Free CFA Level III: Private Wealth Performance Measurement Practice Questions

C is correct.

The appraisal ratio is calculated as the portfolio's alpha (the return earned beyond what is explained by systematic risk exposure) divided by the portfolio's unsystematic (residual or idiosyncratic) risk. It measures the manager's ability to generate abnormal returns per unit of diversifiable risk taken.

A is correct. The appraisal ratio scales the manager's Jensen's alpha by the non-systematic (residual) risk taken to produce it, using the standard deviation of the regression residuals as the denominator:

$$AR = \frac{\alpha}{\sigma_{\varepsilon}} = \frac{1.35\%}{4.50\%} = 0.30$$

Interpreted for the committee, Ironwood generated 0.30 units of beta-adjusted excess return per unit of residual risk relative to its own style benchmark.

A is correct. The information ratio divides active return by tracking error, both measured against the custom small-cap value index in Exhibit 1:

$$IR_{\text{Ardent}} = \frac{1.8\%}{6.0\%} = 0.30$$

$$IR_{\text{Brightmoor}} = \frac{0.0\%}{2.0\%} = 0.00$$

$$IR_{\text{Cassia}} = \frac{3.2\%}{4.5\%} = 0.71$$

The Sortino ratio divides the return in excess of the 3.0% MAR by the downside deviation measured against that MAR:

$$\text{Sortino}_{\text{Ardent}} = \frac{11.4\% - 3.0\%}{6.0\%} = 1.40$$

$$\text{Sortino}_{\text{Brightmoor}} = \frac{9.6\% - 3.0\%}{4.8\%} = 1.38$$

$$\text{Sortino}_{\text{Cassia}} = \frac{12.8\% - 3.0\%}{8.0\%} = 1.23$$

Cassia Street earned the most active return per unit of tracking error, but its 8.0% downside deviation and -31.0% maximum drawdown leave it last on the downside-focused measure the second trustee asked for, while Ardent Ridge ranks first on the Sortino ratio by a narrow margin over Brightmoor. The two rankings answer different questions: the information ratio speaks to benchmark-relative skill, the Sortino ratio to the shortfall risk the trust bears in absolute terms, which is why Vega reports both before the committee weighs Cassia Street's 95 bp fee against its drawdown history.