Intertemporal risk parity: a constant volatility framework for factor investing

29 Sep 2014

Intertemporal risk parity is a strategy that rebalances risky assets and cash in order to target a constant level of ex ante risk over time. When applied to equities and compared with a buy-and-hold portfolio it is known to improve the Sharpe ratio and reduce drawdowns. We apply intertemporal risk parity strategies to factor investing, namely value and momentum investing in equities, government bonds and foreign exchange. Value and momentum factors generate a premium which is traditionally captured by dollar-neutral long–short portfolios rebalanced every month to take into account changes in stock, bond or foreign exchange factor exposures and keep leverage constant. An intertemporal risk parity strategy rebalances the portfolio to the level of leverage required to target a constant ex ante risk over time. Value and momentum risk-adjusted premiums increase, sometimes significantly, when an intertemporal risk parity strategy is applied. Volatility clustering and fat tails are behind this improvement of risk-adjusted premiums. Drawdowns are, however, not smoothed when applying the strategy to factor investing. The benefits of the intertemporal risk parity strategy are more important for factor premiums with strong negative relationship between volatility and returns, strong volatility clustering and fat tails.


The literature on factor investing is extensive and dates back many years. Basu (1977) is often given the credit for uncovering the value premium, even if the idea of value investing is older and has been known about at least since the work of Graham (1949). Value stocks are said to be trading at prices too low for their level of earnings, book value or cashflow and have historically delivered returns above what would be expected from their level of risk. Banz (1981) discovered the size premium arising from investing in small-capitalization stocks. Small-capitalization stocks have also been paying higher returns than expected from their level of risk over time. Jagadeesh and Titman (1993) uncovered the momentum premium arising from investing in stocks with the fastest past trends over horizons of about twelve months. On average, these stocks have also been paying returns above what would be expected considering
their level of risk. Low-risk premium arising from investing in stocks with the lowest volatility or lowest beta was uncovered by Haugen and Heins (1972). Low-volatility stocks have been paying much higher returns than expected considering their level of risk and even manage to outperform the riskier stocks in a number of markets (Haugen and Baker 2012).

Factor investing began attracting attention with the proposal of Fama and French (1992, 1993) of a three-factor model for assessing the alpha in portfolios by estimating not only the exposure to the market portfolio, but also the exposure to value and size premiums. Charhart (1997) extended the Fama–French model to include the momentum premium and Scherer (2011) proposed the addition of low-risk factors to measure exposure to the low-risk premium.

Bender et al (2014) showed recently that the performance of traditional portfolios could be split into beta, alpha and factor-premium contributions. They explain that factor-premium contributions are the portion of alpha that can be captured via systematic investment strategies. Indeed, the key reason to separate alpha-generated from factor exposures from other alpha sources is the fact that factor premiums can be accessed through relatively simple systematic strategies.

Recent research also demonstrates that the increasingly popular smart-beta equity indexes earn their excess returns from exposures to factors. Scherer (2011) showed that minimum variance is essentially exposed to the low-risk premium. De Carvalho et al (2012) extended his work to show that maximum diversification as introduced by Choueifaty and Coignard (2008) is also strongly exposed to the low-risk premium and that risk-parity strategies, as first introduced by Dalio (2005), generate strong exposures to the size, low-risk and value premiums when applied to stock universes. Finally, Chow et al (2011) showed that fundamental indexing, another type of smartbeta equity indexation, is essentially exposed to value premium.

Asness et al (2013) showed that momentum and value premiums are not exclusive of the equity markets but can also be found in other asset classes such as government bonds, foreign exchange or commodities. They also demonstrated that combinations of factor premiums result in better performances than exposures to a single factor premium. This adds to the evidence previously found by Qian et al (2009) that value premium can be captured not only in equities but also in government bonds and foreign exchange.

Capturing factor premiums requires an active strategy that rebalances the portfolio to adjust for factor exposures. Stock exposures to factors change over time and the active strategy must trade accordingly. The most common strategy is to create a long–short portfolio which invests in the stocks with the strongest exposure to the factor and sells short stocks with the weakest exposures. Stocks are equally weighted (and sometimes market-cap weighted) in both the long and short portfolios and the long–short portfolios are periodically rebalanced to a given predefined level of leverage relative to assets under management which is kept constant over time. This factor strategy can also be applied to other asset classes.

As Asness et al (2013) pointed out, there is not one unique active strategy but many different systematic strategies which can be used to capture factor premiums. Neither the volatility of stocks, nor correlations between pairs of stocks, is constant over time. Thus, the constant leveraging of a long–short portfolio is sure to have variable risk over time. Rather than rebalancing to a constant level of leverage, Asness et al (2013) propose instead that the long–short portfolios should be rebalanced toward the leverage which is required to target a given predefined level of ex ante risk. They claim that the strategy which rebalances toward constant ex ante risk delivers better risk-adjusted returns than the strategy which rebalances toward constant leverage, at least before transaction costs and market impact are considered. However, they fall short of explaining why risk-adjusted returns improve when a constant level of risk is targeted. Barroso and Santa-Clara (2013) also suggest that momentum premium in equity markets is better captured if the portfolio is rebalanced toward a constant risk target. They relate the improvement in momentum risk-adjusted returns to the predictability of the momentum risk and also highlight that the management of risk seems to reduce exposure to fat tails.

Perchet et al (2014) recently revealed that the strategy which rebalances the weight of an asset class toward a constant level of ex ante risk, an intertemporal risk-parity strategy, generates superior risk-adjusted returns when compared to a buy-and-hold portfolio, at least before transaction costs and market impact are considered. They show that the improvement in risk-adjusted returns is larger for risky asset classes such as emerging-market equities or high yield. Developed equities and commodities also have higher risk-adjusted returns when managed at a constant risk, however, for investment-grade corporate bonds and in particular for government bonds, the improvement in risk-adjusted returns is negligible. Perchet et al (2014) provide a number of explanations for the improvement in risk-adjusted returns in constant risk strategies. First they highlight that in a world where returns follow normal distributions, the constant risk strategy would be equivalent to the buy-and-hold strategy since the volatility of asset returns would be constant over time. The added value of the constant risk strategy comes from the fact that although volatility is not constant (and not even observable) in the real world, volatility of financial assets tends to form clusters, a property which tends to be stronger in risky assets. Clustering of volatility makes volatility predictable to some extent: when volatility is low it is more likely to remain lowand when is high it tends to remain high. Constant volatility strategies thus reduce the exposure to financial assets in periods of high volatility and increase the exposure in periods of high volatility in such a way that ex post volatility is successfully kept at reasonably constant levels as targeted. If average returns were constant, that would mean increasing the exposure to the financial asset in periods of higher risk-adjusted returns and reducing it in periods of lower risk-adjusted returns. But as shown by Perchet et al (2014), for asset classes such as equities and high yield there is even a negative correlation between returns and volatility which strengthens the effect. Fat tails, which, as revealed by Cont (2000), are present in the distribution of returns of most asset classes, tend to be stronger in periods of higher volatility. Fat tails are then smoothed out by the reduction of the exposure to the financial assets in periods of higher volatility with a positive impact on risk measures such as the value at risk (VaR), conditional value at risk (CVaR) or the size of drawdowns.

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