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Diversification with Negatively Correlated Assets That Both Have Positive Trends

Article Quant Q&A · Author: thisisenfield
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Summary

The document discusses assets that can have positive expected returns while their deviations from those trends are negatively correlated. It distinguishes this pattern from pairs trading, which generally seeks to profit from relative performance, and frames the main application as diversification: holding both assets can reduce portfolio volatility while retaining exposure to their average returns.

Stocks and bonds are offered as a familiar example, with gold and other assets also mentioned. Risk parity is presented as a portfolio approach that can express this idea by allocating in relation to asset risk, such as using inverse volatility or inverse marginal risk contribution. The discussion is qualitative and cautions that reliable negative correlations between individual stocks are uncommon; correlations can vary, and broad market exposure may dominate. No estimation method, backtest, or performance evidence is supplied.

Key ideas

  • Positive expected returns can coexist with negative correlation in deviations from those returns.
  • Diversification can use negative correlation to reduce portfolio volatility.
  • Pairs trading targets relative performance and is distinct from holding two positively trending assets for diversification.
  • Risk parity can allocate exposure in relation to volatility or marginal risk contribution.
  • Negative correlations may be unstable, and market exposure can dominate individual stock relationships.

Tags

Portfolio constructionRisk managementPairs tradingEquitiesFixed income
Full text
# Negatively Correlated Assets with similar medium-term trends


# Negatively Correlated Assets with similar medium-term trends












Theoretically, one could have stock prices with returns $\rho_1(k)$ and $\rho_2(k)$ having mean values $\mu_1$ and $\mu_2$, but still be negatively correlated with $$ \mathbb{E}[(\rho_1(k)-\mu_1)(\rho_2(k)-\mu_2)]<0. $$ Could this kind of model have any practical applications? Could we say that pairs-trading exploits a similar model?

## Answer by demully (score 3)

https://quant.stackexchange.com/a/49145

It is very rare to find stocks that are reliably negatively correlated with each other. At least in absolute (as opposed to relative outperformance) terms. It can happen from time to time, but the positive correlation/beta to market usually prevails as the dominant driver of risk/returns.

This said, the classic example of the phenomenon you're asking about is stocks versus bonds. Both are (usually) priced for positive expected returns, albeit with a negative (or at least zero) correlation when they better/worse than drift. Or gold-vs-bonds, or gold-vs-stocks etc.

The practical application of this kind of thing isn't really pairs-trading. Long-short would capture the spread between two positive returns, by doubling down on the relative risks between the two assets. It's more the essence of diversification - playing for the average, while using the -ve correlation to reduce volatility.

In its purest form, the model most explicitly designed to capture this kind of effect is "risk parity". IE long of both in inverse proportion to their risk (either inverse vol, or inverse marginal contribution to portfolio risk). Albeit this is optimised for the two assets to have returns proportionate to their volatilities. The proportions invested would vary with the precise figures assumed/expected; but the concept is the same.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.