Financial Risk Manager Part 1
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A financial consultant is conducting an analysis to estimate the projected returns for a newly established fund. This fund is designed to mirror the performance movements of the China Shanghai Composite Stock Market Index (SHANGHAI) but with a volatility that is double that of the index. The SHANGHAI index exhibits an expected annual return of 7.6% and a volatility rate of 14.0%. Additionally, the current risk-free rate is 3.0% per annum. Given that the correlation coefficient between the returns of the new fund and the index is perfectly positive (1.0), calculate the expected return of the fund using the Capital Asset Pricing Model (CAPM).
A financial consultant is conducting an analysis to estimate the projected returns for a newly established fund. This fund is designed to mirror the performance movements of the China Shanghai Composite Stock Market Index (SHANGHAI) but with a volatility that is double that of the index. The SHANGHAI index exhibits an expected annual return of 7.6% and a volatility rate of 14.0%. Additionally, the current risk-free rate is 3.0% per annum. Given that the correlation coefficient between the returns of the new fund and the index is perfectly positive (1.0), calculate the expected return of the fund using the Capital Asset Pricing Model (CAPM).
Explanation:
The expected return of the fund using the Capital Asset Pricing Model (CAPM) is calculated by the formula Ri = Rf + βi * (Rm - Rf), where:
- Ri is the expected return on the investment (the fund in this case).
- Rf is the risk-free rate.
- βi (beta) measures the fund's volatility relative to the market index.
- Rm is the expected return on the market index.
Given in the problem:
- Rf (risk-free rate) = 3.0% per year.
- Rm (expected return on the index) = 7.6% per year.
- Volatility of the index (σm) = 14.0%.
- Volatility of the fund (σi) = 2 * σm = 2 * 14.0% = 28.0%.
- Correlation between the fund's returns and the index (ρi,m) = 1.0, indicating a perfect positive correlation.
The beta (βi) is calculated using the formula: βi = (Cov(Ri, Rm) / σi) / (σm)
Since the correlation is perfect (ρi,m = 1.0), the covariance (Cov(Ri, Rm)) is equal to the product of the standard deviations of the fund and the index multiplied by the correlation: Cov(Ri, Rm) = σi * σm * ρi,m = 28.0% * 14.0% * 1.0
Now, substituting the values into the beta formula: βi = (28.0% * 14.0%) / (28.0%) = (14.0%)
Using the CAPM formula: Ri = 0.03 + 2.0 * (0.076 - 0.03) = 0.03 + 2.0 * 0.046 = 0.03 + 0.092 = 0.122 or 12.2%
Therefore, the expected return of the fund is 12.2%, which corresponds to option A.