Answer:
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%
