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 10 % 25 % B 18 % 75 % 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.) b. Could the equilibrium rƒ be greater than 12.00%?

a. The expected rate of return on this risk-free portfolio is 12%.

b. No, the equilibrium rƒ CANNOT be greater than 12.00%. This is because the equilibrium rƒ must be equal to the expected rate of return on this risk-free portfolio.

Explanation:

Given:

The characteristics of two of the stocks are as follows:

Stock            Expected Return        Standard Deviation

  A                        10%                                25%

  B                        18%                                75%

Correlation = –1

a. Calculate the expected rate of return on this risk-free portfolio?

SDA = Standard Deviation of Stock A = 25%, or 0.25

SDB = Standard Deviation of Stock B = 75%, or 0.75

WA = Weight of Stock A = ?

WB = Weight of Stock B = (1 - WA)

Portfolio standard deviation = (WA * SDA) – ((1 - WA) * SDB) = (WA * 0.25) – ((1 - WA) * 0.75)

With a perfect negative correlation, Portfolio standard deviation has is taken to be zero. Therefore, we have:

0 = (WA * 0.25) - ((1 - WA) * 0.75)

0 = 0.25WA - (0.75 - 0.75WA)

0 = 0.25WA - 0.75 + 0.75WA

0.75 = 0.25WA + 0.75WA

WA = 0.75

Therefore, we have:

WB = 1 - WA = 1 - 0.75 = 0.25

Portfolio expected rate of return = (WA * Expected Return of Stock A) + (WB * Expected Return) = (0.75 * 10%) + (0.25 * 18%) = 0.12, or 12.00%

Therefore, the expected rate of return on this risk-free portfolio is 12%.

b. Could the equilibrium rƒ be greater than 12.00%?

No, the equilibrium rƒ CANNOT be greater than 12.00%. This is because the equilibrium rƒ must be equal to the expected rate of return on this risk-free portfolio.

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