Question

Your investment portfolio consists of ​$15 comma 000 invested in only one stocklong dashAmazon. Suppose the​ risk-free rate is 5 %​, Amazon stock has an expected return of 12 % and a volatility of 40 %​, and the market portfolio has an expected return of 10 % and a volatility of 18 %. Under the CAPM​ assumptions, a. What alternative investment has the lowest possible volatility while having the same expected return as​ Amazon? What is the volatility of this​ investment? b. What investment has the highest possible expected return while having the same volatility as​ Amazon? What is the expected return of this​ investment? Hint​: Make sure to round all intermediate calculations to at least five decimal places.​

Answer 1

a)

The CAPM hypothesis states that the effective market is utilized place in the market and has the maximum eminent expected return of any assortment for a given randomness and the smallest variability for a assumed expected return. By allotment utilized place in the market assortment, you can achieve a standard return,

Thus,

Expected Rate of Return = [Risk free Rate + Beta × (Market Risk - Risk free Rate)]

Beta = [Expected Rate of Return – Risk Free Rate] / [Market Risk - Risk free Rate]

Beta = [12% - 5%] / [10% -5%]

Beta = 7/5

Beta =1.4

The final possible instability while taking the same estimated rate of return as Amazon is $21,000 ($15,000 × 1.4) which indicate that it borrows $6,000 ($21,000 - $15,000). Now the -$6,000 is specified as strength benefit. So the volatility of the asset is,

Volatility = [Volatility of Asset x Beta]

Volatility = [18% × 1.4]

Volatility = 0.252 or 25.20%

Therefore the volatility is less than the volatility of Amazon.

b)

The market share has a instability of "n". The corresponding instability of Amazon will be 2.22 (40%/18%). So the assortment with the most notable predictable give back that has a faint variability from Amazon is $33,333.33 ($15,000x 2.22) which will be the market assortment and it also uses $18,333.33 ($33,333.33 - $15,000). Here the -$18,333.33 is specified as strength asset. So the return is,

Expected Return = [Risk free Rate + Beta × (Market Risk – Risk free Rate)]

Expected Return = [5%+ 122 × (10% - 5%)]

Expected Return = [5%+ 122 × 5%]

Expected Return = [0.05+0.111111]

Expected Return = 0.161111 or1 6.11%

Therefore the volatility is higher than the expected return of Amazon.