You want to create a portfolio equally as risky as the market, and you have $1,1

Question

You want to create a portfolio equally as risky as the market, and you have $1,100,000 to invest. Given this information, fill in the rest of the following table: (Do not round intermediate calculations. Round your answers to the nearest whole number, e.g., 32.)

You want to create a portfolio equally as risky as the market, and you have $1,100,000 to invest. Given this information, fill in the rest of the following table: (Do not round intermediate calculations. Round your answers to the nearest whole number, e.g., 32.)

Explanation / Answer

Since the portfolio is as risky as the market, the ? of the portfolio must be equal to one. We also know the ? of the risk-free asset is zero. We can use the equation for the ? of a portfolio to find the weight of the third stock. Doing so, we find:

?p = 1.0 = wA(1.1) + wB(1.2) + wC(1.4) + wRf(0)

Solving for the weight of Stock C, we find:

wC = 0.43

So, the dollar investment in Stock C must be:

Invest in Stock C = 0.43($1,100,000) = $462000

We know the total portfolio value and the investment of two stocks in the portfolio, so we can find the weight of these two stocks. The weights of Stock A and Stock B are:

wA = $110000 / $1,100,000 = 0.10

wB = $264,000/$1,100,000 = 0.24

We also know the total portfolio weight must be one, so the weight of the risk-free asset must be one minus the asset weight we know, or:

1 = wA + wB + wC + wRf = 1 – 0.10 – 0.24 – 0.43 = wRf

wRf = 0.23

So, the dollar investment in the risk-free asset must be:

Invest in risk-free asset = 0.23($1,100,000) = $253000

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