Beware of the numbers

Hedge Funds Nitty-Gritty Series

Post 1 Beware of the Numbers

From my personal experience, some people tend to believe (although the institutional investors community would generally disagree) that when it comes to hedge fund returns, the higher they are the better. In reality, however, the situation is much less clear-cut.

Firsrtly, the risk tolerance and return expectations for every investor are different, and therefore her/his assessment of a high-performance hedge fund will also be different. For instance, there is a general preference for lower risk/lower return funds among Japanese institutional investors. But secondly, and even more importantly, the returns alone don't tell the whole story.

In this post I'd like to describe some of the metrics and concepts that are used for hedge funds due diligence when assessing the risk/return profile (operational and investment strategy due diligence are broad subjects that deserve a separate in-depth review).


1. Frequently used metrics

They are: annualized returns and annualized standard deviation, annualized downward deviation, length of the track record, percentage of positive months and (controversially) Sharpe ratio. A quick look at every metric below.

a) Annualized Returns
This is a fairly straightforward metric. It measures the annual equivalent of the returns delivered by the investment product over a period of time. The reason to bring the returns to a single period is to allow apples-to-apples comparison between products with different period of track record in terms of absolute returns. The general formula here is:

The formula may appear daunting, but it is actually fairly simple. HPR stands for Holding Period Return, which is simply put what the absolute return from the point in time zero to point in time present is (e.g. 0.15 for 15%).  The power part is a little trickier: take the number of observation in one year (e.g. 12 for monthly returns) and divide them by the total number of observation in the data sample (e.g. 18 for 18 months, 6 for 6, etc.).

In practice, when computing this statistic in MS Excel, the easiest way to do is to use the PRODUCT function (assuming you have returns data, and not price or index values to work with). In the sample below I have put together a set of random monthly returns observations to illustrate:

The formula I use here is '=PRODUCT(1+data_sample)^(12/COUNT(data_sample))-1', where data_sample is the B4:B18 range on the spreadsheet. Don't forget to hit [Ctrl]+[Shift]+[Enter] after inputting this formula into a cell to enable it!

b) Annualized Standard Deviation
Similarly to the Annualized Return, Annualized Standard Deviation is the equivalent of volatility of actual returns to what it would be if they occurred during one year. The formula is different though. Without going into how the Standard Deviation is computed, to annualize it, the following formula can be used:

For instance, for monthly returns, we will take square root of 12. Note that instead of the "equal" sign ("=") I use the "approximately equal" sign ("≈") here. Strictly speaking, this also applies to the Annualized Returns: this formula is an approximation, which does not account for compounding. But in most cases this approximation will produce accurate results (see REFERENCE for more information).

In MS Excel, the formula is fairly straightforward. Using the previous example: '=STDEV(data_sample)*SQRT(12)'.

c) Annualized Downward Deviation
The Standard Deviation provides a measure of total volatility, that is, how much the individual results deviate from the mean. But it does not tell us whether this deviation is positive or negative in nature. To more accurately assess the risk of losses associated with an investment, the downward deviation is utilized. It is the same standard deviation, but only applied to the observations of negative returns. It is actually more intuitive in MS Excel format than stated as a formula, so here it is in the example we have used so far:

As you can see in this example, the small share of negative monthly returns (three out of fifteen) produce a much smaller value than the standard deviation. If only all funds were like that.

d) Length of Track Record
Straightforward: the longer the better. By looking at this metric one is trying to answer following questions:

1. Does the manager have sufficient experience?
2. Has the team been stable enough to keep the fund going?
3. And, most importantly, did the fund undergo "stress-testing" by the difficult markets and/or economic conditions?

Naturally, these questions cannot be answered just by looking at the length of track record alone, so it should be used in conjunction with other information.

e) Percentage of Positive Months
This metric addresses the question of how successful the fund manager has been in delivering positive performance. In our arbitrary example it is a hefty 80%, the level very rarely encountered in the real world.

f) Sharpe Ratio
Use of this metric is controversial. CAIA curriculum states that it is not appropriate to assess a hedge fund's returns, as the standard deviation in the denominator will be primarily defined by the benchmark. Academic disputes apart, this is a widely used metric. The general formula is:

where Rp is the fund return, RFR - risk free rate, and σp - the standard deviation of the fund returns.

2. Points of reference

Every hedge fund strategy is different, and often difficult to categorize, but there are some buckets into which one can put a fund with more or less certainty. Understanding what drives returns for each strategy is important in order to asses the attractiveness of a particular fund as a potential investment. For most strategies there would be some points in their (usually not so long) history, where the market conditions made it particularly difficult for a given strategy to deliver positive returns. Comparing a fund performance during these periods can tell you much about how much alpha (i.e. manager skill) is actually delivered by the fund.

For instance, take the case of Japanese equity long/short funds. If you want to see how successful a fund is in delivering absolute returns, it is worth looking at the beginning of 2006, September to November 2008 and September to December 2009 as points of reference. I would personally recommend to pay particular attention to November 2009, as this was a particularly gruesome month for many funds in this space.

REFERENCE:

1. To read a more in-depth discussion of the quantitative nitty-gritty of the hedge funds I recommend "Hedge Funds: Quantitative Insights (The Wiley Finance Series)"
2. The MS Excel file used for examples can be viewed here