The key to mitigating equity risk in portfolios is investing in assets that are negatively correlated with equity markets yet exhibit the potential for a positive expected return. For most of the past 20-plus years, bonds have fulfilled this role in portfolios, aided by a substantial tailwind of stable or falling inflation. On a forward-looking basis, bonds will continue to be a key part of portfolios, but the potential for both positive expected return and negative correlation with equities may be tested at times. Beyond fixed income, the search for positive-expected-return, risk-mitigating assets becomes more challenging.

In this piece, we first review the pros and cons of some other approaches in current use. We then derive some noteworthy portfolio effects achieved by combining investments with negative correlation and positive expected return potential. Similar to optimal portfolio theory, in which diversification is the only “free lunch,” diversifying the approach to equity risk mitigation may be more efficient than using any single method.

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El Autor

Jamil Baz

Co-head of Client Solutions and Analytics

Josh Davis

Gestor de carteras, Estrategias cuantitativas

Graham A. Rennison

Gestor de carteras cuantitativas


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1 The taper tantrum of 2013 coincided with an abrupt and violent shift in correlations, which coincided with large short-term losses in fixed income assets.

The authors propose a regression-based approach to the pricing of interest rates. “Pricing the Term Structure with Linear Regressions” by Tobias Adrian, Richard K. Crump and Emanuel Moench, Journal of Financial Economics 110, no. 1 (October 2013): 110-38.

3 The data is obtained from the Bloomberg subindexes for each of the listed commodities.

4 The term PX,Y is in the denominator. The closer it is to zero, the more the correlation of the portfolio of strategies is magnified versus the average correlation of the strategies.

The “risk-free rate” can be considered the return on an investment that, in theory, carries no risk. Therefore, it is implied that any additional risk should be rewarded with additional return. All investments contain risk and may lose value.

Past performance is not a guarantee or a reliable indicator of future results.

The analysis contained in this paper is based on hypothetical modeling. No representation is being made that any account, product, or strategy will or is likely to achieve profits, losses, or results similar to those shown. Hypothetical or simulated performance results have several inherent limitations. Unlike an actual performance record, simulated results do not represent actual performance and are generally prepared with the benefit of hindsight. There are frequently sharp differences between simulated performance results and the actual results subsequently achieved by any particular account, product, or strategy. In addition, since trades have not actually been executed, simulated results cannot account for the impact of certain market risks such as lack of liquidity. There are numerous other factors related to the markets in general or the implementation of any specific investment strategy, which cannot be fully accounted for in the preparation of simulated results and all of which can adversely affect actual results.

Details of the Basic Trend-Follower: For the purposes of this analysis we set up a simple, transparent hypothetical trend-following strategy. The strategy trades twenty markets: five each in equity index, bond, currency and commodity futures. The strategy trades once per week, taking a long position if the current futures price is above the one year moving average price, and taking a short position if it is below. Each position is scaled inversely to the recent 3-month daily realized volatility of the contract, and the overall strategy is scaled to target 10% volatility using trailing 10-year windows to estimate volatility of the strategy. Some futures markets were unavailable in the early parts of the sample. In those periods, risk allocated to each asset class is kept roughly constant over long periods of time by scaling up the underrepresented sectors. Over short periods, risk can be skewed to some asset classes. Fixed transaction costs estimated from available market data for each futures market, of between 1bp and 10bps, are subtracted from returns. For historical data before 1987, extended hypothetical futures time series are constructed for S&P 500, five-year note futures and currency futures (JPY, DEM, AUD, GBP) before actual trading in those futures markets began. For S&P 500 futures we use daily excess return data from the Ken French database for the top 30% of U.S. stocks with reinvested dividends. For five-year note futures we use the Gurkaynak, Sack, Wright constant maturity Treasury yield data set to estimate daily returns, including roll-down and carry. Delivery option effects are not included in the modelling but would not be expected to bias results. Proxy currency future returns are calculated using risk-free rate data from Dimson, Marsh and Staunton and Bloomberg spot rates, starting in 1973. A useful comparison is with the SG Trend Index, a composite of the top 10 trend-following hedge funds. In order to make a meaningful comparison we add to the returns of the Basic Trend Follower a proxy for collateral returns (we use the Barclays Short Term Treasury index total returns) and adjust for assumed fees equal 2% running plus 20% of gains assessed annually. Annual correlation of these two series is 64% over this period. Average annual total returns are similar at 5.2% and 6.3% for the basic trend follower and SG Index respectively.

Return assumptions are for illustrative purposes only and are not a prediction or a projection of return. Return assumption is an estimate of what investments may earn on average over a 10 year period. Actual returns may be higher or lower than those shown and may vary substantially over shorter time periods. Return assumptions are subject to change without notice.

Figures are provided for illustrative purposes and are not indicative of the past or future performance of any PIMCO product.

All investments contain risk and may lose value. Investing in the bond market is subject to risks, including market, interest rate, issuer, credit, inflation risk, and liquidity risk. The value of most bonds and bond strategies are impacted by changes in interest rates. Bonds and bond strategies with longer durations tend to be more sensitive and volatile than those with shorter durations; bond prices generally fall as interest rates rise, and the current low interest rate environment increases this risk. Current reductions in bond counterparty capacity may contribute to decreased market liquidity and increased price volatility. Bond investments may be worth more or less than the original cost when redeemed. Equities may decline in value due to both real and perceived general market, economic and industry conditions. Commodities contain heightened risk, including market, political, regulatory and natural conditions, and may not be suitable for all investors. Tail risk hedging may involve entering into financial derivatives that are expected to increase in value during the occurrence of tail events. Investing in a tail event instrument could lose all or a portion of its value even in a period of severe market stress. A tail event is unpredictable; therefore, investments in instruments tied to the occurrence of a tail event are speculative. Derivatives may involve certain costs and risks such as liquidity, interest rate, market, credit, management and the risk that a position could not be closed when most advantageous. Investing in derivatives could lose more than the amount invested. The use of models to evaluate securities or securities markets based on certain assumptions concerning the interplay of market factors, may not adequately take into account certain factors, may not perform as intended, and may result in a decline in the value of an investment, which could be substantial. Investors should consult their investment professional prior to making an investment decision.

The SG Trend Index calculates the net daily rate of return for a group of 10 trend following CTAs selected from the largest managers open to new investment. The SG Trend Index is equal-weighted and reconstituted annually and has become recognized as the key managed futures trend following performance benchmark. The S&P 500 Index is an unmanaged market index generally considered representative of the stock market as a whole. The index focuses on the Large-Cap segment of the U.S. equities market. The MSCI World Index is a free float-adjusted market capitalization weighted index that is designed to measure the equity market performance of developed markets. The MSCI World Index consists of the following 24 developed market country indices: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the United Kingdom, and the United States. The RAE Low Volatility International model portfolio contains stocks of large Developed Markets ex-U.S. companies ranked by the Fundamental Index® methodology and further screened by a composite score of yield, volatility, and leverage. Companies are weighted by the product of the fundamental score of each company and a factor that reduces the weight for higher beta companies (and increases those for lower beta companies). The portfolio is rebalanced on a monthly staggered basis. Companies in 23 developed ex US market countries are eligible for inclusion. Prior to 15 April 2015, this benchmark was known as the International RA Low Volatility Equity Income. The RAE Low Volatility US model portfolio contains stocks of large U.S.-listed companies ranked by the Fundamental Index® methodology and further screened by a composite score of yield, volatility, and leverage. Companies are weighted by the product of the fundamental score of each company and a factor that reduces the weight for higher beta companies (and increases those for lower beta companies). The portfolio is rebalanced on a monthly staggered basis. Prior to 15 April 2015, this benchmark was known as the US RA Low Volatility Equity Income. It is not possible to invest directly in an unmanaged index.

Alpha is a measure of performance on a risk-adjusted basis calculated by comparing the volatility (price risk) of a portfolio vs. its risk-adjusted performance to a benchmark index; the excess return relative to the benchmark is alpha. Beta is a measure of price sensitivity to market movements. Market beta is 1. Correlation is a statistical measure of how two securities move in relation to each other.

This material contains the current opinions of the manager and such opinions are subject to change without notice. This material is distributed for informational purposes only. Forecasts, estimates and certain information contained herein are based upon proprietary research and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.


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