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 30% 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= 2. Assume the utility function is U= EU) - 0.5 * Ao2. (Do not round intermediate calculations. Round your answers to 4 decimal places.) U(A = 2) WBills 0.0 0.2 Windex 1.0 0.8 0.6 0.6 0.8 1.0 0.4 0.2 0.0

Answer 1

Ans.

Average annual return above Treasury bill return = 8%

Treasury bill return = 5%

Expected rate of return = 8% + 5% = 13%

Value of A = 2

Standard deviation = 30%

U = E(r) − 0.5 * Aσ2 = E(r) - 0.5 * 2σ2 = E(r) - 1* σ2 = E(r) - σ2

Wbills (a)	Windex (b)	E (r) (c)	SD (portfolio) (d)	(SD)2 (Portfolio) (e)	U(A = 2) (f= c-e)
0	1	0.13	0.30	0.0900	0.0400
0.2	0.8	0.114	0.24	0.0576	0.0564
0.4	0.6	0.098	0.18	0.0324	0.0656
0.6	0.4	0.082	0.12	0.0144	0.0676
0.8	0.2	0.066	0.06	0.0036	0.0624
1	0	0.050	0.00	0.0000	0.0500