Reference no: EM132645143

The Capital Asset Pricing Model (CAPM) identifies the market portfolio as the single risk factor. According to the CAPM, all investors should hold the market portfolio with risk free T-bills, with the precise combination differing across investors depending on their risk aversion. Suppose an investor has mean-variance preferences with risk aversion y = 3.2, i.e. her utility function is given by U = E(rp) - -Var(rp) Note that, for weights Wm and Wf = 1 - Wm invested, respectively, in the market portfolio and T-bills, the return on the overall portfolio is rp = Wmi'm + wfff, where rm denotes the return on the market portfolio and r denotes the return on T- bills. 1.

Suppose that a broad stock market index, such as the S&P 500 Index, is used as a proxy for the market portfolio (a common practice in empirical applications). The average monthly return on the Index is 0.94% and its volatility is 5.53%. T-bills have an average monthly return of .30%. (Note: the T-bill rate does move around in the data but its volatility is very low compared to that of the market. In this exercise, we are going to treat T-bills as risk free, i.e., their volatility is 0.)

Problem 1: What is the optimal portfolio of the market and T-bills for the investor?