Question

Check mi You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below: Asset Investment Stock A $ 141,000 Stock B $139,000 Stock C Risk-free asset Beta .86 1.31 1.46 How much will you invest in Stock C? How much will you invest in the risk-free asset? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Investment in Stock C Investment in risk-free asset

Answer 1

If the portfolio is as risky as the market, then the beta of the overall portfolio should be 1

Total amount invested in the portfolio = 500000

Amount invested in stock A = $141,000

weight of A in the portfolio = w_A = 141000/500000 = 0.282

Amount invested in stock B = 139000

weight of B in the portfolio = w_B = 139000/500000 = 0.278

Suppose the weight of stock C in the portfolio = w_C and weight of risk-free asset in the portfolio = w_F

w_A+w_B+w_C+w_F = 1

0.282+0.278+w_C+w_F = 1

Therefore, w_C+w_F = 1 - 0.282 - 0.278

w_C+w_F = 0.44

Beta of portfolio can be calculated using the formula:

β_P = w_A*β_A+w_B*β_B+w_C*β_C+w_F*β_F​​​​​​​

We know that the beta of portfolio is 1, i.e., β_P = 1

β_A = 0.86, β_B = 1.31, β_C = 1.46

Beta of risk-free asset is zero, so, β_F = 0

w_A = 0.282, w_B = 0.278,

β_P = w_A*β_A+w_B*β_B​​​​​​​+w_C*β_C​​​​​​​+w_F*β_F​​​​​​​

1 = (0.282*0.86)+(0.278*1.31)+(w_C*1.46)+(w_F*0)

1 = 0.6067 + (w_C*1.46) + 0

w_C*1.46 = 1 - 0.6067

w_C*1.46 = 0.3933

w_C = 0.3933/1.46 = 0.269383561643836

Amount invested in C = 0.269383561643836*500000 = 134691.780821918 ~ 134691.78

w_C+w_F = 0.44

w_F = 0.44 - 0.269383561643836 = 0.170616438356164

Amount invested in risk-free asset = 0.170616438356164*500000 = 85308.2191780822 ~ 85308.22

Answers

Investement in stock C	134691.78
Investment in risk-free asset	85308.22