Question

Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, I f. The characteristics of two of the stocks are as follows: Stock Expected Return Standard Deviation 9% 608 5% 408 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 rf be greater than 6.60%? Yes O No

Answer 1

Since there is a perfect negative correlation between the stocks, it means that the stocks move in opposite directions. So the portfolio variance will become equal to 0.Hence a risk-free portfolio can be created and the rare of return for this portfolio in the equilibrium will always be the risk free rate .To calculate the expected return for the portfolio, we should find the value of weights for each stock.

wA = weight of asset A
wB = weight of asset B
sdA = standard deviation of asset A
sdB = standard deviation of asset B
p = correlation of A and B

portfolio variance = wA^2*sdA^2 + wB^2*sdB^2 + 2*wA*wB*p*sdA*sdB

Here p=-1 and implies wAsdA=wBsdB

Let wb be (1-wA)

0.60*wA=0.40* (1-wA) and wA=0.40 and wB= 0.60

E(r)= W_a*E(r_a)+ W_b * E(r_b)

E(R)=(0.40*0.09)+(0.60*0.05)= 0.036+0.003= 0.039 or 39%

b)No as te stocks are perfectly negatively correlated their return has to be same as risk free rate whch is 39%