Question

Consider a Treasury bill with a rate of return of 3% and the following risky securities:

1. Security A: E(r) = .11; variance = .0700
2. Security B: E(r) = .13; variance = .045
3. Security C: E(r) = .19; variance = .1000
4. Security D: E(r) = .10; variance = .03

The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. Which security the investor should choose as part of her complete portfolio to achieve the best CAL?

Answer 1

Step 1- Compute standard deviation:

standard deviation A= .0700^(1/2) = .2645

Standard deviation B = .045 ^ (1/2) = .2121

Standard deviation C= .1000 ^ (1/2) = .3162

Standard deviation D = .03 ^ (1/2) = .1732

Step 2- compute risk-adjusted return:

Risk adjusted return A= .11 / 0.2645 = .4158

Risk adjusted return B= .13 / .2121 = .6129

Risk adjusted return C= .19 / .3162 = .6008

Risk adjusted return D= .10 / .1732 = .5773

​​​​​​The optimal investment is security B because it offers the greatest risk adjusted return.