How to calculate the percentage of portfolio?

2013-12-14 8:16 am
You would like to combine a risky stock X with a beta of 1.68 with US Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the market portfolio. What percentage of the portfolio should be invested in the risky stock?

Thank you for helping!

回答 (9)

2013-12-14 1:25 pm
✔ 最佳答案
If you are familiar with the Security Market Line (SML) used in the Capital Asset Pricing Model (CAPM), you know that the risk free rate plots ON the y-intercept at a beta of 0. Since the market beta is 1, you want to weight your portfolio such that...
(weight of risk free asset x 0) + (weight of stock X * stock X ß) = 1

reducing the above equation...
[where w = weight]
wX * ßX = 1
so...
1 / ßX = wX
1 / 1.68 = 0.59524, or 59.524% should be in stock X,
with the remainder ( 1 - 0.59524) = 0.40476, or 40.476% in the risk free asset (Tbill)

Thus your Portfolio beta = market beta = 1
(wRiskFree * ßRiskFree) + (wX * ßX) = 1
[(0.40476 * 0) + (0.59524 * 1.68) = 1
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2013-12-15 3:45 am
Weight in stock market times beta of 1.68 plus weight in risk free treasury bills times beta of 0 equals 1. This is because the stock market has a beta of 1. The part if the equation dealing with the risk free treasury rate drops out .
So. 1.68x=1

1/1.68 will be your answer. Do the math. Your answer will be about 60%.


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