Given ABC's portfolio is expected to return 14% this year with a risk-free rate of 5% and a market return of 15%, what is the portfolio's beta?

Given ABC's portfolio is expected to return 14% this year with a risk-free rate of 5% and a market return of 15%, what is the portfolio's beta?

• A. 0.8
• B. 0.9
• C. 1.0
• D. 1.2

Answer: (B)

The main idea is CAPM: a portfolio’s expected return equals the risk-free rate plus its beta times the market risk premium. The beta shows how much the portfolio tends to move with the market. To find beta, use beta = (Rp − Rf) / (Rm − Rf). Plugging in the numbers: Rp = 14%, Rf = 5%, Rm = 15%. The market premium is 15% − 5% = 10%. So beta = (14% − 5%) / (10%) = 9% / 10% = 0.9. A beta of 0.9 means the portfolio is expected to be a bit less volatile than the market, moving about 0.9 times the market's moves. If the portfolio had a higher required return with the same rates, the beta would be higher; if it were lower, the beta would be lower.

The main idea is CAPM: a portfolio’s expected return equals the risk-free rate plus its beta times the market risk premium. The beta shows how much the portfolio tends to move with the market. To find beta, use beta = (Rp − Rf) / (Rm − Rf).

Plugging in the numbers: Rp = 14%, Rf = 5%, Rm = 15%. The market premium is 15% − 5% = 10%. So beta = (14% − 5%) / (10%) = 9% / 10% = 0.9.

A beta of 0.9 means the portfolio is expected to be a bit less volatile than the market, moving about 0.9 times the market's moves. If the portfolio had a higher required return with the same rates, the beta would be higher; if it were lower, the beta would be lower.