You want to create a portfolio equally as risky as the market, and you have $500

Question

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 Beta
Stock A $ 134,000 0.79
Stock B $ 146,000 1.24
Stock C 1.39
Risk-free asset

Requirement 1:

How much will you invest in Stock C? (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).)

Investment in Stock C $

Requirement 2:

How much will you invest in the risk-free asset? (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).)

Explanation / Answer

1. Remember that the risk i.e. beta of the market is 1. The risk free asset isn't needed if you are trying to achieve a portfolio that's correlated a 100% to the market. 2. So, you are solving for a "p" portfolio that has a "b" beta of 1 3. So the B(P) = beta of the stock multiplied by the asset weights of the portfolio e.g. then added B(p) = wa(b) + wb(b) + wc(b) + wd(b).....where "w" means the weight of the asset in the portfolio. Once the weights are solved for then you set the dollar amounts to match the desired weights. So, setting up the equation 1 = .79(weight of a)+1.24(weight of b)+1.39(weight of C) The rest is plug and play but one way to get there is a=.5 b=.4 and c=.1 = roughly 1 Your investment in c in this case would be .1(500,000)=c and so on. Make sense?

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