Business Economics 271
Portfolio Theory & Analysis
Prof. John W. Sell

STATISTICS REVIEW
(with application to investment)

On January 1st, you invest $500 in each of two common stocks: WOOCAP selling for $25 per share and GOWNCO, priced at $50 per share.

1. One year later, WOOCAP sells for $29 per share and GOWNCO for $45 per share. Each paid a $1 per share dividend for the year. What is the holding period yield on WOOCAP? On GOWNCO? Show that the holding period yield on the portfolio of the two stocks is 6%. What is the current market value of the portfolio? [Note: assume that the dividends are withdrawn and spent so that they do not become part of the future market value.]

2. Yet another year passes and WOOCAP and GOWNCO are selling for $32.50 and $45 respectively. WOOCAP continues to pay a $1.00 dividend, but GOWNCO has raised its payment to $1.30 in an attempt to make its shares more attractive. Calculate this year's returns and show that the portfolio yield is 10% for this year.

3. Show that the (annual) historical yield has averaged 7.98% with a standard deviation of 2%. [Hint: Is this a sample or a population?]

4. Consider investments for the coming year. Suppose you believe that the probability is .6 that the previous returns were typical, but that there is also a .2 chance that the yield in the year ahead will be higher (say, to 10%) and a .2 likelihood that it will decrease to 7.06%. Calculate the expected yield on your current portfolio and the standard deviation of the expected return. Show that the odds are 2 out of 3 that your actual rate of return will fall between (approximately) 7.2% and 9.2%. Assuming again that you take out the dividend that you calculated in part 2 and invested only the market value of the shares, what is the minimum and maximum value that you would expect the portfolio to have at the end of the year, given the 7.2% to 9.2% range? If one-year T-bills are currently selling at an ask discount of 6.7%, how does this portfolio strategy look relative to your opportunity costs, i.e., how certain are you that the portfolio will do better than the T-bills?

(Rev. 1/02)