Question
Asked Sep 7, 2019
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You would like to combine a highly risky stock with a beta of 2.6 with U.S. Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the overall market. What percentage of the portfolio should be invested in Treasury bills?

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Expert Answer

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Step 1

Beta measures the volatility of a stock with respect to the market. The risk level or beta of the overall market is 1.

Step 2

Suppose the weight of the risky stock in the portfolio be x, then the weight of the treasury bills in the portfolio will be (1-x).
Given that the beta of the stock is 2.6.
Beta of treasury bills is zero.

Step 3
(Weight of the stock)x(Beta of the stock) (Weight of the Treasury
bills)x(Beta of the Treasury bills)-Beta of the overall market
=(x)x(Beta of the stock)(1-x)x (Beta of the Treasury bills)-1
=>xx2.6 (1-x)x0=1
=>xx2.6=1
=>x=1-2.6=0.384615385
=>1-x-1-0.384615385-0.615384615 or 61.54% (Rounded to two decimal places)
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(Weight of the stock)x(Beta of the stock) (Weight of the Treasury bills)x(Beta of the Treasury bills)-Beta of the overall market =(x)x(Beta of the stock)(1-x)x (Beta of the Treasury bills)-1 =>xx2.6 (1-x)x0=1 =>xx2.6=1 =>x=1-2.6=0.384615385 =>1-x-1-0.384615385-0.615384615 or 61.54% (Rounded to two decimal places)

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