What Is Tail Risk Parity?
Tail risk parity allocates capital so that each holding contributes equally to the portfolio's extreme loss rather than to its volatility. It corrects risk parity's assumption that volatility describes risk, while depending on estimates of rare events that are inherently hard to measure.
Risk parity sizes positions so each contributes equally to portfolio volatility. Tail risk parity does the same for the worst case, which is a better question asked with worse data.
How it works
Standard risk parity equalises volatility contribution. A calm asset gets a large weight, a volatile one a small weight, so each adds the same amount of variation.
Tail risk parity equalises contribution to the extreme loss instead, using a measure such as expected shortfall rather than standard deviation.
The distinction is not theoretical. A government bond and a short-volatility strategy can show the same volatility and behave nothing alike in a crisis.
Why volatility is the wrong yardstick
Standard deviation is symmetric and assumes a shape. It treats a distribution as though the middle describes the edges, which is true for a normal distribution and false for financial returns.
A strategy with steady small gains and rare large losses looks calm. Its measured volatility is low throughout the period before its risk appears, so a volatility-based method gives it a large weight.
Which is how volatility-targeted portfolios accumulate exactly the exposures that fail together, and the flaw this method is built to correct.
A worked example
Two holdings, both with 10% annualised volatility. A risk parity allocation gives them equal weight.
Holding A is a diversified bond portfolio. Its worst historical outcome is a drawdown somewhat larger than its volatility suggests.
Holding B sells options. Its volatility is low because nothing has gone wrong, and its plausible worst outcome is a loss many times that figure.
Tail risk parity weights B far lower, correctly, on the basis that its contribution to the portfolio’s worst case is enormous despite identical volatility.
Where the method runs into trouble
Tail estimates need extreme observations. A tail measure calculated from ten years of data rests on the handful of worst days in it, and a handful supports no precise estimate.
Tail correlations are worse still. Estimating how two assets behave together in extremes requires observations of them both in extremes simultaneously, which are rarer again.
And the estimates are unstable. Adding or removing one bad day from the sample can change an allocation materially, which is not a property anybody wants in a sizing method.
So the honest description is a trade rather than an improvement. Volatility is measured precisely and answers the wrong question; tail measures answer the right question imprecisely, and which is better depends on how wrong each is in the situation at hand.
The original data
On this site’s shared series the median bar range is 0.493, the ninetieth percentile 1.101 and the largest single bar 2.338 — the maximum being 4.7 times the median. Drawdown reaches 3.76% at most, with 95% of bars below a prior peak.
A volatility-based allocation is built from the median region. A tail-based one is built from that single 2.338 bar and a few near it, which is the entire difference in reliability between the two approaches expressed in one series.
And rebalancing costs apply: a round trip costs 0.0098, about 2% of the median bar range. A method whose allocations shift when one extreme observation enters or leaves the sample generates turnover, and turnover costs.
What survives from the idea
The critique is sound regardless of the implementation. Volatility genuinely understates the risk of asymmetric strategies, and any allocation method blind to that will accumulate them.
A crude version captures most of the benefit. Simply capping exposure to strategies with insurance-like payoffs achieves much of what the formal method aims at, without estimating anything.
And scenario analysis substitutes for estimation. Asking what each holding would do in a specified stress, rather than fitting a tail distribution, produces a defensible allocation from explicit assumptions.
Which is probably the most useful takeaway. The formal method requires data that does not exist; the reasoning behind it can be applied with judgement and improves a portfolio either way.
The family of methods it belongs to
Equal weighting ignores risk entirely and is surprisingly hard to beat, largely because it estimates nothing.
Mean-variance optimisation uses expected returns and covariances, and is notoriously sensitive to the return estimates, which are the least reliable input available.
Risk parity drops expected returns and uses only volatility, which removes the worst input and keeps a flawed risk measure.
This method drops the flawed risk measure too and substitutes one estimated from far less data. The progression is consistent: each step removes a bad input and increases reliance on what remains, and there is no version that estimates nothing and answers the question.
When it fails
The characteristic failure is precision that the data cannot support. The optimiser produces weights to two decimal places, derived from a tail estimate resting on perhaps five extreme observations across a decade. The output looks rigorous, it is reported with confidence, and removing a single day from the sample would shift the allocations substantially. The method inherits all the uncertainty of its inputs and displays none of it, which makes it more dangerous than an obviously rough approach — false precision invites size that genuine uncertainty would not.
A second failure is assuming tail correlations are stable. They are the least reliably estimated parameter in the whole calculation.
A third is trusting a short sample. Ten years may contain no genuine extreme at all.
A fourth is the turnover, as allocations shift when the estimation window rolls.
And a fifth is thinking the problem is solved. It is better framed than volatility targeting and it still rests on estimating the unestimable.
Related
Tail risk covers the exposure this attempts to budget. Downside risk covers measuring only the losing side. And position sizing covers the practical decision all of this feeds into.
Risk parity’s flaw is real: two assets with the same volatility can have completely different worst cases. This fixes the right problem and pays for the fix with parameters estimated from a handful of extreme observations, which is not obviously better — it is differently wrong.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.