Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio, in equilibrium, will be the risk-free rate. To find the proportions of this portfolio

[with the proportion wAinvested in Stock A and wB= (1 wA) invested in Stock B], set the standard deviation equal to zero.

With perfect negative correlation, the portfolio standard deviation is: P= Absolute value of [wAA-wB B]0 = 5% wA[10% (1 wA)]

wA= 0.6667

The expected rate of return for this risk-free portfolio is:E(r) = (0.6667 10%) + (0.3333 15%) = 11.67%

Therefore, the risk-free rate is: 11.67%

Question is why P= Absolute value of [wAA-wB B]?