Question

# Suppose that many stocks are traded in the market and that it is possible to borrow...

Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rƒ. The characteristics of two of the stocks are as follows: Stock Expected Return Standard Deviation A 5 % 45 % B 10 % 55 % Correlation = –1 a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be substituted for the risk-free asset?) (Round your answer to 2 decimal places.)

For two stock with a correlation of -1, it is possible to form an risk free portfolio without borrowing.

Weight of asset A in such portfolio Wa = SDb/(SDa + SDb)

standard deviation of stock A SDa = 45%

standard deviation of stock b SDb = 55%

=> Wa = 45/(45+55) = 45%

And weight of asset B Wb = 1-Wa = 1 - 0.45 = 55%

Expected return on this portfolio is weighted average return on its assets

=> E(p) = Wa*Ra + Wb*Rb = 0.45*5 + 0.55*10 = 7.75%

So,  expected rate of return on this risk-free portfolio = 7.75%

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