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.

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