Question

You own two risky assets, both of which plot on the security market line. Asset A has an expected return of 12% and a beta of .8. Asset B has an expected return of 18% and a beta of 1.4. If your portfolio beta is the same as the market portfolio, what proportion of your funds are invested in asset A?

Answer 1

Answer:

The proportion of funds invested in stock A is 66.67% or 2/3 of the total investment in the portfolio.

Explanation:

The portfolio beta is the sum of the weighted average of the individual stock betas that form up the portfolio. The portfolio beta is a measure of risk of the portfolio. The formula for portfolio beta is,

Portfolio beta = wA * Beta of A + wB * Beta of B + ... + wN * Beta of N

Where w is the weight of each individual stock in the portfolio.

The beta of the market portfolio is always equal to one. Thus, taking this as portfolio beta, we can calculate the weighatge of each stock in the portfolio.

Let x be the weighatge of investment in stock A

Then (1 - x) will be the weightage of stock B.

1 = x * 0.8  +  (1-x) * 1.4

1 = 0.8x + 1.4 - 1.4x

1 - 1.4  =  -0.6x

-0.4 / -0.6  = x

x = 0.6667 or 66.67% or 2/3

Thus, the proportion of funds invested in stock A is 66.67%