Consider a treasury bill with a rate of return of 5% and the following risky sec
ID: 2682863 • Letter: C
Question
Consider a treasury bill with a rate of return of 5% and the following risky securities: Security A: E(r) = .15; variance = .0400 Security B: E(r) = .10; variance = .0225 Security C: E(r) = .12; variance = .1000 Security D: E(r) = .13; variance = .0625 The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of his complete portfolio to achieve the best CAL would be _________. Answer A. A B. B C. C D. DExplanation / Answer
First we compute the Standard Deviation (SD) for each security (square root of its variance).
SD of A = 0.2
SD of B = 0.15
SD of C = 0.32
SD of D = 0.25
Next we compute the Coefficient of Variation (CV) for each security, where
CV = SD / E(r)
CV of A = 0.2 / 0.15 = 1.33
CV of B = 0.15 / 0.10 = 1.5
CV of C = 0.32 / 0.12 = 2.67
CV of D = 0.25 / 0.13 = 1.92
The security having lowest CV has the minimum volatility (variability) and therefore is least risky. Here it is security A (CV = 1.33, lowest).
So, investor should choose A to minimize risk.
Correct option (A).