Consider a treasure bill with a rate of return of 5% and the following risky sec
ID: 2818314 • Letter: C
Question
Consider a treasure bill with a rate of return of 5% and the following risky securities:
Security A: E(r)= .16; variance = .0400 Security B: E(r) = .10; variance =.0225
Security C: E(r)= .12; variance = .1000 Security D: E(r)= .14; 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 her complete portfolio to achieve the best CAL would be (Security A,B,C or D)_. ( Hint: for full credit you should provide your numerical evidence).
Explanation / Answer
In the risky securities provide, A, B, C and D, as the return increases its variance also increases. B having the lowest return and variance and A having the highest return with highest variance. Standard deviations is the square root of variance. It indicates how risky a security is. But when we are provided with multiple securities with multiple variance associated with them, we calculate coefficient of variation. It is a measure of relatable variability.
Coefficient of variation = (standard deviation/ expected return) * 100
Security A = (.0400/ .16) = 1.25
Security B = (.0225/ .10) = 1.5
Security C = (.1000/ .12) = 2.64
Security D = (.0625/ .14) = 1.79
The coefficient of variation to be less than 1 are considered as low variance while the one more than 1 are considered as high variance. The lower the value of coefficient of variation, the more precise the estimate is.
Hence the ranking for selection of securities would be A, B, D and C. A besides having the highest risk gas such high return so as to fall in with lowest coefficient of variation. Hence, treasury bill can be combined with security A.