Downside Correlation — TWR
Pearson correlation computed only over the loss periods (where at least one of the two reports is down) — captures whether two strategies tend to draw down together, which ordinary correlation can hide.
- Computed from
- Equity curve
- Scope
- Across reports
- Range
- −1 to +1
- Direction
- Lower is better
Downside correlation measures how closely two reports move together — but only over the periods when at least one of them is losing. (Correlation is a single number from +1 to −1: +1 means two things move in lockstep, 0 means they're unrelated, −1 means when one rises the other falls.) Ordinary return correlation averages across every period, calm and stressed alike, so it's dominated by the many quiet days and tells you how the pair behaves on average. Downside correlation throws those calm days out and asks the question that actually decides whether diversification (spreading your risk across strategies so they don't all fail at once) survives a crisis: when one strategy is bleeding, is the other bleeding too — do they crash together? Like return correlation it's a cross-report (portfolio) metric, computed across the reports in a collection.
How it's calculated
ρ_downside = Pearson( rᵢ, rⱼ ) over periods where min(rᵢ, rⱼ) < 0
- rᵢ, rⱼ
- the two reports’ per-period RETURNS (not curve levels) over the overlap
- min(rᵢ, rⱼ) < 0
- the filter — keep only periods where AT LEAST ONE of the two is negative
TWR basis (default): downside correlation of cashflow-neutral returns — the right read for "do these two strategies draw down together," independent of when money was deposited or withdrawn.
What it tells you
This is the read that matters for crisis survival — a portfolio lives or dies by whether its sleeves draw down at the same time. For a portfolio, lower is better.
| Value | Reading | Notes |
|---|---|---|
| +0.7 to +1.0 | Crash together | False diversification — every sleeve bleeds at once, so the combined drawdown is far worse than the average correlation implied. |
| +0.3 to +0.7 | Sink together in stress | Partial joint drawdown — some shared downside risk remains. |
| −0.3 to +0.3 | Independent in the bad times | True diversification — when one bleeds the others are unaffected, so the portfolio drawdown is genuinely smoothed. |
| −1.0 to −0.3 | Tends to offset in stress | One tends to hold up — or profit — when the other is bleeding. Treat a negative reading as a soft hedge, not a guaranteed one: part of it comes from one-down-one-up periods (see Pitfalls). |
Downside vs ordinary correlation
Return correlation averages over all periods. Most periods are calm, so the calm regime dominates the number and it understates how together the pair moves in a crash. Downside correlation drops the calm periods and looks only at the losses, so it sees the regime that actually threatens you.
Read the two side by side. A pair with ordinary 0.2 but downside 0.7 looks diversified on a normal day and behaves like one position in a crisis — the gap between the two numbers is the diagnostic. When they roughly agree, the diversification you measured is the diversification you'll actually get.
Why the gap appears
A low-ordinary / high-downside gap is the fingerprint of a hidden common factor — something two strategies secretly share that only switches on under stress. In calm markets each runs on its own edge and they look independent; in a squeeze the shared factor dominates and they move as one. The usual suspects in forex:
- The same USD funding — in a dollar squeeze (March 2020) everything funded in dollars moves together regardless of "strategy."
- The same broker / liquidity pool — when the liquidity provider widens spreads and gaps prices, both books get stopped out at once.
- The same carry or volatility regime — the August 2024 JPY carry unwind torched a dozen "different" strategies that were all quietly short-volatility / long-carry.
So the gap isn't just a label — it's a prompt: when you see it, go find what the two strategies actually share. That shared thing is the risk you're really carrying.
What high downside correlation does to you
The harm is mechanical. When sleeves draw down in the same periods, their drawdowns stack — they add up instead of partly cancelling. A book of strategies that were truly independent would see a combined worst drawdown far smaller than the sum of the individual ones; a book that crashes together sees its combined max drawdown approach the sum of its parts. That's the difference between a survivable dip and a margin call.
What to do when downside correlation is high across a cluster:
- Size the cluster down as if it were one position — don't budget risk as though you hold N independent bets when, in a crisis, you hold one.
- Add a genuinely different stress factor — a strategy whose bad days are driven by something else (a different funding currency, broker, or market regime), or a real hedge. Adding more strategies from the same family doesn't help; it just buys more of the same hidden bet.
Pitfalls
- Treat it as directional, not precise. The stress events it cares about are rare, so even a "valid" estimate rests on few real crises — and the next crash may have a different driver. It flags the relationship; it doesn't pin it to two decimals. Don't over-trust a +0.71-vs-+0.64 distinction.
- It needs more history than ordinary correlation. The loss filter drops the calm periods, so small overlaps produce a very unstable coefficient — even noisier than ordinary correlation at the same span. EquityTruth uses larger windows and a higher min-obs floor for exactly this reason; still, read it next to how many filtered periods it's based on.
- No single-number N-eff for the downside view. The matrix is filtered pairwise (each cell to its own loss periods), so it isn't positive-semidefinite — the eigenvalue-based effective strategies number is computed on the ordinary Pearson matrix only. Downside tells you tail co-movement pair by pair; you can't roll it into one concentration figure.
- Still linear Pearson. It won't perfectly capture non-linear tail dependence — but it's far better than ordinary correlation at seeing crash co-movement, because it's measured in the crashes.
- The "at least one losing" filter is a trade-off. A stricter "both losing" filter would be a purer joint-crash measure — but on typical 1–3 year histories it leaves too few periods to estimate ρ at all, so EquityTruth keeps every period where at least one leg is down. The cost: one-down-one-up periods read as anti-correlation and can make a tail-dependent pair look milder than a pure joint-crash measure would. So read a high value as a strong signal, and a low value with that dilution in mind.
- Basis matters. TWR vs money-weighted vs dollar carry the same caveats as ordinary correlation; stay on TWR unless you specifically want one of the others.
Related
Return Correlation — the calm-market sibling; always read the two together · Effective Strategies — the portfolio-concentration number (Pearson only) · Max Drawdown — the severity downside correlation predicts.