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Mini Case CH8

John and Marsha on Portfolio Selection The scene: John and Marsha hold hands in a cozy French restaurant in downtown Manhattan, several years before the mini-case in Chapter 9. Marsha is a futures-market trader. John manages a $250 million common-stock portfolio for a large pension fund. They have just ordered tournedos financiere for the main course and flan financiere for dessert. John reads the financial pages of The Wall Street Journal by candlelight.

QUESTIONS 1. Table 8.4 reproduces Johns notes on Pioneer Gypsum and Global Mining. Calculate the expected return, risk premium, and standard deviation of a portfolio invested partly in the market and partly in Pioneer. (You can calculate the necessary inputs from the betas and standard deviations given in the table. Hint: A stocks beta equals its covariance with the market return divided by the variance of the market return.) Does adding Pioneer to the market benchmark improve the Sharpe ratio? How much should John invest in Pioneer and how much in the market?

2. Repeat the analysis for Global Mining. What should John do in this case? Assume that Global accounts for .75% of the S&P index.

John: Wow! Potato futures hit their daily limit. Let's all anereler of gralin cauphinoise. Did you manage to Helge the forward interest rate on that eure loan? Marsha: John, please fold up that paper. (He does so reluctantly.) John, I love you. Will you marry me? John: Oh, Marsha, I love you too, but there's something you must know about mosomething I've never told anyone Marsha: (concerned) Jolui, what is it? John: Ilhink I'm closel iniclexer Marsha: What? Why? John: My portfolio retums always seem to track the S&P 500 market index. Sometimes I do a little better, occasionally a little worse. But the correlation between my returns and the market returns is over 90% Marsha: What's wrong with that? Your client wants a diversified portfolio of large-cap stocks. Of course your portfolio will follow the market. John: Why doestil my clic just buy ari index fund? Why is he paying me? Air Ically willing value by active Tristiagemerit? Tiry, but I guess I'm just un... indexer Marsha: Oh, Jolu, I know you're adding value. You were a star security analyst. John: It's not easy to find stocks that are truly over- or undervalued. I have firm opinions about a few, of course. Marsha: You were explaining why Pioneer Gypsum is a good buy. And you're bullish on Global Mining Joku: Right, Pioneer (Pulls demiwriter notes from his coat pocket) Slock price $87.50 I estimate the expected return as 11% with an annual standard deviation of 32%. That's Iwice the market standard deviation of 16% Marsha: Only 11%? You're forecasting a market retum of 12.5%. John: Yes, I'm using a market risk premium of 7.5% huic the risk-free interest rate is about 5%. That gives 12.5%. But Pioneer's beta is only.65. I was going to buy 30,000 shares this morning, but I lost my nerve. I've got to stay diversified, Marsha: Have you tried moderni portfolio thcory? John: MPT? Not practical. Looks great in textbooks, where they show efficient frontiers with 5 or 10 stock. But I choose from hundreds, maybe thousands, of stocks. Wliere do I get the inputs for 1,000 stocks? That's a Trillium variatices and covariances! Marsha: Actually amily about 500.000, dear. The covariances above the diagonal are the same as the covariances below. But you're right, most of the estimates would be cut-of-date or just garbage. Johur: To say nothing about the expected returns. Garbage in, garbage out. Marsha: But John, you don't need to solve for 1,000 portfolio weights. You only need a handful. Ilere's the trick: Take your benclunark, the S&P 500, as security 1. That's what you would end up with as an indexer. Theti consider a few securities you really know something about. Pivnicet coukl be securily 2, for example. Global security 3. And so on. Then you coull put your wonderful financial mind to work. John: I get it: Active management means selling off some of the benchmark portfolio and investing the proceeds in specific stocks like Pioneer. But how do I decide whether Pioneer really improves the portfolio? Even if it does, how much should I buy? Marsha: Just maximize the Sharpe ratio, dear. John: I've got it! The answer is yes! Marsha: What's the question? John: You asked me to marry you. The answer is yes. Where should we go on our honeymoon? Marsha: How about Australia? I'd love to visit the Sydney Futures Exchange. Pioneer Gypsum Global Mining > TABLE 8.4 John's notes on Pioneer Gypsum and Global Mining. Expected return 11.0% 12.9% Standard deviation 32% 24% Beta 0.65 1.22 Stock price $87.50 $105.00