Asset Allocation

CHAPTER 5Divergence

FALLACY: VOLATILITY SCALES WITH THE SQUARE ROOT OF TIME, AND CORRELATION IS CONSTANT ACROSS RETURN INTERVALS

Investors commonly, and sometimes unknowingly, assume that the standard deviation of asset returns scales with the square root of time. They also make the analogous assumption that correlations are invariant to the return frequency from which they are estimated. Both beliefs rest on the same underlying assumption that returns are serially independent from one period to the next. This assumption is ubiquitous. It is hard-coded into risk and optimization platforms throughout the industry. Many institutions rely on it to determine their strategic asset mix. It is even embedded in the Global Investment Performance Standards (GIPS) to which most investment managers adhere when reporting results to their clients. Unfortunately, it is often incorrect.

We suspect that most sophisticated investors are aware that this assumption does not always hold but presume its impact is negligible. The evidence suggests otherwise. Major asset classes such as private equity and fixed income exhibit significant nonzero autocorrelation. Moreover, pairs of assets such as US and emerging market equities exhibit divergence between short- and long-interval correlations. In this chapter, we present an empirical analysis of this phenomenon across a range of asset classes and investment vehicles. We introduce a measure to quantify the degree of divergence as well as a methodology ...