You want to create a portfolio equally as risky as the market, and you have $1,0

Question

You want to create a portfolio equally as risky as the market, and you have $1,000,000 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 $1,000,000 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

Answer:

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 = $195,000 / $1,000,000 = 0.195

wB = $340,000/$1,000,000 = 0.34

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 *(0.9) + wB*(1.15) + wC*(1.29) + wRf*(0)

Solving for the weight of Stock C, we find:

wC = 0.336046511

So, the dollar investment in Stock C must be:

Invest in Stock C = 0.336046511 x ($1,000,000) = $336046.511

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 = 0.195 + 0.34 + .336046511 + wRf

wRf = 0.128953489

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

Invest in risk-free asset = 0.128953489 x ($1,000,000) = $128953.489

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