Eggs Not Enough: The Truth About Diversification

October 22, 2012

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!

Table 2

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.

Figure 1
(For a larger view, please click on the image above.)

 

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