这题怎么理？beta为什么等于2？

问题如下：

Question An investment advisor is analyzing the range of potential expected returns of a new fund designed to replicate the directional moves of the China Shanghai Composite Stock Market Index (SHANGHAI) but with twice the volatility of the index. SHANGHAI has an expected annual return of 7.6% and a volatility of 14.0%, and the risk-free rate is 3.0% per year. Assuming the correlation between the fund’s returns and that of the index is 1.0, what is the expected return of the fund using the CAPM?

选项：

A.

12.2%

B.

19.0%

C.

22.1%

D.

24.6%

解释：

Explanation:

A is correct. If the CAPM holds, then Ri = Rf + βi * (Rm – Rf).

Beta (βi), which determines how much the return of the fund fluctuates in relation to the index return is expressed as follows:

where i and m denote the new fund and the index, respectively, and Ri = expected return on the fund, Rm = expected return on the index, Rf = risk-free rate, σi = volatility of the fund, σm = volatility of the index, Cov(Ri,Rm) = covariance between the fund and the index returns, and Corr(Ri,Rm) = correlation between the fund and the index returns.

If the new fund has twice the volatility of the index, then σi = 2σi = 2σm, and given that Corr(Ri,Rm) = 1.0, the beta of the new fund then becomes:

Therefore, using CAPM, Ri = Rf + βi * (Rm – Rf) = 0.03 + 2.0*(0.076 – 0.03) = 0.1220 = 12.2%.

Section: Foundations of Risk Management

Learning Objective: Apply the CAPM in calculating the expected return on an asset.

Reference: Global Association of Risk Professionals. Foundations of Risk Management. New York, NY: Pearson, 2022. Chapter 5. Modern Portfolio Theory and the Capital Asset Pricing Model.