If the new fund has twice the volatility of the index, then σi = 2σi = 2σm-有问必答-品职教育专注CFA ESG FRM CPA 考研等财经培训课程

If the new fund has twice the volatility of the index, then σi = 2σi = 2σm

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问题如下：

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：

12.2%

19.0%

22.1%

24.6%

解释：

中文解析：

A正确。如果CAPM成立，那么Ri = Rf + βi * (Rm – Rf).

βi决定了基金的收益率随着指数收益率的变化而变化的程度。

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

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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:

${\beta_{i}=\frac{\operatorname{Cov}\left(\mathrm{R}_{i}, \mathrm{R}_{m}\right)}{\sigma_{m}^{2}}=\frac{\operatorname{Corr}\left(\mathrm{R}_{i}, \mathrm{R}_{m}\right) * \sigma_{i} \sigma_{m}}{\sigma_{m}^{2}}=\frac{\operatorname{Corr}\left(\mathrm{R}_{i}, \mathrm{R}_{m}\right) * \sigma_{i}}{\sigma_{m}}}$

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:

$\beta_{i}=\frac{\operatorname{Corr}\left(\mathrm{R}_{i}, \mathrm{R}_{m}\right) * 2 \sigma_{m}}{\sigma_{m}}=1.0 * 2.0=2.0$

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

= 0.1220 = 12.2%.

If the new fund has twice the volatility of the index, then σi = 2σi = 2σm

volatility不是方差吗？不是σi的平方= 2倍的σm的平方？

If the new fund has twice the volatility of the index, then σi = 2σi = 2σm

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