Mary and Nick Stalcheck have an investment portfolio containing four vehicles. I

Question

Mary and Nick Stalcheck have an investment portfolio containing four vehicles. 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 investment vehicle, they developed their portfolio with the idea of diversifying across various types of vehicles. The portfolio currently contains common stock, industrial bonds, mutual fund shares, and options. They acquired each of these vehicles during the past three years, and they plan to invest in other vehicles 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 stocks 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 planned to ignore taxes, because they feel their earning have been adequately sheltered. Because they did not make any portfolio transactions during the past year all of the Stalcheck

Explanation / Answer

NOTE: I assumed that the 97,000 quote in industrial bonds really means 97%.

Question A
Common stock = [(18.75-17.25)+.20+.20+.25+.25]/17.25 = 13.91%
Industrial bonds = [(1000*96.375%-970)+1,000*9.25%]/970=8.89%
Mutual fund = [(20.02-19.45)+0.60+0.50]/19.45 = 8.59%
Options=(29000-26000)/26000=11.54%

Question B
NOTE:
Common stock = [(18.75-17.25)*(1-15%)+(.20+.20+.25+.25)*(1-15%)]/17.25 = 11.83%
Industrial bonds = [(1000*96.375%-970)*(1-15%)+(1,000*9.25%)*(1-35%)]/970=5.65%
Mutual fund = [(20.02-19.45)*(1-15%)+0.60*(1-35%)+0.50*(1-15%)]/19.45 = 6.68%
Options=(29000-26000)*(1-15%)/26000=9.81%

Question C
Weight of security at the beginning of the year relative to total portfolio
Portfolio value, beginning = 6,900+7,760+9,725+26,000 = 50,385
Common stock = 400*17.25 = 6,900 => 6,900/50,385 = 13.69%
Industrial bonds = 97%*1000*8 = 7.760 => 7,760/50,385 = 15.40%
Mutual funds = 500*19.45 = 9,725 => 9,725/50,385 = 19.30%
Options = 26,000 => 26,000/50,385 = 51.60%

HPR = 13.91%*13.69%+8.89%*15.40%+8.59%*19.30%+11.54%*51.60% = 12.79%

Current income return = 360+740+300 = 1400/50,385 = 2.78%
Common stock = (0.20+0.20+0.25+0.25)*400 = 360
Industrial bonds = 1000*9.25%*8 = 740
Mutual fund = 0.60*500 = 300
Options = 0

Capital gains return = (600-50+285+3,000)/50,385 = 3,835/50,385 = 7.61%
Common stock = (18.75-17.25)*400 = 600
Industrial bonds = [(1000*96.375%-970)*8 = -50
Mutual fund = [(20.02-19.45)*500=285
Options = 3,000

The capital gains form a higher portion of the total holding period returns of the portfolio.

Question D
Jensen's measure = 12.79% - 7.2% - [1.20x(10.1%-7.2%)] = 9.07%

From the above alpha, the Stalcheck portfolio has been over performing the market. However, I believe that it is reasonable to use this measure to evaluate the portfolio as it is the investment vehicles comprising the portfolio were chosen with the goal of getting a better return than the market.

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