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Quant Corner – Dollar Allocation ≠ Risk Allocation

August 17, 2015  | by Jess Gaspar

Industry Knowledge | Risk Management

Does a 70/30 portfolio have 70 percent of its risk in equities?

While this question may appear to channel the old joke ”Is the little red schoolhouse red?”, the answer is clearly that a 70/30 portfolio does not have 70 percent of its risk in equity. In fact, it has nearly 100 percent of its risk in equity.

This first installment of Quant Corner explains why that is the case, and why investors should resist the temptation to move away from a fully diversified portfolio. Technically, the answer boils down to three factors: the differences in volatility between equities and bonds, the low correlation between equities and bonds, and the resulting differences in the correlations of equities and bonds within the total 70/30 portfolio.

Often, when discussing portfolios, we speak in terms of dollar allocations. Seventy percent equities and 30 percent bonds, or 50 percent equities, 15 percent bonds, 15 percent real assets and 20 percent alternatives. These quick characterizations are useful for working through who gets how much money to manage but not for working through who is taking how much of the total portfolio risk. To understand the portfolio risk question, we need to turn to the volatility and correlation of the portfolio’s constituents.

To illustrate the underlying principles, consider the traditional 70/30 benchmark. In the table below are the volatility of total returns since 1997 for the S&P 500 Index, the Barclays U.S. Aggregate Bond Index and a portfolio comprising 70 percent S&P 500 and 30 percent Barclays Aggregate, rebalanced monthly.

In the second row, we see that the S&P 500 has an annualized volatility 4.5x (0.156/0.035) the annualized volatility of the Barclays Aggregate since 1997. This is the first clue: Each dollar allocated to equities has 4.5x as much volatility as each dollar allocated to bonds. On top of that, we are contributing 70 cents to equities for every 30 cents we contribute to bonds. Thus, if we look at the equity and bond pieces in isolation, the equity risk should be 0.156×0.70 relative to the bond risk of 0.035×0.30 for a ratio of 10.5. Equity contributes 10.5x as much risk as fixed income on a stand-alone basis, or 91 percent of total standalone risk. Seems extreme, doesn’t it? But we are not done yet. Due to correlations, the total portfolio risk concentration in equity is actually worse than what a stand-alone look at equities and bonds would suggest.


Due to correlations, a 70/30 portfolio’s risk concentration in equity is even worse than what equity and bond volatility alone would suggest.


Equities are much more highly correlated with the 70/30 portfolio at nearly 100 percent than are bonds at nearly 5 percent. This is because the stand-alone volatility contribution from equities is so large relative to bonds and because equities and bonds are nearly uncorrelated, at -5 percent. The importance of the stand-alone volatility contribution should be apparent from the previous discussion: a pie made of 10.5 parts cherries and one part radishes still tastes reasonably good.

The role of bond correlation merits further discussion. Bonds reflect two different types of risk exposures: credit and duration. Credit risk stems from the risk of downgrade and ultimately default on the bond. Typically, it is positively correlated with equity risk as defaults tend to happen when equities underperform. Duration risk (for “safe” U.S. Treasuries) arises from the potential for interest rates to rise, driving down prices on bond portfolios. As rates typically fall in Treasuries when equities underperform, duration and equity risks tend to be negatively correlated.

On average over long periods of time, the correlations of credit and duration risks with equity risks roughly offset for the Barclays Aggregate, hence the correlation to the S&P 500 at a level close to zero. Given that most of the risk in the 70/30 portfolio arises from equities due to the relative size of the stand-alone contributions, bonds have a nearly zero correlation with the 70/30 portfolio as well.

Looking at more concentrated duration and credit exposures helps to illustrate the point. A portfolio of 10-year-plus U.S. Treasury bonds, which has substantial duration risk but little credit risk, has exhibited a -18 percent correlation with the 70/30 portfolio. In contrast, a portfolio of high yield bonds, which lies outside the investment-grade universe of the Barclays Aggregate and has significantly more credit risk, has exhibited a +64 percent correlation with the 70/30 portfolio.

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If we incorporate the high correlation of equities and the low correlation of bonds to the total portfolio with the large standalone contribution of equities and the small standalone contribution of bonds, we obtain the total contribution of equities and bonds to the 70/30 portfolio’s total risk. For equities, we have 0.70×0.156×0.995=0.109, while for bonds we have 0.30×0.035×0.049=0.001.

Note that the total for equities equals the total for the 70/30 portfolio out to three significant digits. Indeed, equities contribute north of 99 percent of total portfolio risk to the 70/30 portfolio on a percentage basis. Critically, this dramatically exceeds the 70 percent suggested by looking at the dollar allocation.

Thus, at Commonfund, one of our primary objectives is to help clients diversify portfolio exposure beyond the nearly pure equity volatility risk embedded in a simple 70/30 equity/fixed income portfolio. Of course, we also strive to increase expected return.

We believe in, and advocate, a fully diversified approach to portfolio construction that includes not only equities and bonds but also alternatives like hedge funds, private capital and real assets. Our objective is to effectively use the multitude of levers at our disposal: investment diversification, manager selection, market timing and, another potential topic for a future Quant Corner, factor investing.

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Note: This analysis reflects, in part, the impact of the bull market in equities and fixed income since 1997. Thus, results may be period-specific. In particular, historical annualized returns are unlikely to be representative of future returns given current interest rates.

Due to correlations, a 70/30 portfolio’s risk concentration in equity is even worse than what equity and bond volatility alone would suggest.

¹ Note that this need not be true, as in the case of stagflation during the 1970s, but otherwise generally holds true.
² In their 2011 Journal of Portfolio Management article, Jose Menchero and Ben Davis coined the phrase the x-sigma-rho model to describe this decomposition. The x stands for portfolio share of an investment, the sigma for investment’s volatility and the rho for correlation of the investment with the total portfolio. The product of these three variables gives the percentage contribution to risk for each investment.

Quant Corner – Dollar allocation ≠ risk allocation

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Information, opinions, or commentary concerning the financial markets, economic conditions, or other topical subject matter are prepared, written, or created prior to printing and do not reflect current, up-to-date, market or economic conditions. Commonfund disclaims any responsibility to update such information, opinions, or commentary. To the extent views presented forecast market activity, they may be based on many factors in addition to those explicitly stated in this material. Forecasts of experts inevitably differ. Views attributed to third parties are presented to demonstrate the existence of points of view, not as a basis for recommendations or as investment advice. Managers who may or may not subscribe to the views expressed in this material make investment decisions for funds maintained by Commonfund or its affiliates. The views presented in this material may not be relied upon as an indication of trading intent on behalf of any Commonfund fund, or of any Commonfund manager. Market and investment views of third parties presented in this material do not necessarily reflect the views of Commonfund and Commonfund disclaims any responsibility to present its views on the subjects covered in statements by third parties. Statements concerning Commonfund’s views of possible future outcomes in any investment asset class or market, or of possible future economic developments, are not intended, and should not be construed, as forecasts or predictions of the future investment performance of any Commonfund fund. Such statements are also not intended as recommendations by any Commonfund entity or employee to the recipient of the presentation. It is Commonfund’s policy that investment recommendations to its clients must be based on the investment objectives and risk tolerances of each individual client. All market outlook and similar statements are based upon information reasonably available as of the date of this presentation (unless an earlier date is stated with regard to particular information), and reasonably believed to be accurate by Commonfund. Commonfund disclaims any responsibility to provide the recipient of this presentation with updated or corrected information. Past performance is not indicative of future results. For more information please refer to Important Disclosures.

Disclaimer

Information, opinions, or commentary concerning the financial markets, economic conditions, or other topical subject matter are prepared, written, or created prior to printing and do not reflect current, up-to-date, market or economic conditions. Commonfund disclaims any responsibility to update such information, opinions, or commentary. To the extent views presented forecast market activity, they may be based on many factors in addition to those explicitly stated in this material. Forecasts of experts inevitably differ. Views attributed to third parties are presented to demonstrate the existence of points of view, not as a basis for recommendations or as investment advice. Managers who may or may not subscribe to the views expressed in this material make investment decisions for funds maintained by Commonfund or its affiliates. The views presented in this material may not be relied upon as an indication of trading intent on behalf of any Commonfund fund, or of any Commonfund manager. Market and investment views of third parties presented in this material do not necessarily reflect the views of Commonfund and Commonfund disclaims any responsibility to present its views on the subjects covered in statements by third parties. Statements concerning Commonfund’s views of possible future outcomes in any investment asset class or market, or of possible future economic developments, are not intended, and should not be construed, as forecasts or predictions of the future investment performance of any Commonfund fund. Such statements are also not intended as recommendations by any Commonfund entity or employee to the recipient of the presentation. It is Commonfund’s policy that investment recommendations to its clients must be based on the investment objectives and risk tolerances of each individual client. All market outlook and similar statements are based upon information reasonably available as of the date of this presentation (unless an earlier date is stated with regard to particular information), and reasonably believed to be accurate by Commonfund. Commonfund disclaims any responsibility to provide the recipient of this presentation with updated or corrected information. Past performance is not indicative of future results. For more information please refer to Important Disclosures.