Portfolio Evaluation

How is batting average defined? Why could batting average be a misleading performance metric?

Batting average measures the percentage of the time that a manager outperforms the benchmark: Batting Average = number of periods with positive active return / number of periods in sample This is a very crude way to measure relative performance because it throws away all the information about the magnitude of under- or overperformance and risk!

What is the difference between the Sharpe ratio and the information ratio? Can you calculate each using a set of observed portfolio returns

Both ratios are used to measure the performance of investment portfolios. The Sharpe ratio measures the excess return of a portfolio compared to the risk-free rate per unit of risk (standard deviation), while the information ratio measures the excess return of a portfolio compared to its benchmark per unit of active risk (tracking error). A high Sharpe ratio indicates a portfolio with high risk-adjusted returns, while a high information ratio indicates a portfolio with high excess returns compared to its benchmark per unit of active risk.

If a manager has a Sharpe ratio lower than the benchmark, what does this say about the manager's active return?

If a manager has a Sharpe ratio lower than the benchmark, it indicates that the manager's active return (i.e., excess return over the benchmark) is not sufficient to compensate for the additional risk taken on by the manager compared to the benchmark. In other words, the manager is not generating enough excess return to justify the additional risk taken. The Sharpe ratio measures the risk-adjusted performance of a portfolio or manager, and a lower Sharpe ratio suggests that the manager is not effectively managing risk to generate returns.

What is market timing and how is it related to factor tilting?

Market timing is the ability to predict the direction of the market and adjust the portfolio's exposure to market risk accordingly. A manager with market timing ability has 0 < βp < 1 and γp > 0. If so, on average the portfolio is correctly positioned to be defensive when the benchmark is down, and also correctly positioned to be aggressive when the benchmark is doing well.

How are portfolio drawdowns defined? What is the recovery period?

Portfolio drawdown is a measure of the peak-to-trough decline in the value of a portfolio over a certain time period. Specifically, it measures the percentage decline from the highest value of the portfolio to the lowest value that occurs before a new peak is reached. Recovery period measures the amount of time required to earn back losses during the maximum drawdown in order to return to the high water mark.

How do you compute the M2 of an active portfolio? What is the relation between the Sharpe ratio and M2? Why would we want to know the M2 of a portfolio in addition to its Sharpe ratio?

The Modigliani-Modigliani or M-squared measure was proposed as an alternate way of comparing portfolios with different Sharpe ratios. Instead of a ratio, the measure expresses the risk-adjusted performance as an adjusted return, that of a portfolio with the same risk as a market benchmark. Knowing the M2 of a portfolio in addition to its Sharpe ratio can provide a more comprehensive understanding of the portfolio's performance and risk characteristics. It can help to identify whether a portfolio is generating alpha through skillful security selection or by taking on excessive systematic risk.

Considering the above risk-adjusted portfolio metrics (Sharpe ratio, Treynor ratio, Sortino ratio, information ratio, alpha), which is the overall best measure for evaluating the performance of an active manager, and why?

The Sharpe ratio is a good measure of investment efficiency if we are standard mean-variance optimizers thinking about our investments as a whole. More relevant to an active manager evaluated against a benchmark is the information ratio. When evaluating a manager for possible inclusion in a portfolio consisting of many managers, the Treynor ratio is more relevant than the Sharpe ratio. The Sortino ratio is similar to the Sharpe ratio except that it replaces total volatility by a measure of downside risk.

Is it possible for an active manager to be a good manager and have a bad Sharpe ratio? Is it possible for an active manager to have a good information ratio and a bad Sharpe ratio?

The Sharpe ratio only measures the excess return per unit of risk, so a manager could have a strategy with higher risk but also higher returns that still provides value to investors despite a lower Sharpe ratio. Similarly, it is possible for an active manager to have a good information ratio and a bad Sharpe ratio. The information ratio measures the excess return per unit of active risk, while the Sharpe ratio measures the excess return per unit of total risk. Therefore, a manager may be skilled at generating alpha relative to their benchmark but may take on additional uncompensated risk, resulting in a lower Sharpe ratio.

How is the Sortino ratio calculated, what does it measure, and how is it related to the Sharpe ratio? What are the common assumptions for the MAR (minimum acceptable return) used to define downside risk?

The Sortino ratio is related to the Sharpe ratio in that they both measure risk-adjusted performance, but the Sortino ratio focuses specifically on downside risk, while the Sharpe ratio considers total risk. The common assumption for the MAR used to define downside risk is that investors are only concerned with returns that fall below a certain level. This level is often set at the risk-free rate or some other benchmark rate, and is used to capture the idea that investors are only concerned with returns that are less than what they could have earned by investing in a risk-free asset. In practice, the MAR used may vary depending on the investor's preferences and risk tolerance. A more conservative investor may set a higher MAR, while a more aggressive investor may set a lower MAR.

What is the Treynor ratio and how is it related to the Sharpe ratio? When is it appropriate to evaluate a portfolio manager on the basis of their Treynor ratio? What is the Treynor ratio of the Security Market Line?

The Treynor ratio is a measure of investment efficiency, it is the return received per unit of systematic risk. The Treynor ratio and Sharpe ratio are both metrics for measuring risk-adjusted performance, but they differ in how they measure risk. The Sharpe ratio uses the portfolio's total risk (standard deviation), while the Treynor ratio uses the portfolio's beta as a proxy for systematic risk. The Treynor ratio is useful for evaluating portfolio managers who base their investment decisions on systematic risk (low idiosyncratic risk), such as those who follow the capital asset pricing model (CAPM). The Treynor ratio of the Security Market Line is equal to the market risk premium, which is the difference between the expected return on the market portfolio and the risk-free rate, divided by the beta of the market portfolio.

How are upside and downside capture calculated and what do they measure? How are they used to assess the market timing skill of a manager?

To assess the market timing skill of a manager, one can look at their upside and downside capture ratios during periods of market growth and decline, respectively. If a manager consistently outperforms the benchmark during periods of market growth while limiting losses during periods of market decline, it suggests that they may have a skill in timing the market.

What is the Henrikkson-Merton model for market timing? How is it estimated? How are the resulting estimates interpreted?

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