Click here to read my column in Sunday's NY Times.
The topic is whether you should invest in gold as part of your portfolio. After you read the column, you might find the following problem of interest. It is based on roughly plausible assumptions.
Imagine that you start off with a portfolio of 60 percent stocks and 40 percent bonds. The returns on stocks, bonds, and gold are uncorrelated. Stocks earn a higher expected return than bonds. Bonds and gold earn the same lower expected return, but gold returns are three times as volatile as bond returns, as measured by the standard deviation. You want to minimize risk, measured by the variance of your portfolio return, without changing the expected return on your portfolio. How much gold should you buy?
I will leave this problem as an exercise for the reader. But I believe you should be able to come up with a precise numerical answer without resorting to a computer.
Update: Albert Zevelev, a grad student at Penn, posts the correct answer here.