Question

What is the standard deviation of the market portfolio if the standard deviation of a fully diversified portfolio with a beta of 1.25 equals 18%

Answer 1

22.5%

Explanation:

let the standard deviation for market portfolio = σₙ

Also let the standard deviation for fully diversified portfolio = σₓ

To calculate fully diversified portfolio

fully diversified portfolio has σₓ = βσₙ

From the given question beta (β) = 1.25

Also standard deviation for market portfolio (σₙ) = 18% = 0.18

From the equation above, σₓ = βσₙ = 1.25×0.18 = 0.225

= 22.5% (converting to percentage)