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 manage a $250 million common-stock portfolio for a large pension fund. They have just ordered tournedo financiere for the main course and flan financiere for dessert. John reads the financial pages o The Wall Street Journal by candlelight. John: Wow! Potato futures hit their daily limit. Let's add an order of gratia dachhinotse. Dus you manage to hedge the forward interest rate on that earo loas? Marsha: John, please fold up that paper. (He dors so reloctantly) John, Ilove you. Will you marry me? John; Oh, Marsha, Ilove you soo, but... there's something you must know about me - somethieg. r've never told anyone. Marsha: (concerwed) John, what is it? John: I think I'm a closet indexer. Marsha: What? Why? John: My portfolio returns always seem to track the S\&P 500 market index. Sometimes 1 do a litrle better, occasionally a little worse. But the correlation between my returns and the market returns is over 90%. Marsha: What's wroog with that? Your client wants adivenified portolio of harge-cap stocks. Of course your porifolio will follow the market. John: Why doesa't my cliest just buy an inder fond? Why is be paying me? Am I really adling value by active management? I try, but 1 guess Tm jost an ... indexer. Marsha: Oh, John, 1 know you're adding value. You were a star security analyst. John: It's not easy to find stocks that are truly oven-or undervalued. thave firm opiaions about a fews, of course. Marrha: You were explaining why Pioneer Gypoum is a good bay. And you're bullith on Global Mining: John: Right, Pioncer. (Palls handwritten notes from his coat pocket) Stock grice $8730. I estimate the expected return as 11% with an anmal standard deviation of 32%. That's twice the market standard deviatios of 16%. Marshat: Only 11 \%? You're forccasting a market return of 12.5%. John: Yes, I'm using a matket risk premium of 7.5% and the risk-free interest rate is about 58 . That gives 12.5%. But Pioneer's beta is only 65 . I was going to buy 30,000 shures this moorning. but I ksot my nerve. Tve got to stay diversified. Marsha: Have you tried modem portfolio theory? John: MPT? Not practical. Looks great in textbonks, where they show efficient frontiers with 5 es 10 stocks. But 1 choose from husdreds, maybe thousands, of socks. Whicte do I get the inputs for 1,000 stosks? That's a million variances and covariances! Marsha: Actually oaly about $00,000, dear. The covariances above the diagood are the same as the covariances below. But you're right, most of the estimates woald be out-of-date or just garbage. John: To say nothing about the expected returns. Gartage in, gatbage oat. Marsha: But John. you don't need to solve for 1.000 portfolio weights. You cely acod a handiful. Here's the trick: Take yoar benchmark, the S\&P 500 , as security 1 . Thar's whar you would end up with as an indever. Then consider a few securities you really know socsethiag about. Plioseer could be security 2, for ecample. Giobal, security 3. And so on. Then you coeld put your wonderful fimancial mind to work. John: I get it Active manapement means selling off wome of the benchnark portfolio and imvesting the proceeds in specific stocks like Pinener. Bur how do 1 decide ahether Pionecer really improves the portfolio? Even if it does, how mush should t buy? Marsha: Jast maximine the Sharpe natief dear. Johs: I've got it! The answer is yes! Marsha: What is the quention? John: You anked me to marry you. The anwer is yes. Where should we go on our honeymoon? Marsha: How about Australia? Id lowe w vait the Sydney Furures Exchange. QUESTIONS 1. Table 8.4 reproduces John's nokes ce Piceser Gypam and Glokal Mining. Calculate the expected return, tisk premium, and standurd deviation of a portfolio invested partly in the market and partly in Proneer. (Yoe cas calcalate the necessary inpots from the betas and standard deviations given in the tahle Hine A stock's beta equals its covariane with the narket retum divided by the variance of the manct seturn, Does adding Pioncer to the matket benchank imgrone the Sharpe ratio? Hos much should John itsvest in Piuneer and bow much in the maklet? accounts for .75 s of the S\&Pindex
