, PLEASE USE THIS DOCUMENT AS A GUIDE ONLY
QUESTION 1
1. A fund manager is evaluating an equity investment and its risk relative to the market.
1.1. The risk-free rate is 6%, and the return from the market last year was 11%. A hedge fund
manager with a beta of 1.2 has an alpha of 2%. Given the performance of the market last year,
what annual return did the hedge fund manager earn?
The annual return earned by the hedge fund manager is 14%.
Calculate the expected return based on the Capital Asset Pricing Model (CAPM) using the market's
actual return. This is the return the manager would be expected to earn without any alpha.
Formula: Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)
Expected Return = 6% + 1.2 × (11% - 6%)
Expected Return = 6% + 1.2 × 5%
Expected Return = 6% + 6%
Expected Return = 12%
Add the manager's alpha to the expected return to find the actual return earned.
Actual Return = Expected Return + Alpha
Actual Return = 12% + 2%
Actual Return = 14%
According to the text, "Alpha represents the extra return made from superior portfolio management...
The return earned by the hedge fund manager with zero alpha would be... 12%. Because the alpha
equals 4%, the hedge fund manager's return was..." (Hull, 2023, p. 73). Following this same logic,
the manager earned 14%.
1.2. The return of the share depends on economic conditions as follows:
a) Calculate the expected return.
The expected return is the weighted average of the possible returns, where the weights are the
probabilities of each state occurring (Hull, 2023, p. 2).
Expected Return = (0.4 × 18%) + (0.4 × 10%) + (0.2 × -5%)
Expected Return = 7.2% + 4.0% - 1.0%
Expected Return = 10.2%
b) Calculate the variance and standard deviation.
The variance is the probability-weighted average of the squared deviations of each return from the
expected return. The standard deviation is the square root of the variance (Hull, 2023, p. 3).
Variance (σ²) = 0.4 × (18% - 10.2%)² + 0.4 × (10% - 10.2%)² + 0.2 × (-5% - 10.2%)²
Variance (σ²) = 0.4 × (7.8%)² + 0.4 × (-0.2%)² + 0.2 × (-15.2%)²
Variance (σ²) = 0.4 × (0.006084) + 0.4 × (0.000004) + 0.2 × (0.023104)
Variance (σ²) = 0.0024336 + 0.0000016 + 0.0046208
Variance (σ²) = 0.007056 or 70.56%²
QUESTION 1
1. A fund manager is evaluating an equity investment and its risk relative to the market.
1.1. The risk-free rate is 6%, and the return from the market last year was 11%. A hedge fund
manager with a beta of 1.2 has an alpha of 2%. Given the performance of the market last year,
what annual return did the hedge fund manager earn?
The annual return earned by the hedge fund manager is 14%.
Calculate the expected return based on the Capital Asset Pricing Model (CAPM) using the market's
actual return. This is the return the manager would be expected to earn without any alpha.
Formula: Expected Return = Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)
Expected Return = 6% + 1.2 × (11% - 6%)
Expected Return = 6% + 1.2 × 5%
Expected Return = 6% + 6%
Expected Return = 12%
Add the manager's alpha to the expected return to find the actual return earned.
Actual Return = Expected Return + Alpha
Actual Return = 12% + 2%
Actual Return = 14%
According to the text, "Alpha represents the extra return made from superior portfolio management...
The return earned by the hedge fund manager with zero alpha would be... 12%. Because the alpha
equals 4%, the hedge fund manager's return was..." (Hull, 2023, p. 73). Following this same logic,
the manager earned 14%.
1.2. The return of the share depends on economic conditions as follows:
a) Calculate the expected return.
The expected return is the weighted average of the possible returns, where the weights are the
probabilities of each state occurring (Hull, 2023, p. 2).
Expected Return = (0.4 × 18%) + (0.4 × 10%) + (0.2 × -5%)
Expected Return = 7.2% + 4.0% - 1.0%
Expected Return = 10.2%
b) Calculate the variance and standard deviation.
The variance is the probability-weighted average of the squared deviations of each return from the
expected return. The standard deviation is the square root of the variance (Hull, 2023, p. 3).
Variance (σ²) = 0.4 × (18% - 10.2%)² + 0.4 × (10% - 10.2%)² + 0.2 × (-5% - 10.2%)²
Variance (σ²) = 0.4 × (7.8%)² + 0.4 × (-0.2%)² + 0.2 × (-15.2%)²
Variance (σ²) = 0.4 × (0.006084) + 0.4 × (0.000004) + 0.2 × (0.023104)
Variance (σ²) = 0.0024336 + 0.0000016 + 0.0046208
Variance (σ²) = 0.007056 or 70.56%²
