What to Actually Use

The metrics in this chapter are not interchangeable, and most disagreements about “how risky” an investment is turn out to be disagreements about which one is being quoted. A working hierarchy:

For sizing a position you might have to hold through a crisis

Maximum drawdown and CVaR. Both answer the question that determines whether you survive — how bad does it get — and neither depends on returns being normally distributed.

For comparing two strategies over the same window

Calmar if drawdown is the binding constraint, Sortino against your actual required return if shortfall is, Sharpe only when the return distribution is roughly symmetric and you have checked that it is.

For deciding whether a track record means anything

Skewness and kurtosis first, then the deflated Sharpe ratio (section “Sharpe ratio”) to discount for how many strategies were tested before this one was shown to you.

Never on its own

VaR. It is not coherent, it says nothing about the tail beyond its own threshold, and its principal function in practice has been to make concentrated risk look bounded.

The deeper point survives all of them. Every measure here is estimated from a finite sample of a distribution that changes, and the events that determine your outcome are by construction the ones your sample under-represents. Use these numbers to compare and to size — never to convince yourself that a risk has been quantified and therefore controlled.