bre44380_ch08_192-220.indd 220 09/30/15 12:45 PM
220 Part Two RiskJohn: Yes, I’m using a market risk premium of 7.5% and 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 modern portfolio theory?
John: MPT? Not practical. Looks great in textbooks, where they show efficient frontiers with 5 or
10 stocks. But I choose from hundreds, maybe thousands, of stocks. Where do I get the inputs
for 1,000 stocks? That’s a million variances and covariances!
Marsha: Actually only 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 But you’re right, most of the estimates would be out-of-date or just
garbage.
John: 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.
Here’s the trick: Take your benchmark, the S&P 500, as security 1. That’s what you would end
up with as an indexer. Then consider a few securities you really know something about. Pio-
neer could be security 2, for example. Global, security 3. And so on. Then you could put your
wonderful financial mind to work.
John: I get it: Active management means selling off some of the benchmark portfolio and invest-
ing 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.QUESTIONS- Table 8.4 reproduces John’s 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 stock’s beta equals its covariance with the
market return divided by the variance of the market return.) Does adding Pioneer to the mar-
ket benchmark improve the Sharpe ratio? How much should John invest in Pioneer and how
much in the market? - Repeat the analysis for Global Mining. What should John do in this case? Assume that Global
accounts for .75% of the S&P index.
Pioneer Gypsum Global Mining
Expected return 11.0% 12.9%
Standard deviation 32% 24%
Beta 0.65 1.22
Stock price $87.50 $105.00◗ TABLE 8.4
John’s notes on
Pioneer Gypsum
and Global Mining.