This contains data on the annual percentage return on stocks, gold, and Treasury bills over the period from 1987 to 2007. A certain investor would like to determine the percentages of her portfolio to invest in these three asset categories. Her objective is to maximize the expected return on the portfolio while not investing less than 20% or more than 50% in each asset class. You may estimate the expected return on each asset with its average return over the period 1987-2007. The risk index of an asset is measured by the average absolute percentage change over time. You may estimate the risk indices for stocks, gold, and Treasury bills over 1987- 2007. The risk index for a portfolio is the weighted average of the risk indices of its component assets, where the weights are the percentages invested in each asset. For example, in the data we see that the risk index for stocks is 16.9. Our investor would like the risk index of her portfolio to equal 15. (a) What are the optimal percentages to invest in each asset class? (b) Describe how her average return and the percentages invested in each asset change as she increases her acceptable risk index from 15 to 18

Asset Portfolio Gold T-bills 11 Absolute values of returns Stocks Gold T-bills 11 8 14 11 8 -14 44 44 Historical returns (% changes) Year Stocks 1987 11 1988 1989 1990 14 1991 1992 -15 1993 -27 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 vooooo AAVV ooo 00 AAVV 18 31 18 31 NO 10 59 59 99 -25 25 -11 11 -15 15 12 -12 ooOOOO 19 16 OOO 16 22 5 22 17 17 Averages 10.9 18.3 7.4 16.9 28.0 7.4