what is the standard deviation of returns on a well-diversified portfolio with a beta of 1.25 if the standard deviation of the market portfolio equals 18%?

the standard deviation of the portfolio is σP = 22.5%

Step-by-step explanation:

since the variance of the portfolio σP² is

σP² = β²*σM²+σ² (e)

where

β = Portfolio's beta

σM = standard deviation of the market portfolio

σ² (e) = variance of the unexpected returns of the portfolio (diversifiable risk)

for a well-diversified portfolio σ² (e) = 0, then

σP² = β²*σM²

σP=β*σM

replacing values

σP = β*σM = 1.25*0.18 = 0.225 = 22.5%

σP = 22.5%