to meet his or her needs. Such dynamic portfolio management requires portfolio revision.

As economic conditions and individual priorities change, an investor must revise the portfolio by reallocating and rebalancing it. As the risk-return characteristics of the securities change, the investor should eliminate issues that no longer meet his or her objectives. Also, portfolio revision may be needed to maintain an adequate amount of diversification. All these situations require managing, controlling, and possibly revising the portfolio.

16.Formula plans are mechanical methods of portfolio management that try to take advantage of price changes in securities that result from cyclical price movements. Formula plans, part of a conservative strategy, are designed primarily for investors who do not wish to take excessive risk but wish to quickly and favorably adjust their portfolio in response to cyclical security price changes.

17.(a)The dollar cost averaging plan involves investing a fixed dollar amount in a security at fixed time intervals. This is a passive buy-and-hold strategy in which a periodic dollar investment is held constant. If the share price increases, fewer shares are purchased. When the share price declines, more shares are purchased. The hoped-for outcome is growth in the value of the selected security.

(b)A constant-dollar plan uses a two-part portfolio. The speculative portion is invested in securities having high promise of capital gain. The conservative portion consists of low-risk investments such as bonds or money market accounts. If the speculative portion of the portfolio rises a certain percentage or amount in value, the constant dollar plan uses its profits to increase the conservative portion. If the speculative portion declines in value by a specified percentage or amount, funds are transferred to it from the conservative portion.

(c)The constant-ratio plan establishes a desired fixed ratio of the speculative to the conservative portion of the portfolio. An individual rebalances the portfolio whenever the actual ratio differs from the desired ratio by a predetermined amount. With this plan, an investor must decide what is the appropriate target ratio of the two portions of the portfolio and how far from the target ratio the actual ratio should be permitted to stray before one rebalances the portfolio. Since one expects the speculative portion of the portfolio to increase in value more rapidly than the conservative portion, this strategy should function much like the constant-dollar plan.

(d)The variable-ratio plan is a more aggressive strategy. The target ratio between the speculative portion and the conservative portion of the portfolio is varied by the investor and depends on the expected movement in value of the speculative securities. If the investor feels the market movement will be generally upward, he or she increases the proportion in speculative vehicles. If the feeling is bearisha downward marketthe proportion in conservative vehicles is increased. This strategy is not only the most aggressive but also requires more effort by the investor.

18.A limit order can be used to specify the investors minimum sell price or the maximum price the investor will pay to buy the security. The stop-loss order is a type of suspended order that requests the broker to sell a security at the best available price only if it trades at a specific price or lower. A stop-loss order is a particular kind of a limit order that becomes a market order to sell if a stock trades at the trigger price or lower.

If an investor issues a stop-limit order to sell a security with a limit price above the initial purchase price, the investor locks-in or protects the profit she has earned. If the investor issues a stop-limit order to sell a security with a limit price below the initial purchase price, the investor effectively puts a floor on potential losses.

19.The first reason investors should maintain some funds in a low-risk, highly liquid investment is simply to protect against the chance of a total loss. Thus, a low-risk investment acts as a buffer against possible investment adversity.

Second, highly liquid investments can provide funds for use in pursuing future opportunities. A sudden change in economic conditions might make it conducive for an investor to invest more heavily invest in the stock market. In such situations, a highly marketable investment can readily be converted into cash and the proceeds invested in the stock market. An investor with liquid funds can take advantage of these opportunities without disturbing the existing portfolio.

20.The two considerations in timing investment sales are tax consequences and compatibility with investment goals. When there is a capital loss, the investor receives the benefit of a tax deduction. In particular, capital losses provide tax benefits by offsetting capital gains and thereby lowering the investors tax liability. From the point of view of investment goals, a security should be sold if it no longer meets the needs of the portfolios owner. For example, if a particular security increases the risk of the portfolio to an extent that it is undesirable, that security should be sold in the marketplace. Although taxes are important, one should not forget that the dual concepts of risk and return remain the overriding concerns in the portfolio management and administration process.

(Suggested Answers to Investing in Action Questions

Taming the Portfolio Monster (p. 596)

Describe a system for keeping track of portfolio record.

Answer:

The article suggests the following approach to having an organized system. The first would be to organize the paperwork by each brokerage firm and mutual fund. Next list all of your assets categorized by asset categories. Across the top, make columns for cash, domestic bonds, international bonds, domestic stocks and so on. Use rows for the source such as ABC mutual fund and brokerage firm. Add up all of your assets by category, and calculate the percentage of your portfolio for each asset category.

Having an organized system of the portfolio composition would help an investor to make a informed investment decision that fits into his overall investment strategy. The organized records would also provide information on securities sold during the year and would be a major benefit during tax filings.(Suggested Answers to Ethics in Investing Questions

Retirement at Enron (p. 601)

Should Congress require diversification?

Answer:

Investors should be educated to the benefits of portfolio diversification rather than legally prohibited from investing all their money in a single companys stock should they decide to do so. The diversification requirement would have prevented employees of companies such as Microsoft, Intel, Wal-Mart, or Southwest Airlines from reaping huge rewards by putting their retirement money in a company stock. Those who did so were handsomely rewarded by obtaining annualized returns several times higher than diversified portfolios such as S&P 500 over the same period of time.

(Suggested Answers to Discussion Questions

Since the nature of the discussion questions are entirely dependent on what choices students make, answers will vary for each question.

(Solutions to Problems

1.Investor A would more likely be the retired couple because they would want to have low risk. Investor Bs portfolio is much riskier, with a portfolio beta of 1.66 vs. 1.24 for Investor As portfolio.

2.Portfolio A is more likely to be owned by the retired couple. They would be looking for low risk and steady income. Portfolio B pays little or no dividends, but has high capital gains. This is more likely to be owned by someone who does not need current income and can afford to take significant risk.

3.Capital gain $2,500 $1,762 $738

4.

ACostBProceedsB AProfitTradingCostProfitAfter Costs

$2,000.00$9,500.00$7,500.00$20.00$7,480.00

HPR $7,480/$2,000374%

Annualized (12/6)748%

5.HPR (before-tax)

14.98% (13-month holding period)

Tax Calculations

1.Interest$2,000

2.After tax (1 0.31) $1,380

3.Capital gain 1,746

4.After tax (1 0.15) $1,484

5.After-tax income [(2) (4)] $2,864

Therefore, HPR (after-tax)

*For a 13-month holding period.

6.Since the investment was held for over a year, the long-term capital gains rate is appropriate. Under the new law, the rate on dividends and capital gains for an individual in the 33 percent tax bracket would be the same (e.g., 15%). The equation that could be used for all tax brackets is:

Dividend Income (1 dividend tax rate)

Capital Gains distribution (1 capital gain tax rate)

Change in value (1 capital gains tax rate)

Purchase Price

Incorporating the values from the Charlotte Smidts situation we get:

[(0.32 (1 0.15)) (0.38 (1 0.15)) (0.15 (1 0.15))]/8.60

[0.272 0.323 0.128]/8.60 0.723/$8.60 8.41%

7.HPR (pretax)

8.Interest 0.12 ( $100,000 $12,000. Tax 0.25 ( $12,000 $3,000. After tax return $12,000 $3,000 $9,000. $9,000/$100,000 9% after tax return.

9.Value at 1/1/05$264,000

Value at 12/31/05 ($250,000 26,300) 276,300Unrealized capital gain $12,300

HPRp Dividends andInterest ReceivedRealizedCapital GainUnrealizedCapital Gain (Loss)

Initial EquityInvestment+(New(# mos. in port)funds12(w/drawn(# mos. not in port.) funds12

10.Sharpes measure (11.0 6.0)/18 2.78. Your portfolio outperformed the market, but not on a risk/reward basis. Your risk premium was lower relative to your risk taken than the market. This can be seen by the higher Sharpes Measure for the market than for your portfolio.

11.(a)Sharpes measure (SM)

(b)Hector Smiths portfolio, with a SM of 0.43, performed better than Niki Malones, whose SM was 0.397. Hector received more risk premium per unit of risk than Niki.

(c)SMmarket

(d)Based on the SMs, Nikis portfolio performed better than the market (0.397 versus 0.298 for the market).

12.Treynors Measure for the portfolio (12.0 6.0)/1.3 4.62.

Treynors Measure for the market (10.0 6.0)/1 4.0.

Congratulations, your portfolio outperformed the markets risk/return ratio!

13.(a)Treynors measure (TM)

(b)Annas portfolio outperformed Stacys, with a TM of 1.44 versus one of 1.25.

(c)TMmarket

(d)The market outperformed Annas portfolio; its TM was 1.9, compared to 1.44 for her portfolio.

14.Jensens Measure (13.0 6.0) [1.5 (10.0 6.0)] 7 (1.5 ( 4.0) 7 6 1.

The portfolio earned an excess return over the risk-adjusted required rate of return of 1%.

15.(a)Jensens measure( JM) (Total portfolio return Risk-free rate)

Portfolio beta ( (Market return Risk-free rate)]

(rp RF) [bp (rm RF)]

(12.9 7.8) [1.3 (11 7.8)]

5.1 (1.3 3.2) 5.1 4.16 0.94

(b)Chees portfolio, with a JM of .94, outperformed Carris portfolio, with a JM of 0.24. A positive JM indicates that the actual return exceeds the required return. The negative r return on Carris portfolio means that it did not earn its required return.

(c)Based on its positive JM, Chees portfolio has performed better than the market.

16.

MeasureFio FamilyMarket

(a)SM

0.348 0.323

The Fio familys portfolio, with a higher SM, outperformed the market.

(b)TM

4.27 3.10

The Fio familys portfolio, with a higher TM, outperformed the market.

(c)JM (rp RF) (12.8 8.1) N/A

[bp ( (rm RF)] [1.1 ( (11.2 8.1)]

4.7 3.41 1.29

The positive JM (alpha) of 1.29 indicates that the actual return on this portfolio exceeded the required return; it outperformed the market.

(d)Based on all the above measures, the FIO familys portfolio performed better than the market.

17.(a)24 months $300 $7,200 total investment

(b)To find the number of shares purchased each month, divide $300 by the share price:

Number of Shares

MonthYear 1Year 2

January25.826.4

February26.125.5

March26.125.0

April27.325.0

May25.524.7

June25.024.0

July24.223.5

August24.023.1

September24.522.6

October24.023.1

November25.322.4

December26.122.2

Annual Total303.9287.5

591.4 shares

(c)Average cost per share per share(d)Value at end of year 2 591.4 $13.5 $7,983.90

18.Without any action, the speculative portfolio is now worth $25,000 and the MM fund is worth $21,000. The difference is more than the trigger, so the portfolios should be rebalanced. There is $4,000 more in the speculative, so you should move half of that to the MM fund, or $2,000. $2,000/$25 80. Sell 80 shares and purchase 95 shares of the MM fund.

19.You should take no action because the trigger has not been hit.

$25,000/$21,000 1.19.

20.The speculative portion now represents 61% of the total, which triggers the re-balance. The total value is now ($30 ( 1,000) ($19 ( 1,000) $49,000. You want 45% of this to be in speculative, or (0.45 ( $49,000) $22,050. $22,050/$30 735 shares, so you should sell 265 (1,000 735) shares of stock. Then take the proceeds ($7,950 265 ( 30) and purchase 418 shares of the MM fund ($7,950/19). The resulting portfolio is as follows:

Time PeriodStock PriceSharesMM MutualFund NAVSharesStock ValueMM Value

2$30.00735$19.001418$22,050.00$26,942.00

The total value is now $48,992, and the speculative portfolio is 45% of the total.

(Solutions to Case Problems

Case14.1Assessing the Stalchecks Portfolio Performance

This case gives the student an opportunity to compute the holding period return (HPR) for several investment vehicles. The student must recognize that the risk of a particular investment will affect the assessment of its actual performance. To this end, the student is required to use Jensens measure (alpha), which uses portfolio beta to measure risk and the CAPM to adjust for market return, and then draw conclusions.

(a)Before-tax HPRs

HPR for common stock: HPRt

HPR

13.91% for a 1-year holding period

HPR for industrial bonds: HPR

HPR

HPR for mutual fund:

HPR 8.59% for a 1-year holding period

HPR for options:

HPR: 11.54% for a 1-year holding period

(b)After-tax HPRs:

Stock (400 shares): (Reduced rate on dividends)

[400($0.90) (0.85) 400(18.75 17.25)(1 0.38)]/($17.25 ( 400) ($306 $372)/$6,900 $678/$6,900 9.83%

Industrial bonds (8 bonds)

After-tax HPR 8.89% (1 0.38) 5.51% for 1-year holding period

Mutual fund (500 shares):

(Reduced rate on dividend and capital gain distributions)

[500($0.60 $0.50) ( 0.85) 500(20.02 19.45)(1 0.38)]/($19.45 ( 500) ($467.50 $285)/$9,725 $752.50/$9,725 9.67%

Options:

After-tax HPR 11.54% (1 0.38) 7.15% for 1-year holding period

(c)Total investment ($17.25 400) ($970 8) ($19.45 500) $26,000

$6,900 $7,760 9725 26,000 $50,385

$50,385

Total current income ($0.90 400) ($92.50 8) ($1.10 500) $0

360 740 550

$1,650

Total capital gain ($1.50 400) ($6.25 8) ($0.57 500) $3,000

$3,835

HPR (portfolio)

(d)JM (rp RF) [bp (rm RF)]

(10.89 7.20) [1.2 (10.10 7.20)]

3.69 (1.20 2.90) 3.69 3.48 0.21

Using Jensens measure, the actual portfolio return is better than the required return because it is positive. It is reasonable to use this measure, which uses the portfolios beta, to evaluate a four-vehicle portfolio.

(e)This question should lead to discussionit has no pat answer. In general, the portfolio is balanced between current income and growth. The ratio of current income to capital gain is 43 ($1,650/$3,835); one might wish to discuss whether or not this is satisfactory. The returns on each of the investment vehicles appear acceptable; the ones that might require investigation are the bonds and the mutual fund. They have lower before-tax returns than the S&P 500 Stock Composite Index, but they may be somewhat less risky. Probably, the most obvious recommendation is to monitor the portfolio rather than change it at this time.

Case14.2Evaluating Formula Plans: Charles Spruges Approach

This case allows students to use a simplified portfolio to evaluate the four formula plans presented in the text. For ease in computation and discussion, we have assumed that fractional shares can be purchased. Instructors may wish to revise the numbers to eliminate fractional shares.

(a)Price Per Share

End of Period

PeriodConCamFleck

122 1/8 22 1/82

222 7/824 1/2

322 7/825 3/8

4 2228 1/2

522 1/421 7/8

622 1/819 1/4

7 2221 1/2

822 1/423 5/8

1.

Number of Shares Purchased

ConCamFleck

11.3011.30

11.4310.20

11.439.85

11.368.77

11.2411.43

11.3012.99

11.3611.63

11.2410.58

90.6686.75

Note: Remember ConCam is the conservative stock and Fleck is the speculative stock.

2.Total investment: $500 8 $4,000

Average cost per share:ConCam $2,000/90.66 $22.06

Fleck $2,000/86.75 $23.05

3.

Year-end Value

Conservative stock (ConCam)$22 1/4 ( 90.66 $2,017.19

Speculative stock (Fleck)$23 5/8 ( 86.75 2,049.47

Total portfolio

$4,066.66

Percent of Initial Investment

(1)Conservative stock (ConCam)$2,017.19/$2,000.00 100.86%

(2)Speculative stock (Fleck)$2,049.47/$2,000 102.47%

(3)Total portfolio$4,066.66/$4,000.00 101.67%

(b)Constant Dollar Plan: Return speculative value (Fleck) to $2,000 when trigger points are reached.

Price ofSpeculativeStockPrice ofConservativeStockValue ofSpeculativeStockValue ofConservative StockTotalValue

TransactionsShares inSpeculativeShares inConservative

FleckConCamFleckConCam

1.22.12522.125$2,000.00$2,000.00$4,000.0090.4090.40

2.24.50021.8752,214.801,977.504,192.30{Sold 11.5890.4090.40

3.25.37521.8752,293.90*1,977.504,271.40speculative90.4090.40

3a.25.37521.8752,000.002,271.404,271.40shares}78.82103.84

4.28.50022.0002,246.092,284.484,530.5778.82103.84

5.21.87522.251,723.97*2,310.444,034.41{Bought 12.8278.82103.84

5a.21.87522.252,000.002,034.324,034.32speculative91.4391.43

6.19.25022.1251,760.0312,022.893,782.92shares}91.4391.43

7.21.50022.0001,965.752,011.463,977.2191.4391.43

8.23.62522.252,160.032,034.324,194.3591.4391.43

*Trigger points (when value of speculative portion falls below $1,740 or goes above $2,260).

Year-end Value Percent of Initial Investment

Conservative stock (ConCam)$221/4 1/4 91.43 $2,034.32$2,034.32 ( $2,000.00 101.72%

Speculative stock (Fleck)$23 5/8 91.43 $2,160.03$2,034.32 ( $2,000.00 108.00%

Total portfolio$4,194.35$4,194.35 ( $4,000.00 104.86%

(c)Constant Ratio Plan: Rebalance to value of speculative portion equal to value of conservative portion when ratio hits trigger point.

Period

Price ofSpeculativeStock

Price ofConservativeStock

Value ofSpeculativeStock

Value ofConservativeStock

TotalValueRatio ofSpeculativeStock toConservativeStock

Transactions

Shares inSpeculative

Shares inConservative

1.22.12522.125$2,000.00$2,000.00$4,000.001.0090.4090.40

2.24.5021.8752,214.801,977.504,192.301.12{Sold 6.2390.4090.40

3.25.37521.8752,293.90*1,977.504,271.401.16* speculative90.4090.40

3a.25.37521.8752,135.812,135.814,271.621.0shares}84.1797.63

4.28.50222,398.852,398.854,546.711.1284.1797.63

5.21.87522.251,841.222,172.274,013.490.85{Bought 14.0284.1797.63

6.19.2522.1251,620.27*2,160.063,780.330.75*speculative}84.1797.63

6a.19.2522.1251,890.181,890.183,780.361.00shares98.0985.43

7.21.50222,108.941,879.463,988.401.12{Sold 8.8298.0985.43

8.23.62522.252,317.381,900.824,218.201.22* speculative98.0985.43

8a.23.62522.252,109.102,109.104,218.201.00shares}89.2794.79

*Trigger points (when ratio of the value of speculative portfolio to value of conservative portfolio falls below 0.84 or exceeds 1.15)

Note: Numbers may not add exactly due to rounding.

Year-end Value Percent of Initial Investment

Conservative stock (ConCam)$22 1/4 94.79 $2,109.10$2,109.10 ( $2,000.00 105.46%

Speculative stock (Fleck)$23 5/8 89.27 $2,109.10$2,109.10 ( $2,000.00 105.46%

Total portfolio$4,218.20$4,218.20 ( $4,000.00 105.46%

(d)Variable Ratio Plan: Rebalance speculative portion to 46% of the total portfolio value each time the upper trigger point is reached; rebalance speculative portion to 50% each time the lower trigger point is reached.

PeriodPrice ofSpeculativeStockPrice ofConservativeStockValue ofSpeculativeStockValue ofConservativeStockTotalPortfolioValue

Ratio

TransactionsShares inSpeculativeShares inConservative

1.22.12522.125$2,000.00$2,000.00$4,000.000.5090.4090.40

2.24.50021.8752,214.801,977.504,192.300.53{Sold 16.7290.4090.40

3.25.37521.8752,293.901,977.504,271.400.54speculative90.4090.40

4.28.50022.0002,576.401,988.804,656.200.56*shares}90.4090.40

4a.28.50022.0002,099.992,415.214,564.200.4673.68112.06

5.21.87522.2501,611.752,493.344,105.090.39{Bought 29.4373.68112.06

6.19.25022.1251,418.342,479.333,897.670.36*speculative}73.68112.06

6a.19.25022.1251,948.841,948.833,897.670.50shares103.1188.08

7.21.50022.0002,216.871,937.764,164.630.53{Sold 17.52103.1188.08

8.23.62522.2502,435.971,959.784,395.750.55*speculative103.1188.08

8a.23.62522.2502,022.052,373.704,395.750.46shares}85.59106.68

*Trigger points (when ratio of the value of speculative portfolio to the total portfolio value either exceeds 54%, the upper trigger point, or falls below 38%, the lower trigger point.

Year-end Value Percent of Initial Investment

Conservative stock (ConCam)$22 1/4 106.68 $2,373.70$2,373.70 ( $2,000.00 118.69%

Speculative stock (Fleck)$23 5/8 85.59 $2,022.05$2,022.05 ( $2,000.00 101.10%

Total portfolio$4,395.75$4,395.75 ( $4,000.00 109.89%

(e)Formula Plan

Dollar CostAveragingConstantDollarConstantRatioVariableRatio

Year-end portfolio value as a percentage of $4,000 invested

101.67%

104.86%

105.46%

109.89%

Number of transactions to rebalance portfolio0233

In this illustration, the formula plans have performed much the way one would expect. The most passive and lowest-risk plandollar cost averaginghas the lowest year-end value as a percentage of the $4,000 investment. It also requires the least rebalancing transactions. Therefore, both its transactions and information costs are zero.

The other three plans show increasing year-end values as one moves from the one with the lowest activity and riskthe constant dollar planto highest activity and riskthe variable ratio plan. While the low-risk constant-dollar plan requires two rebalancing transactions, the higher-risk constant ratio and variable ratio plans require three rebalancing transactions. The variable ratio plan, which has a year-end value nearly 10 percent above the amount invested, is clearly superior. However, one must recognize that the variable ratio plan is clearly the most risky alternative. Charles may have decisions to make. Clearly, given the share price data provided and Charles trigger points, the variable ratio plan would have proved most beneficial to him during the past year. It may be interesting to speculate about the results if price actions had been different. The instructor may wish to pursue this line of inquiry to gain a further understanding of formula plans.

(Outside Project

Chapter 14Assessing Mutual Fund Performance

When risk-adjusted, market-adjusted rate of returns such as Jensens measure are not easy to calculate, other comparisons need to be made. For instance, it is generally difficult to find the beta values of various mutual funds; therefore Jensens measure is not a useful measure. Instead, performance can be evaluated by comparing the HPRs of similar funds that are assumed to have similar risk characteristics. This project asks you to do just that.

Use The Wall Street Journal, Barrons, or some other source to obtain thorough, readable information on mutual funds. Obtain this information dated one year earlier and select five similar funds managed by different fund management companies. Calculate the holding period return (HPR) for each fund over the period from a year ago to the present. Barrons and other sources provide the dividend and capital gains distributions for the period. If investment performance is considerably different among the funds, you may want to further investigate their managements through such sources as Weisenberger Investment Companies, which should be available in your public or university library. Try to assess the risk and return behaviors of these funds and use these comparisons to explain any differences you found in their HPRs

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