Hedge Fund Quantitative Analysis: Measuring Returns and Risk

At this point in the book, we have collected the basic info from the hedge fund manager, done an initial review, and had a phone interview. Now comes the numbers part. Chapter 6 of “Hedge Fund Analysis” by Frank J. Travers is about crunching performance data, and it is packed with formulas and statistics.

Don’t worry. I will keep it simple.

Where We Are in the Process

Here’s the thing - up until now, most of the work has been qualitative. Talking to people, reading documents, forming opinions. But now we are at a tipping point. If the fund passes these quantitative tests, the workload goes up significantly. We are committing to a full portfolio review, onsite meetings, background checks, the whole deal.

So the numbers better look good.

Travers uses the fictional “FCM” fund as his case study and compares it against four other hedge funds plus some market indexes (S&P 500, Russell 2000, HFRI Equity Hedge Index). Let’s go through the key metrics he covers.

Absolute Return Measures

These are the metrics that tell you how well a fund performed on its own or compared to a benchmark. No fancy regression math yet, just straightforward performance ratios.

Sharpe Ratio

Probably the most popular hedge fund metric out there. The formula is:

Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Portfolio Volatility

In plain English: how much extra return did you get for each unit of risk you took? Higher is better.

In Travers’ analysis, FCM and Fund Three had the best Sharpe ratios. The S&P 500 and Russell 2000 actually had negative Sharpe ratios for that period (Dec 2006 to Nov 2011, which includes the 2008 crisis).

Information Ratio

Similar to Sharpe, but instead of subtracting the risk-free rate, you subtract a benchmark return, and divide by tracking error.

Information Ratio = (Portfolio Return - Benchmark Return) / Tracking Error

This one is often viewed as a measure of the manager’s skill. It answers: how much extra return did you generate per unit of active risk? FCM and Fund Three came out on top again.

MAR and Calmar Ratios

These measure return versus drawdown risk. The MAR ratio uses data since inception, the Calmar ratio uses the last three years.

MAR Ratio = Annualized Return / Maximum Drawdown

Pretty intuitive. If a fund returned 10% per year but had a maximum drawdown of 25%, the MAR ratio is 0.4. But if another fund returned 8% with only an 8% drawdown, its MAR ratio is 1.0. Clearly better.

Fund Three had the highest MAR ratio because it had the smallest drawdown (only -8.2%). FCM came in second. The others scored much lower, with drawdowns ranging from -25% to -54%.

Sortino Ratio

Here’s the problem with the Sharpe ratio: it penalizes both upside and downside volatility equally. But as an investor, you don’t care about upside volatility. Nobody complains when returns are higher than expected.

The Sortino ratio fixes this by only looking at downside deviation in the denominator.

Sortino Ratio = (Portfolio Return - Minimum Acceptable Return) / Downside Deviation

FCM and Fund Three came out on top by a wide margin here too.

Omega Ratio

Most of these ratios assume returns follow a normal bell curve distribution. But hedge fund returns often don’t. The Omega ratio handles this by using the actual return distribution, not a theoretical one. It calculates the likelihood of achieving a target return.

Higher Omega = higher chance of hitting your target. Simple as that.

Absolute Risk Measures

Now we flip to the other side of the coin. These metrics focus specifically on risk and volatility.

Standard Deviation

The classic. Standard deviation tells you how spread out the returns are from the average. Low standard deviation means returns cluster tightly around the mean. High means they are all over the place.

Fund Three and FCM had the lowest standard deviation. Fund One and the Russell 2000 had the highest. No surprises there.

Downside Deviation and Semideviation

Downside deviation is like standard deviation but only counts returns below a minimum acceptable return (set at 0% in the book, meaning “just don’t lose money”). Semideviation is similar but uses the mean return as the cutoff instead.

Both metrics told the same story: FCM and Fund Three had the least downside risk.

Skewness

Skewness tells you if the return distribution is lopsided. For a perfectly normal distribution, skewness is zero.

• Positive skew means the right tail is longer. You get smaller, more frequent losses and bigger, less frequent gains. This is what you want.
• Negative skew means the left tail is longer. Smaller gains but bigger losses lurking out there. Not great.

One important detail Travers points out: whether you use monthly or quarterly data can change the skewness number significantly. For FCM, the monthly and quarterly skewness values were quite different. So always check multiple time periods.

Kurtosis

This one is about how “peaked” or “fat-tailed” your return distribution is.

• Kurtosis above 3 means “fat tails,” more extreme returns (both good and bad) than a normal distribution would predict.
• Kurtosis below 3 means “thin tails,” a flatter distribution with fewer extreme events.

FCM had the lowest kurtosis, meaning its returns were more normally distributed than the others. That is generally a good sign because it suggests fewer nasty surprises hiding in the data.

Drawdown Analysis

This is one of my favorite sections. Maximum drawdown is the largest peak-to-trough loss a fund has experienced. But Travers goes deeper and also looks at:

• Length of drawdown - how many months from peak to trough
• Recovery time - how many months to get back to the high water mark

FCM’s worst drawdown was -11.5% over 8 months (Sep 2008 to Apr 2009), and it took another 8 months to recover fully. Compare that to Fund Four, which dropped -26.9% and still hadn’t recovered more than 2.5 years later. That’s a massive difference.

Gain/Loss Ratio

Simple metric. Average gain for all positive months divided by the absolute value of average loss for all negative months.

If this ratio is above 1, your winning months are bigger than your losing months on average. FCM was the only fund in the group above 1. Its average monthly gain was 2.15% while Fund Three’s was only 1.38%.

Regression-Based Statistics

Now we get into the relationships between fund returns and benchmark returns.

Beta and Alpha

Beta measures how sensitive a fund’s returns are to a benchmark. Beta of 1 means the fund moves with the market. Below 1 means less volatile than the market. Above 1 means more volatile.

Alpha is the value added by the manager after accounting for market exposure. In simpler terms, the return the fund generates when the market return is zero.

FCM had the highest alpha values compared to both the HFRI Equity Hedge and Russell 2000 indexes. That is exactly what you want to see in a hedge fund, returns that come from skill, not just market exposure.

Correlation

Correlation ranges from -1 to +1. High correlation means the fund moves in lockstep with the benchmark. Low correlation is desirable because it means the fund provides diversification.

FCM and Fund Three had the lowest correlation to the indexes. This, combined with their high alpha, paints a picture of skilled managers who aren’t just riding the market.

Treynor Ratio

Similar to the Sharpe ratio, but uses beta instead of standard deviation in the denominator:

Treynor Ratio = (Portfolio Return - Risk-Free Rate) / Beta

This measures excess return per unit of market risk specifically. Fund Three came out on top due to its very low beta, with FCM close behind.

Peer Group Analysis

The last piece is comparing the fund against a universe of similar hedge funds. Travers recommends using percentile rankings and quartile distributions to see where your fund stands.

FCM ranked in the first quartile (top 25%) across most time periods. The only exception was the most recent one-year period where it was in the upper part of the second quartile. Still solid.

One warning Travers gives: your peer group has to be appropriate. If you are comparing an equity long/short fund against a universe that includes macro funds and fixed income funds, the comparison is meaningless. Build your peer groups carefully and update them over time.

The Bottom Line

After running all these numbers, FCM looks strong across basically every metric. Highest Sharpe ratio, highest information ratio, highest alpha, lowest kurtosis, best gain/loss ratio, strong peer group ranking. Fund Three was the closest competitor, especially on risk metrics.

But here’s an important reminder from the chapter’s opening quote by Alvin Toffler: “You can use all the quantitative data you can get, but you still have to distrust it and use your own intelligence and judgment.”

Numbers tell a story, but they don’t tell the whole story. Past performance is not a guarantee. The quantitative analysis is just one part of the due diligence puzzle. Next up, Travers takes us into portfolio analysis, where we look at what’s actually inside the fund.

Previous: Chapter 5: Initial Interview (Part 2) Next: Chapter 7: Portfolio Analysis (Part 1)