The target downside deviation is calculated using the formula:

$\text{Target Downside Deviation} = \sqrt{\frac{\sum (X_i - B)^2 \cdot I(X_i \leq B)}{n - 1}}$

where:

• $X_i$ is the return for each period,
• $B$ is the target return (5%),
• $n$ is the total number of observations (5),
• $I(X_i \leq B)$ is an indicator function that includes only returns less than or equal to the target.

Steps:

1. Identify returns below the target (3%, 2%, 4%).
2. Calculate squared deviations for these returns: $(3-5)^2 = 4$, $(2-5)^2 = 9$, $(4-5)^2 = 1$.
3. Sum the squared deviations: $4 + 9 + 1 = 14$.
4. Divide by $n - 1 = 4$: $14 / 4 = 3.5$.
5. Take the square root: $\sqrt{3.5} \approx 1.87$, rounded to 1.9%.

Why not A or C?

• A incorrectly uses $n = 5$ instead of $n - 1$.
• C includes all returns, not just those below the target, leading to an overestimation.