Explanation

Target semideviation (also called downside deviation) measures the dispersion of returns below a specified target or minimum acceptable return. The formula for target semideviation is:

$\sigma_{target} = \sqrt{\frac{\sum_{i=1}^{n} \min(R_i - T, 0)^2}{n-1}}$

Where:

• $R_i$ = individual return
• $T$ = target return
• $n$ = number of observations

Key Insight: When the target return is set equal to the mean return ($T = \mu$), the target semideviation will be less than or equal to the standard deviation. This is because:

1. Standard deviation considers deviations from the mean in both directions (positive and negative)
2. Target semideviation only considers deviations below the target (negative deviations from the target)

In this specific case:

• Mean return ($\mu$) = 2.2%
• Target return ($T$) = 2.2%
• Standard deviation ($\sigma$) = 2.5%

Since the target equals the mean, the target semideviation will be less than the standard deviation because:

• Standard deviation includes all deviations from the mean (both above and below)
• Target semideviation only includes deviations below the mean
• By definition, the sum of squared deviations below the mean is less than the total sum of squared deviations from the mean

Mathematically: $\sigma_{target}^2 = \frac{\sum (R_i - \mu)^2 \cdot I(R_i < \mu)}{n-1}$ $\sigma^2 = \frac{\sum (R_i - \mu)^2}{n-1}$

Since $\sum (R_i - \mu)^2 \cdot I(R_i < \mu) \leq \sum (R_i - \mu)^2$, it follows that $\sigma_{target} \leq \sigma$.

Therefore, the correct answer is A: less than 2.5%.

Note: The target semideviation would only equal the standard deviation if all returns were below the target, which is not the case for a normally distributed portfolio with mean equal to the target.