A few weeks back, CFM attended a hedge fund awards ceremony in London and a great time was had by all…, this despite having left empty handed!
Hedge fund awards are a peculiar thing. Of course, the firm is proud of its achievements, but, at the same time, winning an award based on a year of performance is very sensitive to the statistical fluctuations of a noisy P&L – akin to the same statistical effects and biases that we experience on a daily basis when developing trading strategies.
Some readers might even have heard of the mythological ‘hedge fund award curse’ – the story goes that as soon as winning an award, a hedge fund is likely to go out of business. This old wives’ tale is actually a genuine statistical effect and can be illustrated in the following way:
- Take 30 realisations of a 1-year P&L with a Sharpe ratio of 0.5
- Select only those hedge funds that received an award, the ‘medal winners’
- Look at the subsequent, future performance of the selected winners’ P&Ls
Tautologically, of course, an award winner will revert back to the mean of a 0.5 Sharpe ratio following a year of outperformance. Some of the competitors in the plot perform very poorly, albeit only through a statistical fluctuation or bad luck.
The subsequent underperformance of the award winner constitutes a reversion to the mean rather than a mean reversion.
Such effects explain why one-off hedge fund award winners do not (on average) live up to the hype! Perhaps, also, such award-winning funds are more susceptible to excessively raising capital, trading too much, and as a result bringing their Sharpe ratio down further due to higher trading costs reinforcing the feeling of a curse!
Taking one of the simulated P&Ls and doubling its Sharpe ratio to 1 yields an average of four times as many awards won in the 20-year period. Rather than selecting one off winners of the award, allocators should therefore focus on managers that have repeatedly and consistently won hedge fund awards over many years.
Have you seen our trophy cabinet by the way?
 The P&L is generated as rt = μ + ϵt where rt is a daily return, ϵt is a bell-shaped random number with a volatility of 15% (we use a student’s t distribution with 4 degrees of freedom to model fat tails) and μ is a constant added every day such that the Sharpe ratio equals 0.5
 Mean reversion refers to a strategy (often from statistical arbitrage in market neutral equity portfolios) where returns are serially anti-correlated – so if a stock rises it then subsequently falls and vice versa. Reversion to the mean, illustrated here, involves no such anti-correlation of price returns.
 This also explains where in-sample biases come from.
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