# Appraisal Measures

Performance appraisal is typically done using a set of appraisal measures. Appraisal metrics measure the risk-adjusted performance of a manager to distinguish between luck and skill. Performance appraisal is the final step of the performance evaluation process

On this page, we discuss 7 popular appraisal measures in more detail. The description we provide here is a brief introduction to each measure. Some of the measures are discussed in more detail elsewhere and we link to those pages. The measures we will discuss are the Sharpe ratio, the Treynor Ratio, the Information Ratio, the Appraisal Ratio, the Sortino Ratio, Capture Ratios, and Drawdown.

## Sharpe ratio

The Sharpe ratio is calculated as the excess return over the risk-free rate (numerator) divided by the standard deviation (denominator). It is the most popular risk-adjusted performance measure. One drawback with the Sharpe ratio is that it does not differentiate between volatility that is upside versus downside. Therefore, with the Sharpe ratio, there is a penalty for all volatility, even if it is good volatility.

## Treynor ratio

The Treynor ratio is similar to the Sharpe ratio, but the denominator for the Treynor ratio is beta. Thus, the Treynor ratio only considers systematic risk rather than total risk. With the Treynor ratio, the universe of appropriate benchmarks is limited to only those that assume efficient markets. The Treynor ratio is only useful in evaluating portfolios that have systematic risk and do not have unsystematic risk.

## Information ratio

The information ratio is used to measure a portfolio’s performance against the benchmark but accounts for differences in risk. The numerator is the difference between the mean returns of the portfolio and the benchmark, respectively. The denominator is known as the tracking risk.

## Appraisal ratio

The appraisal ratio is calculated as alpha divided by standard deviation of the residual/unsystematic risk. ALpha is excess return, which is calculated as the return earned by the portfolio minus the return suggested by CAPM. The appraisal ratio is therefore the ratio of returns from active management over the risks of active management.

## Sortino ratio

The Sortino ratio only considers the standard deviation of the downside risk. That is in contrast to the Sharpe ratio, which considers total risk. The formula for the Sortino ratio looks as follows

where rT is the minimum acceptable return or MAR, sigma is the target semi-standard deviation or target semideviation.

The Sortino ratio is more appropriate for investments with non-normal (nonsymmetrical) return distributions. For investments that have non symmetrical or skewed return distributions, such as hedge funds or options, the Sortino ratio is more appropriate than the Sharpe ratio.

## Capture ratios

Capture ratios determine the manager’s relative performance when markets are up or down:

• The upside capture ratio is the return when the market is up divided by the market returns when markets are up
• The downside capture ratio is the return when the market down divided by the market return when markets are down.

Ideally, the upside capture ratio should be higher than 1 and the downside capture ratio should be smaller than 1. Finally, the capture ratio is equal to de upside capture ratio divided by the downside capture ratio.

The interpretation of the capture ratio is the following:

• capture ratio = 1: symmetrical return profile
• capture ratio > 1: positively asymmetrical (convex) return profile
• capture ratio < 1: negatively asymmetrical (concave) retur nprofile

A convex return profile implies that there is greater upside capture than downside capture, which is a desirable trait.

## Drawdown

Drawdown duration is the total time required to fully recover a drawdown from when the drawdown commences up to when the cumulative drawdown is zero. Maximum drawdown occurs at the very end of the drawdown phase and at the very start of the recovery phase: it is the point at which the cumulative drawdown is at its highest.

## Summary

We discussed different appraisal measures that can be used to assess whether an investment manager exhibits skill or was just lucky.