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 = wA = 141000/500000 = 0.282
Amount invested in stock B = 139000
weight of B in the portfolio = wB = 139000/500000 = 0.278
Suppose the weight of stock C in the portfolio = wC and weight of risk-free asset in the portfolio = wF
wA+wB+wC+wF = 1
0.282+0.278+wC+wF = 1
Therefore, wC+wF = 1 - 0.282 - 0.278
wC+wF = 0.44
Beta of portfolio can be calculated using the formula:
βP = wA*βA+wB*βB+wC*βC+wF*βF
We know that the beta of portfolio is 1, i.e., βP = 1
βA = 0.86, βB = 1.31, βC = 1.46
Beta of risk-free asset is zero, so, βF = 0
wA = 0.282, wB = 0.278,
βP = wA*βA+wB*βB+wC*βC+wF*βF
1 = (0.282*0.86)+(0.278*1.31)+(wC*1.46)+(wF*0)
1 = 0.6067 + (wC*1.46) + 0
wC*1.46 = 1 - 0.6067
wC*1.46 = 0.3933
wC = 0.3933/1.46 = 0.269383561643836
Amount invested in C = 0.269383561643836*500000 = 134691.780821918 ~ 134691.78
wC+wF = 0.44
wF = 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 |
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