Diversification, Crisis Correlations, and Tail-Risk Management

# Why does it "say" portfolio diversification not suitable during market turmoil?


# Why does it "say" portfolio diversification not suitable during market turmoil?












Currently I am trying to get a hold of MPT, asset allocation and related applications.

While reading a particular resource, it says diversification works best for "normal" financial markets and provides less risk reduction during market turmoil.

- Can someone explain how and why less risk buffer during crisis?

- How or why does correlation between assets in portfolio increase during such?

- Can't we have a diversified portfolio like 7-12 approach which could withstand financial crisis and still perform better?

- If can't then what's the approach for crisis in terms of managing investments?

- How to find low correlated asset to shield and perform front of crisis?

## Answer by user2763361 (score 6, accepted)

https://quant.stackexchange.com/a/10534

Accurately stated: Diversification helps during turmoil, but helps less as what would be expected by using $w^T \Omega w$ as the portfolio variance where the off-diagonal covariances are estimated during tranquil periods.

This is because correlations and covariances change during turmoil, typically increasing. This reduces the benefit of diversification since the off-diagonal elements, $\sigma_{i,j}(t)$, tend to now be larger when $t$ belongs to a turmoil regime.

This is true only up to the point of assets that suffer from contagion. In fact the exact opposite is true for assets that are considered to be safe haven assets, such as gold, some currencies (USD,JPY,CHF,perhaps GBP) and some government fixed income instruments. Here, diversification works better during market turmoil since these assets can be relied on in most cases to increase in value during such conditions. Thus the statement is true only assuming you are investing in assets that suffer from contagion.

In addition, the extent to which contagion (technically defined as an increase in general comovement - which itself is not technically defined - between asset prices during crises) exists at all not a settled question. I refer you to Forbes and Rigobon (2001) and follow up papers. This is because the fact that $\sigma(t)$ tends to increase during crises causes a bias in $E[(\rho(t))]$ where $\rho$ is the Pearson estimator and $E$ is the expectation. Note that this was the state in mid 2000s, and the literature could have settled the question since then. Wavelets and copulas have both shown it in at least one paper which are not susceptible to such biases in a way that I am aware of; the FB (2001) result is for Pearson's correlation.

From a portfolio management perspective, I recommend looking into time-varying multivariate copulas of the flavour of the Symmetrized Joe-Clayton Copula and later derivatives such as the SCAR in order to calibrate the left-tail comovement during turmoil periods. I am aware of only a very small contagion literature that takes this approach but I feel it is the best approach for this question.

However many practitioners will take a qualitative, and not quantitative approach. Many in the industry actually refuse to rely on any sort of mathematical optimisation due to the estimation error in $E[R(t)]$ and $\hat{\rho(t)}$ (as well as pure ignorance of academic literature since Markowitz), and will instead try to diversify by using a subjective mish-mash of sector exposure, style exposure, factor exposure, country exposure, asset class exposure, and so on. I am not against this approach. This is only possible on the asset-class level optimisation (although this can still be applied at the stock level, for example, by using Black-Litterman).

## Answer by vonjd (score 7)

https://quant.stackexchange.com/a/10536

This is indeed a subtle point. What is generally meant with this statement is that correlation is going up in bear markets, so it is not so much the "turmoil" part (i.e. volatility per se) but the "trend" (i.e. negative in this case) part. Putting it another way is that when you control for volatility not the correlation but the covariance (which is the part entering the optimization algorithm for MPT) is going up in bear market regimes.

There are several ways to tackle this:

One way is that you can impose a dynamic risk management overlay, i.e. you can try to identify in which regime you are at the moment (with whatever method, e.g. stress indicators, hidden markov models etc.) and leave the market (e.g. partially) in times of unrest.

Another way is to have a look at the temporal correlation structure of different markets, assets etc. so that you try to find which ones preserve or develop a more beneficial set in times of crises (there is a good paper from Kritzman, which I cannot find right now).

A third way would be to try to model the dependence structure with more sophisticated methods, like copulas or random matrix theory.

You can of course also try to combine all or some of the methods above.