A remedial lesson in statistics

You can always tell when financial market volumes start to dry up because brokers start organizing a seemingly endless sequence of ancillary ways to add value. Economist meetings, golf outings, and dinners tend to feature prominently on this list. As such, Macro Man has spent a fair few evenings over the past several weeks at roundtable discussion meetings, wherein traders and investors gather together to exchange views and grumble about the market.

And grumble we have. It has become rather evident at these discussions that Macro Man is not the only person in the market to be frustrated by the triumph of beta over alpha. Indeed, a common theme has been frustration over the low level of risk premia, the failure of market timing, and the continued success of what most consider to be relatively naïve, beta like strategies across markets. Far from being the greedy coupon-clippers that are often portrayed in the popular press, the people with whom Macro Man has spoken have felt underinvested and unhappy for much of the past few months, if not longer.

One of the most commonly cited factors causing dissatisfaction has been the relatively short-term time horizon of many investors. Now, fund-of-funds investors have always had an itchy trigger finger, and that will probably never change. In that industry, “what have you done for me lately” isn’t just an investment strategy, it’s a way of life. However other investors, both in hedge funds and in long-only products, are also increasingly demanding a steady stream of positive performance with shallow and infrequent drawdowns.

Now, there are of course exceptions to every rule, and it would be foolhardy to suggest that no one out there has the wherewithal to look beyond a couple of weeks when taking an investment decision. Yet surely where there is smoke there’s fire, and traders and fund managers are being pushed by natural selection towards strategies delivering steady positive returns. This, of course, is the virtual definition of a volatility selling or carry strategy, which clips coupons every day until the black swan event wipes out the bulk of accumulated profits in one fell swoop. To date, the black swan hasn’t really made an appearance, so these strategies continue to fare well and attract new assets. Investors, it would appear, want all of the upside of taking risk, with none of the downside.
Now if a strategy could generate the return distribution above in perpetuity, it would of course be worth pursuing whole-hog. The problem, of course, is that strategies that generate such returns at any point in time usually have an extremely fat tail lurking on the left side of the distribution somewhere in their future. Macro Man thought it would be worthwhile to review basic principles of statistics to review just how often even skilled managers can generate negative returns when not pursuing a strategy designed to maximize the probability of positive return at any particular point in time.

Imagine we have an investor whose true skill is known to deliver a Sharpe ratio of 1- say an annualized excess return of 10% per year, with a volatility of returns of 10%. What are the chances in any given time period that this investor makes money with his trading activities (ignoring, for the purposes of this exercise, any cash component of return, as well as any management or performance fees charged)? While Nassim Nicholas Taleb, among others, have pointed out that high-frequency returns are mostly the result of noise, it is worth looking at graphic representations of return distributions to illustrate just how powerful this effect is.

How likely is it that a Sharpe ratio 1 strategy will lose money on any given day? 47.5%, as it turns out- a little less that you’d get from flipping a coin.

Extending the horizon to weekly does little to alter the likelihood of success. A Sharpe ratio 1 manager will still lose money during 44.5% of the weeks he is running the strategy.

How about monthly? Our manager still loses money just under two out of every five months.

Extending the frequency to quarterly improves the chances of success, but not by as much as you’d expect. Our Sharpe ratio 1 manager still loses money in just over 30% of the quarters in which he runs the strategy. By this point, some itchy trigger investors may already be thinking of heading for the exits, potentially missing out on the manager’s skill in coming quarters.

Even when measured on an annual basis, a Sharpe ratio 1 manager will still lose money one out of every six years. Unfortunately, in the current climate, many investors will not be along for the ride in the other five.

Now, all of these probabilities are based on normal distributions, which we all know do not accurately describe financial market returns. Yet Macro Man’s perception is that many underperforming managers have done so through buying, rather than selling, risk premia. If so, it is probably reasonable to expect a degree of outperformance during fat tail events.

By way of disclosure, Macro Man does not have any particular axe to grind here. He has not suffered any sort of redemption in his real job, and his performance this year is positive- though as with the blog portfolio, perhaps not as positive as it could be had he focused exclusively on beta strategies. However, observing the degree of frustration amongst fellow professional investors has been eye-opening. When he sees things like structured product selling of 15 year S&P 500 vol and 10 year EUR/USD vol, when these implied volatilities are at all time lows, he begins to wonder if the apotheosis of vol-selling, carry driven strategies has finally run its course, and that the time is finally ripe for buying value and/or tail risk. When the 10 year straddle in EUR/USD is given at less than 12.5 big figures, the risk/reward of taking the other side of vol selling begins to look awfully attractive.