A return series is not a strategy

A track record is a compression. Annualized return, volatility, Sharpe ratio, maximum drawdown and beta each summarize a single realized path of outcomes. The compression is useful, and it is lossy. What it discards is most of what an investor needs in order to judge whether the next period will resemble the last.

This note sets out what a return series cannot tell you, why that matters most for strategies whose behavior changes with market conditions, and what a strategy description has to contain instead.

What the compression discards

A return series cannot, by itself, tell you:

• why the return should exist;
• what risk is being transferred, and to whom;
• which market states change the strategy's economics;
• what the strategy does when those states change;
• which exposures are embedded in the returns;
• where the strategy can fail; or
• whether the observed behavior was intended, accidental or the product of fitting.

None of these is exotic. They are the questions a careful allocator asks in diligence. The difficulty is that the return series is usually the only artifact that is standardized, so it ends up carrying weight it cannot bear.

An old illustration

Lo (2001) makes the point with a hypothetical fund that systematically sells out-of-the-money put options on the S&P 500. Over the 1990s its simulated record is exceptional: high average returns, few losing months, a Sharpe ratio most managers would envy.

Nothing in that record is false. It is an accurate account of the states that occurred. The strategy's defining exposure, a large and nonlinear loss in a sharp market decline, lives in states the sample rarely visited. The statistics describe the premium the fund collected. They say almost nothing about the risk it was paid to carry.

The same pattern appears in real strategies. Mitchell and Pulvino (2001) find that merger-arbitrage returns are largely uncorrelated with the market in flat and rising markets but positively correlated with it in severe declines, a profile they compare to selling uncovered index puts. Agarwal and Naik (2004) find that many equity-oriented hedge fund strategies carry payoffs resembling a short put on the market index. Fung and Hsieh (2001) find the opposite shape in trend-following funds, whose returns resemble a lookback straddle. In each case the economically important feature of the strategy is its shape across states, and a single set of summary statistics is poorly suited to showing it.

Three things a track record cannot identify

Mechanism. Two strategies with the same Sharpe ratio can be earning compensation for a risk someone else wants to shed, exploiting an informational or structural advantage, or benefiting from a historical accident. Only the first two should be expected to persist, and they persist for different reasons and fail in different ways. The return series cannot tell them apart. A mechanism statement can, because it makes predictions beyond the returns: if a return is an insurance premium, it should be larger when demand for insurance is higher, and losses should concentrate in the states being insured against. Those predictions can be checked.

State dependence. Summary statistics average over market states. A strategy whose exposure changes with conditions, whether through an explicit policy or mechanically through optionality, does not have a single level of risk. Its averaged statistics describe a strategy that did not exist on any particular day. We develop this point for beta in a separate note.

Hidden exposure. Returns can carry exposures that were never intended or reported: short volatility inside a nominally market-neutral book, credit and liquidity risk inside a carry strategy, equity sensitivity that appears only in drawdowns. These exposures are often invisible in calm samples, which is exactly when track records are built.

What a description should contain instead

The object that needs describing is the strategy, not its output:

mechanism → state → policy → positions → exposures → outcomes

accompanied by the constraints and costs of implementation, the ways the strategy can fail, the evidence for each relationship, and the history of versions that produced the record.

The return series remains essential. It is the ledger of outcomes that every other part of the description has to be reconciled with. But the other links each make a claim that can be checked against something other than the returns. The policy can be checked against the positions actually held. The stated exposures can be checked against behavior within states. The mechanism can be checked against the conditions that should strengthen or weaken it. A description built this way is testable rather than merely persuasive, and it can be wrong in specific, observable ways.

Questions that follow

In place of "how did it perform?", the questions become:

1. What is the mechanism, and what observation would contradict it?
2. Which states change the strategy's economics, and what does the policy do in each?
3. What are its conditional exposures, particularly in the states where the rest of a portfolio is under stress?
4. Which evidence is simulated, which was produced after the specification was frozen, and which was observed in production?
5. What would trigger a review of the strategy?

A manager who can answer these has a strategy. A manager who can only produce the return series has a record of what one realization of the market paid.

References

Agarwal, V., and N. Y. Naik (2004). "Risks and Portfolio Decisions Involving Hedge Funds." Review of Financial Studies 17 (1): 63–98.

Fung, W., and D. A. Hsieh (2001). "The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers." Review of Financial Studies 14 (2): 313–341.

Lo, A. W. (2001). "Risk Management for Hedge Funds: Introduction and Overview." Financial Analysts Journal 57 (6): 16–33.

Mitchell, M., and T. Pulvino (2001). "Characteristics of Risk and Return in Risk Arbitrage." Journal of Finance 56 (6): 2135–2175.