One of the most vexing problems in investment management is that diversification seems to disappear when investors need it the most. Of course, the statement that “all correlations go to 1 in a crisis” is both an oversimplification and an exaggeration. But it has been well documented that correlations tend to increase in down markets, especially during crashes (i.e., “left-tail events. (Page 2)
Our goal in this article is to encourage practitioners to take action on such findings. Full-sample correlations are misleading. Prudent investors should not use them in risk models, at least not without adding other tools, such as downside risk measures and scenario analyses. (Page 2)
Not only did correlations increase on the downside, but they also significantly decreased on the upside. This asymmetry is the opposite of what investors want. Indeed who wants diversification on the upside? Upside unification (or antidiversification) would be preferable. During good times, we should seek to reduce the return drag from diversifiers. (Page 2)
During left-tail events, diversified portfolios may have greater exposure to loss than more concentrated portfolios. (Page 3)
How correlations change during extreme markets can be estimated in several ways. For example, Longin and Solnik (2001) and Chua et al. (2009) used “double conditioning.” They isolated months during which both assets moved (up or down) by at least a given percentage. We used a similar approach, but we conditioned on a single asset, as follows (Page 3)
Unlike Longin and Solnik’s (2001) approach, “single conditioning” measures differences in tail correlations based on which market drove the selloff. For some correlations, such as the stock–bond correlation, this difference can be substantial, and it adds information on the correlation structure. (Page 3)
First, we isolated months in our data sample during which US stocks, x, were down by, say, 5% or more (we calibrated thresholds, θ, to correspond to percentiles). Next, we calculated a correlation between stocks and bonds in this subsample, denoted corr( ) x y, | x < −5% .We also calculated the correlation between stocks and bonds when bonds, y, were down by 5% or more, denoted corr( ) x y, | y < −5% . As we will show, in this case, we found that bonds diversify stocks during stock selloffs but stocks do not diversify bonds during bond selloffs. Double conditioning would fail to reveal this lack of symmetry in the diversification between the two assets. (Page 3)
For each asset pair, we simulated two normal distributions with the same full-sample correlations, means, and volatilities as those we observed empirically. Then, we compared the empirical subsample correlations with their simulated normal counterparts. Also, under normality, downside and upside correlation profiles should be identical. Therefore, when left-tail and right-tail correlations are compared, the conditioning bias does not matter much because it “washes out.” Any asymmetry we found indicates a departure from normality. (Page 3)
The further one goes into the tails, the smaller the sample. At the top or bottom 1% or 5% of the distribution, a single outlier may significantly bias correlations up or down. (Page 3)
To do so, we used an exponentially weighted approach, as illustrated and derived in Appendix A. To our knowledge, this approach, although simple and intuitive, has not been used in prior studies; hence, perhaps we are making a modest methodological contribution to the measurement of conditional correlations. (Page 3)
We calibrated the model in such a way that observations further into the tails receive exponentially larger weights, and we fixed the half-life at the percentile under consideration. (Page 4)
When US stocks were rallying (in their 99th percentile), their correlation with non-US stocks dropped all the way to –17%. During the worst 1% selloffs in US stocks, however, their correlation with non-US stocks rose to +87%. This asymmetry reveals that international diversification works only on the upside. Longin and Solnik (2001), focusing on the correlations between the United States, France, Germany, the United Kingdom, and Japan, reported similar results for stocks at the country level. (Page 4)
We found similar results across risk assets. Figure 2 provides a comparison of left-tail and right-tail correlations for key asset classes.4 The focus is on US stocks versus other risk assets because the equity risk factor dominates the volatility factor (and exposure to loss) in most portfolios (see, for example, Page 2013) (Page 5)
Diversification fails across styles, sizes, geographies, and alternative assets. Essentially, all the return-seeking building blocks that asset allocators typically use for portfolio construction are affected. The asymmetry for the stock–MBS (mortgage-backed securities) correlation is notable. (Page 6)
Unfortunately, all the styles, including the market-neutral funds exhibit significantly higher left-tail than right-tail correlations A simple explanation could be that most hedge fund strategies are short volatility. Some are also short liquidity risk, which is akin to selling an option (Bhansali 2010). (Page 6)
Although many investors have become skeptical of the diversification benefits of hedge funds, the belief in the benefits of direct real estate and private equity diversification has been persistent. (Page 6)
Most investors know, however, that there is more to these statistics than meets the eye. Private assets’ reported returns suffer from the smoothing bias. In fact, Pedersen, Page, and He (2014) showed that the private assets’ diversification advantage is almost entirely illusory. (Page 6)
Not only is the true equity risk exposure of private assets higher than is implied by their reported returns on average, but their left-tail exposures are much higher. (Page 7)
Rolling annual correlations are less sensitive to the smoothing bias than those calculated on quarterly returns. As explained in Pedersen et al. (2014), reported quarterly returns for private assets represent a moving average of the true (unobserved) marked-to-market returns. (Page 7)
Page, Simonian, and He (2011) explained that systemic liquidity risk tends to manifest itself during stock market crashes. A systemic liquidity crisis can be compared with a burning building, in which everyone is rushing for the door, with one exception: In financial markets, to get out (sell), investors must find someone to take their place in the building (a buyer). (Page 7)
The failure of diversification across public and private return-seeking asset classes has led, in part, to the popularity of risk factors. (Page 7)
Again, we focused on diversification versus US stocks. Our results show that several risk factors do indeed appear to be more immune to the failure of diversification than are asset classes. (Page 8)
In addition, momentum strategies that sell risk assets in down markets provide left-tail diversification. (Page 8)
Portfolio insurance strategies, for example, can explicitly replicate a put option (minus the gap-risk protection). Hence, as expected, in Figure 5, currency and cross-asset momentum have much lower left-tail than right-tail correlations with US stocks. Our results also show, however, that risk-on factors, such as size (i.e., small minus big stocks) and currency carry, may fail to diversify stocks when needed. (Page 8)
The example of the currency carry trade illustrates the impact of regime shifts on correlations, which may explain the widespread risk-on/risk-off characteristic of return-seeking asset classes and risk factors. Financial markets tend to fluctuate between a low-volatility state and a panic-driven, high-volatility state (see, e.g., Kritzman, Page, and Turkington 2012). I (Page 9)
A partial answer is that macroeconomic fundamentals themselves exhibit regime shifts, as documented for inflation and growth data. Also, we surmise that investor sentiment plays a large role. In normal markets, differences in fundamentals drive diversification of risk asset returns. During panics, however, investors often “sell risk” irrespective of differences in fundamentals. (Page 9)
When market sentiment suddenly turns negative and fear grips markets, government bonds almost always rally because of the flight-to-safety effect (Gulko 2002). In a sense, duration risk may be the only true source of diversification in multi-asset portfolios. (Page 10)
The stock-bond correlation is difficult to estimate, however, and can change drastically with macroeconomic conditions.6 Johnson, Naik, Page, Pedersen, and Sapra (2014) explained that when inflation and interest rates drive market volatility more than business cycles and risk appetites do, the stock-bond correlation often turns positive (Page 10)
Although the correlations are generally low, when bonds sell off, stocks can sell off at the same time. Ultimately, investors should remember that stocks and bonds both represent discounted cash flows. Unexpected changes to the discount rate or inflation expectations can push the stock-bond correlation into positive territory— especially when other conditions remain constant. (Page 11)
We have shown that during crises, diversification across risk assets almost always fails, and even the stock-bond correlation may fail in certain market environments (Page 11)
Conditional betas, for example, take into account changes in relative volatilities as well as correlations. In theory, it is possible for the correlation between two assets to increase while the volatility of the diversifier decreases relative to the main engine of growth in the portfolio. (Page 11)
Ultimately, we chose to study correlations as they measure diversification directly, and correlations have been used widely in prior studies. (Page 11)
We recommend that investors avoid the use of full-sample correlations in portfolio construction— or, at least, that they stress-test their correlation assumptions. Scenario analysis, either historical or forward-looking, should take a bigger role in asset allocation than it does. A wide range of portfolio optimization methodologies directly address nonnormal left-tail risk and, ipso facto, the failure of diversification. The most flexible is full-scale optimization. (Page 11)
Finally, investors should look beyond diversification to manage portfolio risk. Tail-risk hedging (with equity put options or proxies), risk factors that embed short positions or defensive momentum strategies, and dynamic risk-based strategies all provide better left-tail protection than traditional diversification. The strategy of managed volatility is particularly effective and low-cost approach to overcome the failure of diversification. (Page 12)
Importantly, because managed volatility scales down risk assets when volatility is high, it often offsets left-tail correlation spikes and thereby reduces exposure to large losses without sacrificing returns on the upside. (Page 12)
Conditional correlations reveal that during market crises, diversification across risk assets almost completely disappears. Moreover, diversification seems to work remarkably well when investors do not need it—during market rallies. This undesirable asymmetry is pervasive across markets. (Page 12)
The good news is that tail risk– aware analytics, as well as hedging and dynamic strategies are now widely available to help investors manage the failure of diversification. (Page 12)