Suppose that many stocks are traded in the market and that it is possible to bor

Question

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 9 % 45 % B 13 % 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.) Rate of return % b. Could the equilibrium rƒ be greater than 10.80%? Yes No

Explanation / Answer

a.

Since A & B are perfectly negatively correlated, a risk-free portfolio can be created and its rate of return in equilibrium will be the risk free rate. To find the proportions of this portfolio (with WA invested in A and WB = 1 – WA), set the standard deviation equal to zero. With perfectly negative correlation, the portfolio standard deviation reduces to

P= Abs[WAA - WB B ]
0 = 45WA – 55(1 – WA)
WA = 0.55

So, WB = 1 – 0.55 = 0.45

The expected rate of return on this risk-free portfolio:
=> 0.55x0.09 + 0.45x0.13 = 10.80%

b. This can not be greater than 10.80%

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.