Measuring Downside-Conditional Correlation Between Funds
Summary
The document considers how fund-of-funds investors can distinguish correlation during favorable periods from co-movement during losses. Two candidate funds may have similar overall correlations with an existing holding, yet differ in whether their relationship is concentrated on rising or falling days. The discussion suggests comparing correlations within defined market regimes, such as bear and bull periods, and points to asymmetric correlation as a broader framework.
A related approach is to calculate semi-correlation, which accounts for the direction of price movements. Semi-variance, semi-covariance, and semi-beta are mentioned as related downside-sensitive measures. The document offers conceptual guidance and cites research on extreme correlation, bear-market correlation, tail dependence, and realized semi-correlations, but it provides no empirical comparison or formula for choosing a threshold. Results depend on how regimes or movement directions are defined; filtering observations where both returns are positive is one possible analysis, not a complete prescription.
Key ideas
- Overall correlation can conceal whether co-movement occurs mainly during gains or losses.
- Calculate correlations separately across market regimes to study asymmetric dependence.
- Semi-correlation incorporates the direction of price movements.
- Semi-variance, semi-covariance, and semi-beta are related downside-sensitive measures.
- Regime definitions and sample selection affect the resulting estimates.
Tags
Full text
# Theory about *bad* correlation or downside correlation # Theory about *bad* correlation or downside correlation For fund of funds comparing the returns of two funds and measuring their correlation. It is good correlation when they both go up and bad correlation when they both go down. So if B and C have the same correlation to our existing fund A, but main contribution of cor(AB) is the good days while main contribution of cor(AC) is the bad days, we would prefer to add B to the portfolio. Is there an adjusted 'correlation' measure to take that into account? Can I remove the data points when both A and B are positive and calculate the correlation of remaining data? ## Answer by Dimitri Vulis (score 2) https://quant.stackexchange.com/a/81323 I think you are looking for the "asymmetric correlation". The most basic approach is to first identify regimes, like "severe bear market" or "mild bull market", to split up the history into the regimes, and then to calculate Pearson's $\rho$ separately under each regime. There are more complicated approaches, not necessarily giving better insight. Some relevant papers: Longin, Solnik. Extreme correlation of international equity markets. https://doi.org/10.1111/0022-1082.00340 Campbell, Koedijk, Kofman. Increased Correlation in Bear Markets. https://doi.org/10.2469/faj.v58.n1.2512 Jondeau. Asymmetry in tail dependence in equity portfolios. https://doi.org/10.1016/j.csda.2015.02.014 ## Answer by ysimsek (score 2) https://quant.stackexchange.com/a/81329 You can also check semi-correlations in which direction of price movements are taken into account. Similar concepts like semi-variance and semi-covariance and semi-beta are also well studied in the literature. Paper: Bollerslev, Patton, Zhang: Equity clusters through the lens of realized semicorrelations. https://doi.org/10.1016/j.econlet.2021.110245
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.