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Suppose that many stocks are traded in the market and that it is possible to borrow atthe risk-free rate, rf. The characteristics of two of the stocks are as follows:ExpectedReturnStandardStockDeviation25%75%A6%B10%Correlation=-1a. Calculate the expected rate of return on the risk-free portfolio? (Hint: Try to construct arisk-free portfolio using stocks A and B.) (Enter your answer as a percentagerounded to 2 decimal places.)Expected rate ofreturnb. Could the equilibrium rf be greater than, equal to, or less than your answer in #a?greater thanequal toless than

Question
Suppose that many stocks are traded in the market and that it is possible to borrow at
the risk-free rate, rf. The characteristics of two of the stocks are as follows:
Expected
Return
Standard
Stock
Deviation
25%
75%
A
6%
B
10%
Correlation
=-1
a. Calculate the expected rate of return on the risk-free portfolio? (Hint: Try to construct a
risk-free portfolio using stocks A and B.) (Enter your answer as a percentage
rounded to 2 decimal places.)
Expected rate of
return
b. Could the equilibrium rf be greater than, equal to, or less than your answer in #a?
greater than
equal to
less than
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Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rf. The characteristics of two of the stocks are as follows: Expected Return Standard Stock Deviation 25% 75% A 6% B 10% Correlation =-1 a. Calculate the expected rate of return on the risk-free portfolio? (Hint: Try to construct a risk-free portfolio using stocks A and B.) (Enter your answer as a percentage rounded to 2 decimal places.) Expected rate of return b. Could the equilibrium rf be greater than, equal to, or less than your answer in #a? greater than equal to less than

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Step 1

Please see the white board for the expression for standard deviation of a portfolio. The symbols have their usual meaning in the world of investment management.

Portfolio Risk = a, = wixaj+ wjxoj+2 xwjxw2x Cov (R, R2)
wixoj+ wzxa^+2xwjxW2x P120102
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Portfolio Risk = a, = wixaj+ wjxoj+2 xwjxw2x Cov (R, R2) wixoj+ wzxa^+2xwjxW2x P120102

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Step 2

Part (a)

A riskfree portfolio will hve its standard deviation as 0.

Hence, we have to solve the following two equations:

w1 + w2 = 1; w1σ1 – w2σ2 = w1 x 25% - w2 x 75% = 0

If two securities are perfectly negatively correlated then py2
-1, and hence portfolio risk is minimum at wy x o1 , W2 % O2
help_outline

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If two securities are perfectly negatively correlated then py2 -1, and hence portfolio risk is minimum at wy x o1 , W2 % O2

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Step 3

Hence, w1 = 3w2

Hence, 4w2 = 1; Hence, w2 = ¼ = 0.25 and w1 = 3 x ¼ = 0.75

Hence, the expected rate of return of the risk free portf...

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