Suppose that there are many stocks in the security market and that the characteristics of stocks A and B are given as follows:
Stock | Expected Return | Standard Deviation | ||||||
A | 14 | % | 7 | % | ||||
B | 18 | 9 | ||||||
Correlation = –1 | ||||||||
Suppose that it is possible to borrow at the risk-free rate, rf. What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B.) (Do not round intermediate calculations. Round your answer to 3 decimal places.)
Risk Free Rate? %
Given,
Stock | Expected Return | Standard Deviation |
A | 14% | 7% |
B | 18% | 9% |
Correlation = –1 |
Since Correlation between two stock is -1, creating a risk free portfolio is possible using weights
WA = SDB/(SDA + SDB)
So, WA = 9/(7+9) = 0.5625
and WB = 1 - WA = 1-0.5625 = 0.4375
So, risk free rate = weighted average return of stocks = 0.5625*14 + 0.4375*18 = 15.75%
value of the risk-free rate = 15.75%
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