Question

You want to invest ​$40 000 in a portfolio with a beta of no more than 1.46 and an expected return of 13.4​%. Bay Corporation has a beta of 1.08 and an expected return of 11.5​%, and City Limited has a beta of 1.8 and an expected return of 15.16​%. The​ risk-free rate is 6​%. Is it possible to create this portfolio investing in Bay Corporation and City​ Limited? If​ so, how much will you invest in​ each?

Answer 1

	Beta	Expected Return
Bay Corporation	1.08	11.50%
City Limited	1.8	15.16%

Beta of Bay Corporation = β₁ = 1.08, Beta of City Limited = β₂ = 1.8

Expected Return of Bay Corporation = E[R₁] = 11.5%, Expected Return of City Limited = E[R₂] = 15.16%

Let W₁ be the percentage of weight of Bay corporation in the portfolio

So the percentage of weight of City Limited is 1-W₁

It is given that the expected return of the portfolio is 13.4%. We calculate the expected return of the portfolio using the below equation:

E[R_p] = W₁*E[R₁] + W₂*E[R₂]

Therefore, Expected return of the portfolio consisting of Bay Corp and City Limited is 13.4% and is given by :

E[R_p] = W₁*11.5% + (1-W₁)15.16% = 13.4%

11.5%*W₁ - 15.16%*W₁​​​​​​​+15.16% = 13.4%

3.66*W₁​​​​​​​ = (15.16%-13.4%) = 1.76%

Therefore, W₁​​​​​​​ = 1.76/3.66 = 0.48, W₂ = 1-W₁​​​​​​​=0.52

Now Beta of the portfolio is calculated using below formula:

β_p =  W₁​​​​​​​* β₁ + W₂​​​​​​​* β₂ = 0.4808*1.08+0.5192*1.8 = 1.4537

It is given that beta of the portfolio should not be more than 1.46. Now if we invest around 48.08% in Bay Corporation and 51.92% in City Limited, the beta is 1.4537 (less than 1.46) and the return is 13.4%. Hence, It is possible to create this portfolio.

Investment in Bay Corporation = 48.08%*40000 = $19,232

Investment in Bay Corporation = 51.92%*40000 = $20,768