Skewness measures asymmetry in market returns. Equity markets are negatively skewed — large losses are more likely than large gains of equal size. Ignoring this asymmetry in retirement simulations understates downside risk, because the worst scenarios for retirees are exactly the ones that skewness makes more probable.
Skewness is a statistical measure of asymmetry in a probability distribution. A symmetric distribution (like the normal) has zero skewness — losses and gains of equal magnitude are equally likely. Negative skewness (left skew) means the left tail is longer: large losses occur more frequently than large gains. Equity returns tend to be negatively skewed, especially over short horizons.
How It Works
- Negative skewness: left tail is heavier — sharp crashes are more common than sharp rallies
- Zero skewness: symmetric distribution — gains and losses are equally distributed
- Positive skewness: right tail is heavier — large gains are more common than large losses
Monthly equity returns typically exhibit skewness of -0.5 to -1.0, meaning the distribution of returns is tilted toward more frequent and larger negative outcomes.
Retirement Lab models skewness via the Fernandez-Steel transformation, which applies a gamma parameter to the Student's t-distribution. A gamma less than 1 produces negative skewness; gamma equal to 1 is symmetric; gamma greater than 1 produces positive skewness.
Why It Matters for Retirement Planning
Skewness and kurtosis work together to define tail risk. Kurtosis tells you extreme events are more frequent; skewness tells you the extreme losses are more frequent than the extreme gains.
For retirees, this is a double penalty:
- Sequence-of-returns risk makes early losses devastating
- Negative skewness makes those early losses more likely than symmetric models suggest
A Monte Carlo simulation using a skewed fat-tailed distribution produces lower success rates than one using a symmetric distribution — even with the same mean, volatility, and kurtosis — because it correctly weights the downside scenarios that matter most.
Frequently Asked Questions
- Why are stock market returns negatively skewed?
- Markets tend to crash faster than they rally due to panic selling, leverage unwinding, and liquidity crises. A 30% decline can happen in weeks, while a 30% gain typically takes months or years. This structural asymmetry produces negative skewness in return distributions, especially over shorter time horizons.
- How does skewness affect retirement planning?
- Negative skewness means large losses are more probable than large gains. For retirees withdrawing from their portfolio, this amplifies sequence-of-returns risk — the downside events that damage retirement plans the most are precisely the ones that occur more frequently than a symmetric model predicts.