Investment Performance and Risk Statistics

The recent market volatility probably has you wondering how your strategy has fared through this unprecedented time. Disruptive market environments tend to reveal critical information about active managers that help investors see those that truly add value, and those that don’t. So, what should you do to evaluate your actively-managed strategy and how can you help your clients and prospects understand how your strategy performed during these difficult times? Read on.

Investment Performance in Up-Markets vs Down-Markets

During the long bull market run over the last 10+ years, investment firms have been able to effectively market their actively managed investment strategies with an emphasis on pure performance with little, if any, focus on risk. Consistent outperformance in up-markets is great, but it does not demonstrate how the strategy will react to a market downturn. Risk always goes hand-in-hand with performance and is increasingly important to discuss with clients and prospective clients as we navigate the highly volatile downturn we are currently experiencing.

Statistics used to present the results of actively managed strategies should do more than simply show the returns of the strategy vs. the returns of the benchmark. While returns show us where the strategy and benchmark ended and how much they changed over a stated period of time, they do not show how bumpy the road was to get there.

Investment performance and risk statistics should be used to help tell the story of how your firm actively manages the presented strategy. If your strategy description says that it will outperform in up-markets and provide protection on the downside, you should be presenting performance appraisal measures and risk statistics, such as Jensen’s Alpha, Sharpe ratio, Treynor ratio, up and down-market capture ratios, etc. that back-up those claims.

Types of Investment Risk

When assessing investment risk there are two main risk indicators to look at 1) systematic risk (i.e., market risk) and 2) total risk, which includes both systematic risk and unsystematic risk (i.e., security specific risk).

Systematic Risk Statistics

The most common way to assess the systematic risk of a strategy compared to its benchmark is by looking at the strategy’s beta. Beta measures the sensitivity of a strategy to market movements. If the strategy returns move perfectly in sync with the benchmark return then the strategy’s beta as compared to that benchmark is 1 (i.e., they are perfectly correlated).

If every time the benchmark goes up 1% the strategy goes up 1.2% and every time the benchmark goes down 1% the strategy goes down 1.2% then the beta is 1.2. This means that the portfolio has increased its systematic risk (perhaps through adding leverage, but otherwise replicated the index). In this case, the portfolio manager has increased the strategy’s systematic risk and volatility as compared to the benchmark, but the manager has not added alpha. This strategy will outperform on the upside and underperform on the downside.

To determine if the portfolio manager has “added alpha,” you can calculate Jensen’s alpha for the strategy. Jensen’s alpha measures how much the strategy outperformed its expected return, with the expected return determined based on the risk-free rate plus the beta-adjusted benchmark return. If the portfolio manager is truly “adding alpha” (through stock selection, over/underweighting sectors, etc.) and not just increasing systematic risk in their active management, then the strategy’s Jensen’s alpha should be positive.

Demonstrating positive alpha over a sustained period of time demonstrates to clients and prospects of the strategy that the active decisions made by the portfolio manager resulted in an increased return without increasing systematic risk.

Total Risk Statistics

Total risk is generally measured with standard deviation. Standard deviation has become more commonly presented, especially since the 3-year annualized ex-post standard deviation became required for GIPS Reports; however, this information may not be easily understood by readers of a performance report without some explanation.

If your investment strategy has returns that outperformed the benchmark AND has a standard deviation that is lower than the benchmark’s standard deviation, you can emphasize to your clients and prospects that you have outperformed the benchmark while taking less risk to do so (i.e., you had a less bumpy ride than the benchmark to get to your end result).

If your strategy’s returns did not outperform the benchmark, but your standard deviation is lower than that of the benchmark, you still may have outperformed the benchmark when looked at on a risk-adjusted basis. The most common way to assess this is with the Sharpe ratio.

The Sharpe ratio is one of the most popular performance appraisal measures. It measures excess return per unit of total risk. You can easily calculate this by taking your strategy’s average return minus the average risk-free rate and dividing that by the strategy’s standard deviation.

The Sharpe ratio is a ranking device, so the strategy’s Sharpe ratio on its own does not mean much. You should complete the same calculation for the benchmark and compare the two. If your strategy’s Sharpe ratio is higher than the Sharpe ratio of the benchmark then you can explain to your clients and prospects that you outperformed the benchmark on a risk-adjusted basis. For more information on how to calculate the Sharpe Ratio, see our latest blog What is the Sharpe Ratio.

In the volatile markets we are facing at the moment, outperforming the market (or your strategy’s benchmark) on a risk-adjusted basis may be more important than having outright higher returns. With the high volatility we are currently experiencing, returns could be changing significantly every day. The presentation of returns without consideration, discussion, and demonstration of risk only tells one part of the story.

By including risk as a second dimension of performance you will be able to exhibit skill over luck and demonstrate how your strategy is prepared to perform regardless of the market conditions we face over the coming months and years.

Tools to Calculate Risk Statistics

Depending on your strategy, there are a number of other statistics that can help you analyze how your investment performance has fared through the current market conditions. If you would like to calculate some of these measures on your own, please see Longs Peak’s Performance Appraisal Statistics Cheat Sheet for formulas.

In addition, Longs Peak calculates performance appraisal measures and risk statistics for our clients that can be used internally as part of your portfolio management feedback loop, and externally to help demonstrate the success of your active management to clients and prospects. Below are some samples of the reports we create. We would be happy to calculate or discuss any of these statistics with your firm.


If you have questions about investment performance and risk statistics, we would be love to help. Longs Peak’s professionals have extensive experience helping firms with their investment performance needs. We can do anything from providing ad-hoc investment performance calculations to operating as your fully outsourced investment performance team. Please to email Sean Gilligan directly at for more information.

What is the Sharpe Ratio?

The Sharpe Ratio is calculated as the strategy’s mean return minus the mean risk-free rate divided by the standard deviation of the strategy. The Sharpe Ratio measures the excess return for taking on additional risk.

The Sharpe Ratio is one of the most popular performance appraisals measures and is used to compare and rank managers with similar strategies.

Sharpe Ratio Formula

What is a Good Sharpe Ratio?

The Sharpe Ratio is a ranking device so a portfolio’s Sharpe Ratio should be compared to the Sharpe Ratio of other portfolios rather than evaluated independently.

Since the Sharpe Ratio measures excess return per unit of risk, investors prefer a higher Sharpe Ratio when comparing similarly managed portfolios.

As an example, suppose two similar strategies, Strategy A and Strategy B, had the following characteristics over one year. For this period, the average risk-free rate is 0.1%.

Please note: the Sharpe Ratio calculation below has monthly measures as inputs and then annualizes the final result.

Although the strategies perform similarly, the Sharpe Ratios differ significantly due to their differences in volatility (i.e., standard deviation). Because Strategy B has a much higher Sharpe Ratio, it would be preferred over Strategy A to an investor deciding between the two.

Sharpe Ratio Interpretation

The Sharpe Ratio is intended to be used for strategies with normal return distributions; it should not be used for a strategy that treats upside and downside volatility differently. The Sharpe Ratio treats both types of volatility the same. For example, if a manager is looking for high reward investments then upside volatility can be a good thing, but the Sharpe Ratio penalizes the strategy for any type of volatility. For return streams with non-normal distributions, such as hedge funds, the Sortino Ratio may be more appropriate.

Why is the Sharpe Ratio Important?

The Sharpe Ratio is important when assessing portfolio performance because it adjusts for risk. Comparing returns without accounting for risk does not provide a complete picture of the strategy.

The Sharpe Ratio is commonly used in investment strategy marketing materials because it is the most widely known and understood measure of risk-adjusted performance.

Sharpe Ratio Calculation: Using Arithmetic Mean or Geometric Mean

Because the Sharpe Ratio compares return to risk (through Standard Deviation), Arithmetic Mean should be used to calculate the strategy return and risk-free rate’s average values. Geometric Mean penalizes the return stream for taking on more risk. However, since the Sharpe Ratio already accounts for risk in the denominator, using Geometric Mean in the numerator would account for risk twice. For more information on the use of arithmetic vs. geometric mean when calculating performance appraisal measures, please check out Arithmetic vs Geometric Mean: Which to use in Performance Appraisal.

Annualized Sharpe Ratio

When calculating the Sharpe Ratio using monthly data, the Sharpe Ratio is annualized by multiplying the entire result by the square root of 12.

Arithmetic vs Geometric Mean: Which to use in Performance Appraisal

Most performance appraisal measures utilize a mean return in its calculation. This can be in the form a geometric mean or a simple arithmetic average. Because both types of means can be used, it raises the question: Which measure should be applied?

When calculating performance, we are accustomed to calculating returns geometrically (i.e., including compounding). Because of this, many investment managers use the geometric mean in appraisal calculations as it is easy to use the reported time-weighted return, rather than separately determining the arithmetic mean. But using geometric mean is not the most appropriate choice when evaluating risk-adjusted appraisal measures.

When calculating performance appraisal measures that compare return to risk, such as Sharpe ratio, the return used in the numerator of the ratio should be the arithmetic mean of the return stream, not the geometric mean. In many cases, the difference between using the arithmetic mean versus geometric mean will be immaterial; however, the greater the volatility in the return stream, the more material the difference will be. Let’s look at a simple example that demonstrates this effect:

Strategies with significant volatility have lower geometric means than arithmetic means (7.5% vs. 8.4% for Portfolio 2 above). This is because the geometric mean penalizes the return stream for risk-taking. In the case of the Sharpe Ratio, the standard deviation (which also accounts for risk-taking) in the denominator will be higher as a result of this higher volatility (1.5% for Portfolio 1 vs. 14.2% for Portfolio 2). In this case, using the geometric mean therefore results in a penalty for risk in both the numerator and denominator of the ratio.

Because risk is already being accounted for in the denominator, there is no need to include it in the numerator; in fact, including it would be double-counting the risk taken. As a result, for measures like Sharpe Ratio, it is more appropriate to use the arithmetic mean than geometric mean.

Although, in many cases, using the geometric return will not have a material effect on the outcome when comparing risk-scaled performance measures, it is technically more accurate to use the arithmetic mean. Its implications are more relevant when evaluating strategies with higher volatility.