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 her complete portfolio to achieve the best cal would be a. security a b. security b c. security c d. security d
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Security A, Option A is correct
Variance of each security is given. Compute standard deviation of each security. Square root of variance of each security is the standard deviation.
Security A = = 0.2
Security B = = 0.15
Security C = = 0.316
Security D = = 0.25
Now, compute coefficient of variance of each security to compute its volatility as as shown below:
Security A = 0.2 ÷ 0.15 = 1.33
Security B = 0.15 ÷ 0.1 = 1.5
Security C = 0.316 ÷ 0.12 = 2.63
Security D = 0.25 ÷ 0.13 = 1.92
The security with minimum coefficient of variance is least variable or risky. In this case, Security A has the least coefficient of variance of 1.33, so investor should select security A with risk free asset to create a portfolio that gives best CAL.