Question

Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 34% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5% Calculate the utility levels of each portfolio for an investor with A-3. Assume the utility function is U = 0-0.5 Ao(Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places.) WBills U( A3) Windex 1.01 0.2 0.67 0.41 08

Answer 1

	Portfolio Return =Rp=w1*R1+w2*R2
	R1=Return of Asset 1=Return of T bills=5%
	R2=Return of Asset 2=Return of Index=(5+8)%=13%
	w1=Weight of asset1=Weight of T-bill
	w2=Weight of Asset2=Weight of Index		1156
	Portfolio Expected Return =Rp=w1*5+w2*13
	Portfolio Variance =Vp
	Vp=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov (1,2)
	S1=Standard Deviation of Asset 1=T bill standard Deviation=0
	S2=Standard Deviation of Asset21=Index standard Deviation=34%
	Cov(1,2)=Covariance of Returns of Asset 1 and Asset 2=0
	Vp=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov (1,2)
	Portfolio Variance =Vp=(w2^2)*(34^2)=1156*(w2^2)
	U=Rp-0.5*A*Vp; A=3
	U=Rp-0.5*3*Vp=Rp-1.5*Vp
		w1	w2	Rp	Vp	Rp-1.5*Vp
		Wbills	Windex	Expected Return	Portfolio Variance	U(A=3)
		0.0	1.0	0.13	0.1156	-0.0434
		0.2	0.8	0.114	0.073984	0.003024
		0.4	0.6	0.098	0.041616	0.035576
		0.6	0.4	0.082	0.018496	0.054256
		0.8	0.2	0.066	0.004624	0.059064
		1.0	0.0	0.05	0	0.05