Question

You manage an index fund that is an exact replica of the market index. The market expected annual rate of return is 19.5% with a standard deviation of 16.5%. Annual T-bill rate is 4.5% 2. a. A client of yours wants you to invest 80% of his portfolio in your fund and 20 % in T-bill money market fund. What is the expected return and standard deviation of this client's portfolio? b. What are the Sharpe ratios of your fund and client's portfolio? c. Suppose your client prefers to invest in your fund a proportion y which maximizes the expected return on his portfolio subject to the constraint that the portfolio's standard deviation will not exceed 10 % i. What is the investment proportion, y? i. What is the expected rate of return on your client's portfolio? iii.What is the degree of risk aversion (A) of this client? d. Briefly explain whether an investor should expect a higher return from holding Portfolio A versus Portfolio B under capital asset pricing theory (CAPM). Assume that both portfolios are fully diversified. Portfolio A Portfolio B Systematic risk (beta) 0.8 1.0 Specific risk for each individual security in the portfolio. High Low

Please answer the questions above. Thank you!

Answer 1

	Index fund=Asset 1,T Bill=Asset 2
	Return of asset1=R1=	19.50%
	Return of asset2=R2	4.50%
	Standard deviation of asset 1=S1	16.50%
	Standard deviation of asset 2=S2=	0
	Covariance(1,2)=Corr(1,2)*S1*S2	0
	w1=Investment in asset (Index Fund)	0.8
	w2=Investment in asset 2(T-bill)=	0.2
	Portfolio Return
	w1*R1+w2*R2=0.8*19.5+0.2*4.5=	16.50%
	Portfolio Variance=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)
a	Portfolio Variance=(0.8^2)*(16.5^2)=				174.24
	Portfolio Standard Deviation=Square Root(Variance)				13.2
b	Sharp ratio=(PortfolioReturn-Riskfree rate)/(PortfolioStandard Deviation)			Riskfree Rate=T billreturn		4.50%
	Sharp   ratio=(16.5-4.5)/13.2=	0.90909091
	Portfolio Return =Rp=w1*19.5+w2*4.5…….Equation(1)
	Vp=Portfolio Variance=(w1^2)*272.25…………Equation (2)
c	FromAllPossible portfolios
	Investment portion y=w1=	0.6	60%
	Return	13.50%
	Standard Deviation	9.90%		ALL PUSSIBLE PORTFOLIOS Vp(Using SpSqu Rp w1 19.5 Equation (2) are root SR- (Rp- 5)/Sp of Vp w1 w2 +w2*4.5 Weight Weight of Portfolio SHARP Portfolio of Portfolio Std. Deviatio Return(%) Index n(%) T-Bill RATIO Variance 4.5 0.825 0.90909 0.05 0.95 5.25 0.680625 2.7225 1.65 0.90909 0.1 0.9 6 0.15 0.85 2.475 0.90909 6.75 6.125625 0.2 0.8 3.3 0.90909 7,5 10.89 0.25 0.75 8.25 17,015625 4.125 0,90909 0.3 0.7 4.95 0.90909 24.5025 0.35 0.65 9.75 33.350625 5.775 0.90909 0.4 0.6 6.6 0.90909 10,5 43,56 0.45 0.55 11.25 55.130625 7.425 0.90909 0.5 0.5 8.25 0.90909 12 68.0625 0.55 0.45 12.75 82.355625 9.075 0.90909 0.6 0.4 9,9 0.90909 13.5 98.01 0.65 0.35 14,25 115.02563 10.725 0.90909 0.7 0.3 11.55 0.90909 15 133.4025 15.75 153.14063 0.75 0.25 12.375 0.90909 0.8 0.2 13.2 0.90909 16,5 174.24 0.85 14.025 0.90909 0.15 17.25 196.70063