We have heard of the 120 minus your age heuristic used to determine relative allocations between stocks and bonds, and the virtues of the 60/40 stock and bond allocation mix. There is an entire industry devoted to determining how much risk individual investors should take in their portfolios. The supposition remained that over the long-term, stock returns should outperform bond returns due to the equity risk premium.

Investment advisors then consulted with their clients about their specific financial situation to determine how much equity market volatility was appropriate. What if that entire industry, cadres of academics, and generations of investors were simply looking at this problem backwards? What if instead of trying to determine how much equity risk was appropriate for an expected return we should have been asking how much should we really be earning for that risk?

Examining corporate bond returns from the Barclays U.S. Corporate Bond Index, and the historic returns of the S&P 500 Index (NYSEARCA:SPY) since the advent of the former index in 1973 yields some interesting observations. Over this thirty-eight year sample period, equities with an average annual return of 11.26% outperformed bonds by 262 basis points per year. While this figure is certainly less than practitioners and academics' estimates of the long-run equity risk premium, the absolute outperformance is meaningful. One hundred thousand dollars invested in bonds in 1973 would be worth $2.23 million at the end of 2011, 61% less than the $3.59mm that the same amount invested in equities would have grown to over the same period.

Of course, the person invested fully in equities saw their hair grow gray a little quicker over those thirty-eight years. The standard deviation of the annual returns of the S&P 500 was 18.35% per year, assuming normality of investment returrns, this dispersion indicated that the broad stock market had approximately a 68% chance of producing an annual return of between -7.1% and 29.6%. (The average return fell inside this range in 24 of 38 years, or 63% of the time.) Comparatively, the standard deviation of the returns of the bond index at 9.06% was less than half that of stocks, indicating that the broad investment grade corporate bond market had approximately a 68% chance of producing an annual return of between -0.4% and 17.7%. (The average return fell inside this range in 28 of 38 years, or 74% of the time.)

The third column, the Risk Parity Portfolio, solves for a leverage amount applied to the bond return stream that equates to the risk of the equity market. This leverage figure of 2.025x makes the variance of returns of bonds and stocks equal over the sample period. Instead of being equally weighted in dollar terms, how we commonly think of asset allocation, the investor is instead equally weighted in risk terms. The riskiness of the bond portfolio, levered by just over one full turn, and the equity portfolio are now each one-half of the risk of the portfolio. That $100,000 invested in 1973 in a risk parity fashion would grow to $34.6mm rather than the $3.6mm value of the equity-only investor for the variability of returns.

The fourth column, the Return Neutral Portfolio, solves for a leverage amount applied to the bond return stream that equates to the average return of the equity market. This leverage figure of 1.304x applied to the bond portfolio returns gives the investor a return equal to a portfolio fully invested in equities, but with much lower return variability. This level of variability would provide a return equal to equities, but with the variability of an unlevered portfolio invested in 70% fixed income and 30% equities.

While figuring out the leverage that should have been applied ex-post using historical data may seem like purely beneficial hindsight and data mining with little future application, what this data implies does have important ramifications for your asset allocation. If equities do not provide high enough returns per dollar of risk, then investors should prefer lower risk assets. Because these lower risk assets do not meet the individual's return target in unlevered form, investors are taking additional risk in the form of equities for which they are not adequately compensated.

Clifford S. Asness, co-founder of the hedge fund AQR Capital Management, Andrea Frazzini, and Lasse H. Pederson recently authored "Leverage Aversion and Risk Parity," which points to investors inability to obtain leverage or aversion to leverage as the reason why investors would take uncompensated risk in equities to reach their target return rather than own a levered fixed income portfolio. The authors tested this risk-parity theory across time, asset classes, and countries and demonstrated that high beta assets produced low alpha relative to levered lower beta assets.

Because obtaining leverage is often viewed as an institutional game, readers may not give proper credence to this theory's application to their own portfolio. Managing leverage does require obtaining financing, potentially utilizing derivatives, managing counterparty relationships and margin accounts, or a combination thereof. These tasks are no longer out of reach for a typical retail investor. There are four ways for retail investors to allocate funds to a risk-parity strategy: the traditional method of buying bonds or bond funds on margin in a brokerage account, leveraged closed-end funds, exchange traded funds with embedded leverage, and risk-parity mutual funds.

Leveraged closed end funds can take care of the management of this process for the individual investor as these funds can issue senior securities against their assets to provide embedded leverage, and typically carry financing around thirty percent of their asset value. This level of leverage is consistent with the risk neutral portfolio example with closed end funds charging investment expenses from 1 - 2% per annum. These expenses would seem like a tremendous discount if the 623 basis point outperformance for like risk between standalone equities and the risk-parity portfolio is replicable over the next 38 years.

The ever-expanding universe of leveraged ETFs includes the Proshares Ultra Investment Grade Bond ETF (NYSEARCA:IGU), which seeks a return equal to twice the daily performance of a liquid investment grade bond index. This fund carries a management fee of 0.95%. The fund's inception date was in April 2011, and it continues to trade with extremely thin volume. With a limited history to gauge tracking error and thin liquidity, it is not an ideal investment candidate, but a hopeful harbinger of future investment grade bond leverage instruments.

AQR Capital Management, whose co-founder co-authored the aforementioned article on risk-parity investing, offers the AQR Risk Parity Fund (AQRIX). As the idea of risk parity gathers steam in the investment community expect more investment vehicles to be launched with this strategy at their foundation.

While risk parity investing performed well over two trailing generations, and AQR has provided a theoretical justification for why this strategy should outperform on a risk-adjusted basis, future long-term asset returns remain uncertain. Many will counter that historically low interest rates have pushed bond prices to obscene heights, and that levering bond investments prospectively will provide low or negative forward returns. These investors must believe that equities will outperform bonds in future periods by enough of a margin to warrant the higher relative variance of returns.

Others may counter that the risk parity strategy is predicated on a continued negative correlation between equities and fixed income, which may not hold in the future. We have seen developed economies in Europe (e.g. Italy, Spain) whose sovereign markets, credit markets, and equity markets have all become positively correlated during the current crisis.

Like any area of financial markets, future performance of this or any other strategy remains uncertain, but hopefully this idea of risk parity investing expands readers' horizons to a different way to think about achieving incremental risk-adjusted returns.

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