Rebalancing Risk

Nicolas M Granger

Man Group

Douglas Greenig

Independent

Campbell R. Harvey

Duke University – Fuqua School of Business; National Bureau of Economic Research (NBER)

Sandy Rattray

AHL / Man Systematic Strategies

David Zou

Man Group plc – AHL Man Systematic Strategies

Abstract:

While a routinely rebalanced portfolio such as a 60-40 equity-bond mix is commonly employed by many investors, most do not understand that the rebalancing strategy adds risk. Rebalancing is similar to starting with a buy and hold portfolio and adding a short straddle (selling both a call and a put option) on the relative value of the portfolio assets. The option-like payoff to rebalancing induces negative convexity by magnifying drawdowns when there are pronounced divergences in asset returns. The expected return from rebalancing is compensation for this extra risk. We show how a higher-frequency momentum overlay can reduce the risks induced by rebalancing by improving the timing of the rebalance. This smart rebalancing, which incorporates a momentum overlay, shows relatively stable portfolio weights and reduced drawdowns.

Rebalancing Risk – Introduction

Constant-mix strategies, such as allocating 60% of the value of a portfolio to equities and 40% to bonds, are used extensively by pension funds and other long-term investors. In such strategies, the investor periodically rebalances the portfolio so that each asset class is a constant fraction of portfolio value rather than allowing the allocation to drift as asset prices change.

Constant-mix strategies have intuitive motivations, but we believe key properties of these strategies are poorly understood by many investors. In particular, rebalancing can magnify drawdowns when there are pronounced divergences in asset performance. Such divergences are usually driven by equities, and in late 2008 and early 2009, some rebalanced strategies underperformed passive strategies by hundreds of basis points.

In traditional 60/40 portfolios, the vast majority of the risk (ca. 85%) comes from the allocation to equities.1 Equity indices, in addition to generally having much higher volatilities than bond indices, have fat downside tails, i.e. large negative returns and sharp drawdowns occur more frequently than large positive returns. Constant-mix strategies not only inherit these properties, but actually exacerbate the drawdowns.

We demonstrate how the opposing return profile of a momentum overlay can help to mitigate the added risk introduced by the rebalancing process. Although momentum trading itself has produced long-term positive returns, even without any assumptions of positive performance, momentum acts to improve the risk and drawdown properties of the constant-mix portfolio according to both theoretical and historical analyses.

We provide a technical appendix which gives analytic explanations for the results described in the main body of the paper. This appendix provides the theoretical arguments to elucidate how the rebalancing process can change the risk properties of the portfolio and how a momentum overlay can help. The appendix is provided principally to demonstrate that the results in this paper are of an analytic nature and are not dependent on the particular realization of history seen in the empirical data. If one can take this on trust, reading the appendix is purely optional.

Rebalancing Risk: Fixed weights vs. drift weights

A passive buy-and-hold strategy is an alternative to a constant-mix strategy. Under buy-and-hold, one simply buys a portfolio (e.g. 60% equities/40% bonds) and holds it without trading for a period of time.2 The capital allocation within the portfolio will obviously drift as market prices change, but the investor remains passive. In contrast, the active rebalancing in the constant-mix strategy will restore the target fixed weights. We shall also call the buy-and-hold approach a drift-weight portfolio, to be contrasted with fixed weights under rebalancing.

The motivations behind a constant-mix strategy are straightforward. First, drift weights may become extreme as assets diverge. In 2013, the S&P500 delivered a total return of 31.9%, while the S&P 7-10 Year U.S. Treasury bond index declined by 6.1%3. A 60/40 portfolio would have drifted over 2013 to a 68/32 portfolio, and, with a repetition of these returns in 2014, a 74/26 portfolio. In practice, few if any investors remain passive indefinitely as drift weights become extreme. At some point, the investor is likely to adjust the weights. The constant-mix strategy sensibly puts this adjustment process on a regular schedule.

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