Articles

Eggs are Not Enough: The Truth About Diversification

By Feifei Li

OCTOBER 2012 Read Time: 10 min


We learn in finance theory that diversification simply means not putting all your eggs in one basket.

Simple as the idea is, most investors do not hold portfolios that are even close to being truly diversified. Two reasons make this sensible objective difficult to achieve. First, most investors are not disciplined enough to implement diversification. To illustrate my point, pause and check whether you are willing to reduce equities when the trailing 12-month return on stocks is 20+ percentage points higher than bonds?

Second, but not less importantly, most investors do not actually diversify their equity risk with their investment decisions; they are still exposed to a significant negative shock. Returning to our initial definition, many portfolios look like a truck with several baskets of eggs loaded on it. Clearly, investors’ eggs are vulnerable to the truck tipping over.

This issue of Fundamentals will show why it is so important to get your estimates of risk correct in asset allocation decisions.

Source of True Diversification
Many of my Chinese friends who are not in the finance field view having Apple, Facebook, and a few more hot stocks in their brokerage accounts as providing sufficient diversification. Luckily, like most Chinese people, they also love to own real estate and put huge amounts of money in savings accounts. So, to a degree, they are more diversified than they think they are.

My more investment-sophisticated friends own a portfolio with multiple asset classes including equities, bonds, commodities, etc. And within each category, they diversify across geographical or economic regions. For example, they hold both U.S. Treasuries and Emerging Market Sovereign Bonds. They also believe they are adequately diversified. They are better diversified than my less sophisticated friends, but they are probably not adequately diversified.

The truth is, diversification across multiple asset classes is not sufficient. An adequately diversified portfolio should also be diversified over time and over different economic regimes. Yes, the tactical element in your allocation!

In standard finance applications, asset class volatilities and correlations are usually assumed to be constant over time for simplicity. For example, Harry Markowitz’s mean-variance optimization requires that the asset class variance–covariance matrix is known and constant over the holding horizon. While this simplified assumption reduces the complexity of the models and their calculations, it could also lead to sub-optimal portfolios and risk management solutions. If equity market volatility is time-varying and is negatively correlated with equity market returns, ignoring this counter-cyclicality could lead to excess allocation to stocks when forward-looking risk for stocks is high. Furthermore, if equity market volatility is positively correlated with the volatilities of other asset classes, ignoring this correlation would again lead to an overall overconcentration in risky assets.

Macro Factor Influence
To demonstrate that common macro factors indeed drive the movements in financial assets, Table 1 illustrates volatilities for 16 asset classes in expansionary and recessionary environments over the period 1997–2012. As Table 1 shows, equities tend to experience a sharp spike in volatility when an economy is in a recessionary period compared to an expansionary period.1 This sharp increase in equity market volatility often goes together with rising volatilities in other pro-cyclical asset classes such as commodities, high yield, and long credit. 


The results in Table 1 suggest that shocks to equity valuation often spill over to other markets, and that liquidity-driven selling and the reduction in liquidity provision in the capital market are often systemic across various asset classes. This observation is confirmed by the correlation data. For this data set, the average of correlations across all 16 asset classes nearly doubles to 0.50 in recessionary stages from 0.28 in expansionary periods. Their correlations with the S&P 500 Index average 0.62 in economic downturns in contrast to 0.39 in expansions.

The evidence presented illustrates two points: (1) the second moments (i.e., volatilities and correlations) of asset classes’ returns change drastically during different business cycle phases; and (2) true diversification is harder to achieve in recessions than in expansions.

To address the cyclicality issue, many people introduce correlation timing techniques such as regime-switching models and recession forecasting models into the asset allocation process. We can illustrate the advantage of introducing the time-varying variance–covariance matrix vividly by using a forecasting model with 100% hindsight. If we can predict NBER recession dates with 100% precision, the optimal portfolio of the 16 asset classes will give us an annualized return of 10.96% and a volatility of 10.05%, versus a return of 10.37% and volatility of 12.6% for the portfolio utilizing the long-term average covariance for optimization.

Let’s say we cannot achieve 100% accuracy on when the economic regime shifts. Even when our dates are three months earlier or later than the actual regime switching dates, the portfolio still provides a Sharpe ratio much higher than the static model. In fact, when the business cycle (here we use NBER cycle definition) forecast model predicts a bit earlier than the actual switching dates, the Sharpe ratio of the portfolio is slightly better than the optimal one with perfect precision.2

The picture in Table 2 is pretty clear—once you get the second moments estimates right, your asset allocation practice can be a lot more effective!


Is This Time Different?
Since the Global Financial Crisis, we have seen a shift in the cross-asset classes’ correlations. Asset classes seem to be more correlated than they used to. The trailing 10-year average pair-wise correlations among the 16 asset classes have jumped to 0.44 today from the level of 0.28 prior to Lehman’s debacle in September 2008. Not surprisingly, people are asking whether this shift is a permanent structure break or just a cyclical peak. We believe it is too early to tell. After three and a half years, the short- to medium-term correlations based on 1-year or 3-year time periods have come down, but the 5-year and 10-year numbers continue to drift higher (see Figure 1). So, is this time really different? Probably not.


Conclusion
Diversification remains one of—and perhaps the most important—consideration as investors design their investment portfolios. Asset classes have distinct volatility, correlation, and risk premium characteristics in both recessionary and expansionary periods. Employing long-term historical relationships across asset classes could lead to substantial underperformance when regime shifts happen because volatilities for various risky asset classes tend to be low in equity bull markets and high in equity bear markets.

Investors should pay attention to how they achieve diversification in their portfolios. In recessionary periods, correlations between asset classes rise. Investors need to ensure they shift their asset allocation as regimes change. Capturing this time-varying characteristic is important for obtaining mean-variance portfolio optimization. When the road is smooth and straight, investors can carry as many baskets of eggs that they want. But when it is bumpy and twisted, investors need to diversify the goods they are bringing to market—adding carrots, corn, and sweet potatoes in the event that their vehicle drives off the road.

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Learn More About the Author

Feifei Li

PhD, FRM
Director, Head of Investment Management


Endnotes
1. We use the NBER recession dates to determine whether a period is Expansionary or Recessionary.
2. This result is not all that surprising given the well-known fact that NBER cycle definition tends to lag behind capital market movements.