Two strategies: momentum with monthly mean 1.0%, standard deviation 5%, skew -1.2 and a 35% worst drawdown; mean reversion with 0.7%, 2.5%, skew -2.0 and 18%. Where does each return come from, which earns more per unit of risk, and which is more dangerous?

Mean reversion earns more per unit of risk, Sharpe 0.97 against 0.69, and it is also the more dangerous book. Momentum is paid for riding trends that others are slow to join and loses when trends reverse; mean reversion is paid for providing liquidity to forced sellers and loses when the selling is right. Levered to momentum's volatility, mean reversion would earn about 16.8% a year but its worst month, skew included, would be about -18% against momentum's -15%.

Think of two shopkeepers. One stocks whatever sold well last season and rides the fashion until it turns; the other buys stock that a rival is dumping in a panic and sells it back when calm returns. The first is a trend followerA strategy that buys what has been rising and sells what has been falling, betting that moves continue because investors react to news slowly., the second a liquidity provider. Momentum is paid because investors underreact to news and then pile in late, and it loses when a trend breaks all at once; mean reversion is paid because someone needs to sell now and will pay for the service, and it loses when the seller knew something. Both are compensation for a risk, which is why neither Sharpe ratio is 3.

Annualise first, because monthly figures hide the comparison. Mean scales with 12, standard deviation with the square root of 12. Momentum: 12% a year on 17.3% volatility, Sharpe 0.69. Mean reversion: 8.4% on 8.7%, Sharpe 0.97. So mean reversion earns about 40% more per unit of volatility. The interviewer's which makes more money is a trap inside this: at equal capital momentum makes more, but a desk can lever the mean-reversion book 2 times to match momentum's volatility and would then earn about 16.8% a year against 12%. Per unit of risk, and therefore per unit of capital once leverage is free to vary, mean reversion wins.

The Sharpe ratio sees only the standard deviation, and the two skews say the standard deviation is hiding different things. A skew of -2.0 means the mean-reversion book's losses arrive in rare, large months: the forced seller was right, the stock kept falling, and every position lost at once. Use a Cornish-FisherAn adjustment to a normal quantile that bends it for skew and fat tails, so a worst-case month reflects the shape of the returns rather than only their spread. adjustment for the worst month at the 1% level: momentum comes out near -15.0% against -10.6% on a normal curve, mean reversion near -8.8% against -5.1%. On its own capital mean reversion looks tamer. Levered 2 times to match volatility, which is how a desk would actually run it, its worst month becomes about -17.6% and its worst drawdown about 36%, a little beyond momentum's on both counts, and arriving faster.

So the answer has two halves. Mean reversion is the better strategy per unit of risk and the more dangerous one to run at size, because its risk is in the tail where the Sharpe ratio does not look, and because liquidity provision fails exactly when the whole market needs liquidity. Momentum's drawdown of 35% is larger in absolute terms but arrives through a slow reversal that a drawdown rule can cut; a mean-reversion crash happens in days. The drawdown per unit of annual return, the Calmar ratio, is 0.34 for momentum and 0.47 for mean reversion, and leverage does not change it, which is a useful check that the comparison holds at any size.

State the limits. Ten years of monthly data is 120 observations, and the skew of -2.0 may rest on three or four months; its standard error is large. The Cornish-Fisher figure is an approximation that breaks down for extreme skew. And the two books are usually negatively correlated, which is the real answer to which should you run: both, sized so that each one's bad month is survivable.