Question

Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 18%. The standard deviation on the factor portfolio is 16%. The beta of the well-diversified portfolio is approximately:_________
Consider the single-factor APT. Stocks A and B have expected returns of 15% and 18%, respectively. The risk-free rate of return is 6%. Stock B has a beta of 1.0. If arbitrage opportunities are ruled out, stock A has a beta of:__________

Answer 1

Answer and Explanation:

The computation is shown below:

1. For Beta^2

= Standard Deviation of Well Diversified Portfolio^2 ÷ Standard Deviation of factor Portfolio^2

= (18%^2 ÷ 16%^2)^0.5

= 18 ÷ 16

= 1.125 or 1.13

And,

2. Expected Return = Risk free rate + Beta ×Factor

18% = 6% + 1 × F

F = 12%

The Beta of A is

= (15% -  6%) ÷ 12%

= 0.75

We simply applied the above formula so that the correct value could come

And, the same is to be considered