31 Capital Asset Pricing Model and Arbitrage Pricing Theory. [40] (3) Suppose that an investor with preferencs Chirp. oft," 2 hp * scalp : a > U optimally chooses a portfolio composed oFonly two assets: 3 single risky asset with expected return ,uJ and variance of return 0'} and a riskFree asset which yields r0. Denote by q the proportion of the portfolio invested in the risky asset, and by [LP = qy} + (E qlro the expected return on the portfolio Af ter deriving the expression for the portfolio risk-return tradeotf. derive the investor's optimal proportion of initial wealth invested in the risky asset. [10] (b) Now assume that the asset market is frictionless and invstors can freely borrow or lend at a risk-free rate, but that they are constrained to invest in portfolios that 'blend' the riskless asset and one risky asset Suppose that in equilibrium, the only two available risky assets yield p} = 0.11 with a standard deviation of a, = \"JR and m = (UT) with a standard deviation of m = 0.0.9. What is the riskwfree rate of interest in this market? If the investor wishes to hold a portfolio with a standard deviation of \".11, how should s/he optimally allocate her/his initial wealth? [10]