Two strategies show me the same average return and the same volatility, and one of them keeps me up at night while the other barely registers. For a long time I could not explain the difference cleanly. The average was identical. The standard deviation was identical. And yet holding one felt fine and holding the other felt like waiting for a shoe to drop that always dropped eventually.
The thing I was feeling has a name, and it is the third moment of the return distribution. Skewness. It is the number that tells you whether your surprises tend to land on the good side or the bad side, and it is almost never in the headline stats people quote when they pitch a strategy.
Computing it by hand so it stops being abstract
Skewness sounds fancy but the arithmetic is short. You take a series of returns, and you do three passes over it.
- Find the mean. Add up every return, divide by the count. Call it m.
- Find the standard deviation. For each return, take the difference from the mean, square it, average those squares, then take the square root. Call it s. This is the second moment, the thing everyone already reports.
- Find the skew. For each return, take the difference from the mean, divide by s, and cube it. Average those cubes. That average is your skewness.
The cube is the whole trick. Squaring a deviation throws away its sign, which is why volatility treats a big up day and a big down day as the same size of surprise. Cubing keeps the sign. A return far above the mean contributes a big positive number, a return far below the mean contributes a big negative number, and the cube weights the far ones much more heavily than the near ones. So skewness is a weighted vote on which tail is doing the heavy lifting. Positive means the rare huge moves are wins. Negative means the rare huge moves are losses.
One caveat before you trust a number you compute this way. Skewness estimated from a short series is noisy, and it is dominated by a handful of extreme observations. If your series only has one or two big outliers, the skew you calculate is really just a statement about those one or two days. Historically you want a few hundred observations at minimum before the number means much, and even then treat it as a rough read rather than a precise constant.
Trend following versus selling premium
The two archetypes that make this concrete are a trend follower and a premium seller, because their payoffs are close to mirror images.
A trend follower cuts losers fast and lets winners run. Most trades are small losses or scratches. The strategy bleeds a little most of the time, pays commissions, sits through long stretches of nothing. Then occasionally a real move shows up, the kind that lasts, and one trade pays for a year of small losses. That return series has a lot of little negatives and a few enormous positives. Positive skew. It usually feels bad to hold, because most days you are losing small amounts and questioning the whole thing, and the payoff is lumpy and impossible to schedule.
Selling premium is the opposite shape. You collect a small amount over and over, and most of the time nothing happens and you keep it. The equity curve is smooth and satisfying and slopes gently up, which is exactly why it is so easy to size too large. Then the move you were implicitly short shows up, and one event gives back weeks or months of collected premium in a session or two. Lots of little positives, a few enormous negatives. Negative skew. It feels wonderful to hold right up until it does not.
Here is the part that matters. Those two strategies can post the same average return over a full cycle. The mean does not distinguish them. Volatility barely distinguishes them either, because a smooth curve with rare cliffs can have modest measured standard deviation right up until the cliff. Skewness is the stat that actually separates them, and it separates them along the exact axis you experience as a human being holding the position.
What to actually do with this
The practical move is to stop looking at average return in isolation and start pairing it with the shape. A few rules of thumb I keep coming back to.
- Compute skew on the same series you compute Sharpe on. If the Sharpe looks great and the skew is strongly negative, be suspicious. A high Sharpe with negative skew often means you are getting paid smoothly to carry a tail you have not seen fire yet.
- Look at the worst single day and the worst week next to the average. If one bad day erases a quarter of gains, you are holding a negative-skew payoff whether or not the label says so.
- Size negative-skew strategies for the tail, not for the smooth part. The smooth part is a liar about how much you can hold. The right size is the one that survives the cliff you have not measured yet.
- Expect to underhold positive-skew strategies emotionally, and pre-commit to the rules so you do not quit them during the boring bleed, which is precisely when the big move tends to arrive.
None of this changes which strategy is correct for you. Positive skew and negative skew are both legitimate, and plenty of good operators run negative-skew books on purpose with eyes open and sizing to match. The point is to know the shape you signed up for before the market tells you. When I am comparing candidate strategies inside Blockcircle's backtester, the skew of the return series is one of the first things I check after the equity curve, because the equity curve is the thing designed to seduce me and the skew is the thing that tells me what it will cost.
The mean tells you where a strategy ends up. Skewness tells you what the ride there does to you, and whether the bad surprises are the kind you shrug off or the kind that end the account. It is one extra pass over the same numbers you already have, and it answers a question the average is structurally unable to answer.