Consider a T-bill with a rate of return of 5 percent and the following risky securities:

Security A: E (r) = 0.15; Variance = 0.04

Security B: E (r) = 0.10; Variance = 0.0225

Security C: E (r) = 0.12; Variance = 0.01

Security D: E (r) = 0.13; Variance = 0.0625

From which set of portfolios, formed with the T-bill and any one of the 4 risky securities, would a risk-averse investor always choose his portfolio?

A. The set of portfolios formed with the T-bill and security A.

B. The set of portfolios formed with the T-bill and security B.

C. The set of portfolios formed with the T-bill and security C.

D. The set of portfolios formed with the T-bill and security D.

E. Cannot be determined.

The set of portfolios formed with the T-bill and security C since security C

has the highest reward to volatility ratio.

Explanation:

Step 1: Determine the reward to volatility ratio

The reward to volatility ratio can be expressed as;

r=R (p) - E (r) / s

where;

r=reward to volatility ratio

R (p) = rate of return

E (r) = expected risk

s=standard deviation

Step 2: Determine r for Security A

For security A;

R (p) = 5%=5/100=0.05

E (r) = 0.15%=0.15/100=0.0015

s=√variance=√0.04=0.2

replacing;

r = (0.05-0.0015) / 0.2=0.2425

Step 3: Determine r for Security B

For security B;

R (p) = 5%=5/100=0.05

E (r) = 0.10%=0.10/100=0.001

s=√variance=√0.0225=0.15

replacing;

r = (0.05-0.001) / 0.15=0.33

Step 4: Determine r for Security C

For security C;

R (p) = 5%=5/100=0.05

E (r) = 0.12%=0.12/100=0.0012

s=√variance=√0.01=0.1

replacing;

r = (0.05-0.0012) / 0.1=0.488

Step 5: Determine r for Security D

For security D;

R (p) = 5%=5/100=0.05

E (r) = 0.13%=0.13/100=0.0013

s=√variance=√0.0625=0.25

replacing;

r = (0.05-0.0013) / 0.25=0.1948

The set of portfolios formed with the T-bill and security C since security C

has the highest reward to volatility ratio.