Cutting Edge Introduction: Followers Of Fashion

Cutting Edge Introduction: Followers Of  Fashion

Focusing on how often a trading strategy ends on the winning side can distract from the question of whether it profits on average. The key is in the return distribution’s skew – and at least for trend-following strategies this can be directly controlled. Laurie Carver introduces this month’s technical articles

Asset price bubbles are often driven by investors on winning streaks that then spectacularly fail in the following bust, known in financial folklore as picking up pennies in front of a steamroller. The track record of such traders looks great – until their gains are wiped out. But the flipside of this – tail risk strategies – can get a bad rap, as the big win that makes up for a long history of small losses may take time to arrive
Trend-following strategies can sometimes appear this way – racking up a large fraction of losing trades – but may still have positive expected returns over a sufficiently long horizon because of the outsize gains when a trend kicks in. This effect means the distribution of trading returns of pure trend-following strategies are positively skewed, even if market returns are not, as Richard Martin, chief quantitative investment officer at Longwood Credit Partners argues in Momentum trading: ’skews me. It is this skewness of returns that allows the strategy to retain earnings while the market moves away from the trend, regardless of what the expected daily return is.

Martin uses results from the theory of complex functions to derive analytic formulas for the skew in the simple case where the position taken is an exponentially weighted moving average, and shows it has a characteristic shape as a function of the number of trading days in the return period, decaying slowly after a peak. Two datasets are examined, one on Swiss franc-US dollar futures, and one on S&P 500 futures.

“If you rate fund managers using a win ratio or the Sharpe ratio, you leave yourself open to this effect of a big loss wiping out your gains further down the line,” says Martin. “For instance, if you wrote protection on high-grade corporates, you’d make money about 99% of the time, but that last 1% of the time you might lose very badly. In the trend-following case, the strategy is simple enough that it’s possible to get hold of that effect in the skew.”

Once trend following is mixed with the reverse strategy – investing counter to trends – more general skewness profiles can be generated. There is a trade-off between the short-term negative skew of the counter-strategy and the positive skew of the trend. “The idea is the market can vibrate back and forth, so you try to cash in on some of the short-term mean reversion as well. It’s dependent on the investment horizon – the long-term survival probability of the strategy is linked to having positive skew at that timescale,” he says.

What is perhaps most striking is the generality of the results – they are independent of assumptions about expected returns – and the wide skew shapes that can be realised. “It seems quite robust with respect to expected returns, which is good because unless you believe the efficient market hypothesis – in which case it’s zero – then you don’t really know much about that,” says Martin. “But the tractability of these strategies to analysis of the skewness means you can tailor them to generate particular shapes for how gains and losses are distributed.”

Also this month, Vladimir Piterbarg, head of quantitative research at Barclays in London, returns to the effect of collateral agreements on derivatives pricing following his celebrated article published by Risk in 2010 (Risk February 2010, pages 97–102). Cooking with collateral attempts no less than a re-examination of the foundations of derivatives pricing in an all-collateralised world. It turns out many classical arguments are still valid, provided one keeps track of the right rate at which collateral appreciates interest.

Until a standardised credit support annex becomes a reality, removing some of the non-standard features of collateral agreements – such as exposure values that trigger collateralisation, or the option to choose which currency to post in – they should be treated as embedded derivatives (Risk September 2011, pages 24–27). In this latter case, Piterbarg gives a simple model to value the contract, based on a first-order expansion of the spread between the rates earned on the different currencies.