Question

Case Problem 13.1 Assessing the Stalchecks’s Portfolio Performance LG3 LG4 Mary and Nick Stalcheck have an investment portfolio containing 4 investments. It was developed to provide them with a balance between current income and capital appreciation. Rather than acquire mutual fund shares or diversify within a given class of investments, they developed their portfolio with the idea of diversifying across various asset classes. The portfolio currently contains common stock, industrial bonds, mutual fund shares, and options. They acquired each of these investments during the past 3 years, and they plan to purchase other investments sometime in the future. Currently, the Stalchecks are interested in measuring the return on their investment and assessing how well they have done relative to the market. They hope that the return earned over the past calendar year is in excess of what they would have earned by investing in a portfolio consisting of the S&P 500 Stock Composite Index. Their research has indicated that the risk-free rate was 7.2% and that the (before-tax) return on the S&P 500 portfolio was 10.1% during the past year. With the aid of a friend, they have been able to estimate the beta of their portfolio, which was 1.20. In their analysis, they have planned to ignore taxes because they feel their earnings have been adequately sheltered. Because they did not make any portfolio transactions during the past year, all of the Stalchecks’s investments have been held more than 12 months, and they would have to consider only unrealized capital gains, if any. To make the necessary calculations, the Stalchecks have gathered the following information on each investment in their portfolio. Common stock. They own 400 shares of KJ Enterprises common stock. KJ is a diversified manufacturer of metal pipe and is known for its unbroken stream of dividends. Over the past few years, it has entered new markets and, as a result, has offered moderate capital appreciation potential. Its share price has risen from $17.25 at the start of the last calendar year to $18.75 at the end of the year. During the year, quarterly cash dividends of $0.20, $0.20, $0.25, and $0.25 were paid. Industrial bonds. The Stalchecks own 8 Cal Industries bonds. The bonds have a $1,000 par value, have a 9.250% coupon, and are due in 2024. They are A-rated by Moody’s. The bonds were quoted at 97.000 at the beginning of the year and ended the calendar year at 96.375%. Mutual fund. The Stalchecks hold 500 shares in the Holt Fund, a balanced, no-load mutual fund. The dividend distributions on the fund during the year consisted of $0.60 in investment income and $0.50 in capital gains. The fund’s NAV at the beginning of the calendar year was $19.45, and it ended the year at $20.02. Options. The Stalchecks own 100 options contracts on the stock of a company they follow. The value of these contracts totaled $26,000 at the beginning of the calendar year. At year-end the total value of the options contracts was $29,000. Questions a.   Calculate the holding period return on a before-tax basis for each of these 4 investments. b.   Assuming that the Stalchecks’s ordinary income is currently being taxed at a combined (federal and state) tax rate of 38% and that they would pay a 15% capital gains tax on dividends and capital gains for holding periods longer than 12 months, determine the after-tax HPR for each of their 4 investments. c.   Recognizing that all gains on the Stalchecks’s investments were unrealized, calculate the before-tax portfolio HPR for their 4-investment portfolio during the past calendar year. Evaluate this return relative to its current income and capital gain components. d.   Use the HPR calculated in question c to compute Jensen’s measure (Jensen’s alpha). Use that measure to analyze the performance of the Stalchecks’s portfolio on a risk-adjusted, market-adjusted basis. Comment on your finding. Is it reasonable to use Jensen’s measure to evaluate a 4-investment portfolio? Why or why not? e.   On the basis of your analysis in questions a, c, and d, what, if any, recommendations might you offer the Stalchecks relative to the revision of their portfolio? Explain your recommendations

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Answer 1

Q.a. Holding period return on a before tax basis

Holding period return = (Total appreciation in value over the year) / (Total value at the start of the year)

For common stock=((18.75-17.25)+.20+.20+.25+.25)/17.25=13.91%
Here, (stock price appreciation + the dividends)/Stock price at the start of the year

For industrial bonds=((1000*(96.375%)-970)+1000*9.250%)/970=8.89%
Here, (year end coupon + Bond price at year end) / Bond price at start of the year

For mutual fund=((20.02-19.45)+0.60+0.50)/19.45 = 8.59%
Here, (Capital gain + dividend distributions) / Value using NAV at start of the year

For options=(29000-26000) / 26000=11.54%
Here, (Appreciation of options contract during the year) / Value of options contract at start of the year

Q.b. After-tax HPR

Here, the only difference is that the tax of 15% is deducted before calculating the holding period return.

For common stock=((18.75-17.25)*(1-(15%)) +(.20+.20+.25+.25)*(1-(15%))) / 17.25 = 11.83%
For industrial bonds = ((1000*(96.375%)-970)*(1-(15%)) + (1,000*(9.25%))*(1-(35%)))/970 = 5.65%
For mutual fund = ((20.02-19.45)*(1-(15%)) + 0.60*(1-(35%))+0.50*(1-(15%)))/19.45 = 6.68%
For options= (29000-26000)*(1-(15%)) / 26000 = 9.81%

Q.c. Before-tax portfolio HPR and evaluating the return relative to its current income and capital gain component

First, we calculate the total value of the portfolio at the beginning
Common stock = 400*17.25=6900
Industrial bonds = 97%*1000*8=7760
Mutual funds = 500*19.45=9725
Options = 26000
Hence, the portfolio value at the beginning = 6900+7760+9725+26000 = 50385

Hence the weight assigned for the common stock = 6900/50385 = 13.69%
Hence the weight assigned for industrial bonds =7760/50385 =15.40%
Hence the weight assigned for Mutual funds =9725/50385 =19.30%
Hence the weight assigned for Options =26000/50385 =51.60%

Before tax portfolio Holding Period Return = (13.91%*13.69%) + (8.89%*15.40%) + (8.59%*19.30%) + (11.54%*51.60%) =12.79%

For calculation of current income return, current income
Of common stock =(0.20+0.20+0.25+0.25)*400=360
Of industrial bonds =1000*9.25%*8 =740
Of mutual fund =0.60*500 =300
Of options = 0

Current income return =(360+740+300)/50385=1400/50385 = 2.78%

For calculation of capital gains income return, capital income
Of common stock = (18.75-17.25)*400=600
Of industrial bonds = (1000*96.375%-970)*8= -50
Of mutual fund = (20.02-19.45)*500=285
Of options = 3000
Capital gains return = (3000 +285+ 600-50)/50385 = 3835 /50385= 7.61%

Hence, the capital gains form a higher portion out of the before-tax total holding period returns of the portfolio

Q.d.
Jensen’s alpha =(Before tax portfolio Holding Period Return)- (Risk-free rate) – (Beta*(Market return S&P500-Risk-free rate))
Jensens alpha = 12.79% - 7.2% - (1.20*(10.1% -7.2%))= 9.07%

The alpha has been generated indicates that the portfolio has been giving better return than the market ( S&P500).
Yes, Jensen’s alpha can be used to evaluate a portfolio since it the overall objective is to achieve a return greater than the market return. However, Jensen’s alpha doesn’t take into account the portfolio volatility into account.

Q.e.
Since the common stock is the one which has the highest HPR, and also carry less weight in the portfolio, its weight can be increases.
Also, the weight for options in the portfolio is the highest, which can be reduced to a certain extent
.