Selecting an Appropriate Benchmark

Introduction

I have the privilege of working with two of the sharpest minds in the industry. Last week I had a discussion with them via email about selecting a suitable benchmark for the strategies I run. I was specifically questioning them on the use of cash returns as a benchmark. This is a contentious issue in the industry – many folk disagree with cash as a benchmark because they don’t understand the reasons for its use. I found the answers to my questions clear and concise, providing easy to understand insights into cash as a benchmark. The discussion has implications for QuantLab that runs the same strategies referred to in the discussion. QuantLab is currently benchmarked against the JSE Top 40, but theoretically it should be benchmarked against cash returns, or government treasury bills. Another useful benchmark, to determine relative skill, would be an appropriate hedge fund index. Neither of these – treasury bills nor hedge fund index – are currently used in QuantLab to benchmark performance. In light of this, I will look to add both of these at some future point. I thought that you’d find the discussion interesting so I’ve included it in today’s post.

The Discussion

PJ: I know that we currently use cash returns to benchmark performance, but I don’t agree that adequately reflects the risk in the fund. Cash basically has zero volatility, which is not the case with our fund. I guess we need to find a benchmark with the same generic risk drivers. Not sure what this is though?

Director: Cash is the official benchmark and – because we do not hold any systematic, long-term exposure to any risk asset/class – is also theoretically the correct answer even if there is a difference in volatility. A benchmark does not need to exhibit the same vol characteristics in order to be valid; small cap equities for example would have much higher volatility than large cap yet both can accurately be benchmarked against an all-share index. In fact, volatility relative to the benchmark (akin to beta in the mean-variance world) becomes one of the key risk statistics that an investor should be concerned with.

The next best comparator would be to recognise we are an “active trading strategy” and therefore the benchmark would be “other active trading strategies” or the “universe of active trading strategies”, which is proxied by one or more hedge fund indices, covering either the entire HF universe or more granular ones like stat arb or LS equity.

Given there is no neat answer like there would be for an active equity fund, we show our performance against most of the above in our materials, including things like the Sharpe Ratio (which captures risk-adjusted returns against cash).

PJ: Thanks for the insights. How do we display skill or “alpha” – residual returns over and above our risk budget – when benchmarked against a risk-free portfolio? A comparative HF index appears more sensible?

Director: In order to determine skill in an absolute sense, your starting point needs to be the portfolio you would hold if you have no views at all.
In our case, that is 100% cash.
For other strategies, the starting point could be an equity index or a bond index if that is what would be held if the manager had no active views.
Skill is then displayed by examining how many units of return are added per unit of additional risk (generally [active] volatility). i.e. typically a Sharpe Ratio or an Information Ratio.
The fact that your starting point is a risk-free, zero-volatility point is not important. Mathematically the demonstration of skill would be the same regardless of the benchmark.*

If you benchmark yourself against a HF index, you determine relative skill; that is, whether you have more or less skill than others trying to do the same thing. That only becomes relevant once we have determined you have some skill in the first place, and in that case the client would correctly be asking how does your skill compare with the skill of others.
– Are you a high-skill or a low-skill operator? For this we would look at e.g. typical observed thresholds for Sharpe Ratios, being something like SR > 1.0 = lots of skill, SR 0.5-1.0 = skilled, SR 0.0-0.5 = low skill, SR = 0.0 = no skill and conversely for negative numbers.
– Are your results visibly better or worse than your peer group, if there is one? This can be answered by looking at e.g. comparative equity fund performance risk-adjusted return or Sharpe Ratio ranking, bond performance ranking, HF index etc depending on the strategy in question.

Beyond that there are many other questions related to skill such as:
– Is there enough skill to cover any costs, fees, expenses or other slippage? We show net returns so presumably that answers itself.
– Is your strategy unique or are there other barriers to investment for me to the point where any skill you may have – even low skill – is worth having because it diversifies my total portfolio in a meaningful way? For example you may be the only operator with an appropriate fund structure so I might invest with you even if you have below average skill.
– Has the skill been commoditised? That is, could I get the same result in an easy-to-obtain, replicated fashion, say through an ETF which executes the same strategy in a less person-dependent or human-error-prone way? Could be very relevant for e.g. a long-only small-cap strategy where well-defined ETFs already exist tracking the various small-cap indices therefore the case for giving money to a run-of-the-mill, low-skill small-cap manager is not strong.
– Is your skill repeatable going forward, including how dependent it might be on an environment, the presence of particular market participants or events, and on you yourself being around?
– Where along the risk axis are you positioned? The skill you have may be packaged in a way that is unattractive because the risk level at which you operate is too high or too low or too erratic.

and so on.

*there are of course provisos to this: an inappropriately chosen benchmark could suggest there is skill when in fact there is none. Example: a passive equity manager chooses (inappropriately, because it is not his default portfolio) to benchmark himself against cash. In this case the excess volatility is just equity vol and excess return just passive equity return. His apparently skilful management is a sham.

Hope you found my post interesting. As always, I welcome your comments. Until next week, happy trading!

Happy Trading,
PJ

Passionate about generating and sharing quantified trading models that empower individuals to trade successfully. I founded www.sutherlandresearch.com to realise my passion.

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