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stocks have historically outperformed the overall market. However, the evidence seems to indicate that the anomaly has weakened since its discovery by academic researchers. Related to the volatility anomaly is the betting against beta anomaly, which has documented that portfolios consisting of low-beta stocks have outperformed the market in the past.17 The explanation for the betting against beta anomaly is rather similar to the one set forth for the low volatility anomaly. Many investors are unwilling or unable to use leverage to increase the betas of low-beta portfolios. During periods of rising market prices, investors want to be invested in high-beta stocks. As a result, high-beta stocks are bid up, which reduces their future returns. Therefore, those investors who are willing and able to use leverage should experience a higher risk-adjusted return through investing in low-beta stocks.

      2.4.4 Four Rationales for Risk Parity That Can Be Rejected

      Market participants have set forth other arguments in support of the risk parity approach, such as that it has performed well in the past, that it produces well-balanced portfolios, or that the resulting portfolios are well diversified in terms of risk. These arguments can be rejected. First, it is clear that going forward, low-risk fixed-income instruments of developed and most emerging economies will not perform as well as they did during the past 20 years, as many bonds now have yields far below the historical returns in their respective markets. Therefore, risk parity portfolios that overweight fixed income are unlikely to repeat their historical performance.

      Second, the argument that the portfolios will be well balanced is imprecise and appears to belong to marketing materials rather than an economically sound investment report. It is unclear what is meant by “well balanced” and why it should lead to superior risk-adjusted performance.

      Third, it is important to note that risk parity may introduce risks that are absent in other strategies. The fact that risk parity portfolios require investors to use leverage may indicate that they are not directly comparable to equally volatile portfolios that do not use leverage. Funding liquidity risk, which was discussed earlier in this chapter, introduces a risk associated with leverage that is not present in unlevered portfolios. For example, during periods of market stress, the investor may be asked to reduce the portfolio's leverage and therefore liquidate the portfolio at the most inopportune time.

      A fourth unsupported rationale for risk parity is that it can exploit anomalies that exist in alternative asset markets. However, there have been no studies to show that the low volatility or betting against beta anomalies work in the alternative investment area. That is, the low-risk strategies may or may not provide the highest risk-adjusted returns. While there is some evidence that levered low-risk portfolios of traditional asset classes may provide attractive risk-adjusted returns, there is no evidence that such a strategy could work in the alternative investment area. Compared to portfolios of liquid traditional assets, funding of levered portfolios of alternative investments is likely to be more difficult and more expensive.

      It is important to note that because some alternative investments have low volatility and low correlations with other asset classes, the allocations to alternative investments using the risk parity approach will be relatively high compared to market weights and typical institutional portfolios. Exhibit 2.5 is an example of how risk parity may lead to unusually high allocations to low-risk investments, including alternatives. There is an equally high allocation to the HFRI index in the minimum volatility portfolio. As previously stated, risk parity relies on leverage aversion and low volatility anomalies to justify increased allocations to low-risk assets. However, using leverage to increase the return on a low volatility portfolio that contains significant allocations to alternative assets may not be possible or desirable.

      While risk parity may be a viable approach to asset allocation, it does not represent a trading strategy that can be employed by active managers seeking to maximize risk-adjusted return, because risk parity does not require or use any estimate of expected return. The risk parity approach may be suitable for institutional and high-net-worth investors who do not face substantial constraints on their asset allocation policies and who are able to use leverage to adjust the total risk to meet their target total risk.

      2.4.5 Equally Weighted and Volatility-Weighted Portfolios

      Risk parity is one approach to creating a low volatility portfolio. Another approach is to use an equally weighted portfolio. An equally weighted portfolio is, by definition, rather well diversified and, in practice, is likely to have relatively high allocations to less risky assets. The reason is that in most applications, equity serves as both the largest asset class and the riskiest. Thus, equal weighting typically underweights equities relative to a market portfolio. Another approach, as seen previously, is to use mean-variance optimization to identify the minimum variance portfolio.

Finally, a volatility-weighted portfolio can be used to create a low volatility portfolio by weighting each asset inversely to its volatility. In this approach, the weight of each asset class is shown in Equation 2.16.

(2.16)

EXHIBIT 2.8 Portfolio Weights and Their Properties

      Source: Bloomberg, HFRI, authors' calculations.

      This means that the portfolio weight for each asset class is proportional to the inverse of its volatility. The denominator is the sum of the inverses of the return volatilities of all assets. This ensures that the weights will add up to one.

The volatility-weighed approach and the risk parity approach are rather similar. The difference between the two is that the risk parity approach takes into account the diversification that each asset offers, whereas the volatility-weighted approach allocates the portfolio solely on the basis of each asset's stand-alone risk (i.e., each asset's volatility). The volatility-weighted approach is identical to the risk parity approach when there are only two assets or when all correlations between each pair of assets are the same. In other words, if all correlations are identical, all assets offer equal diversification benefits, and thus risk parity and volatility weighting are equivalent. Exhibits 2.8 and 2.9 expand the results reported in Exhibits 2.5 and 2.6 to include information on a volatility-weighted portfolio.

      One advantage of the risk parity, volatility-weighted, and minimum volatility approaches displayed in Exhibits 2.8 and 2.9 is that they do not require estimates of expected returns as inputs. As discussed in Chapter 1, expected returns are very difficult to predict, and a long history of returns is needed to obtain accurate estimates. This is particularly relevant when alternative investments are considered, because many of them lack the long history that traditional asset classes have.

EXHIBIT 2.9 Risk Contributions of the Three Asset Classes

      * Because of rounding errors, the columns do not add up to the total.

      Source: Bloomberg, HFRI, authors' calculations.

      2.5 Factor Investing

      Factor investing is a recent development in the area of asset allocation, and some aspects of it are closely tied to the developments of certain hedge fund strategies. This section offers a brief introduction to this topic; detailed discussions of this approach can be found in Ang (2014). The basic ideas behind factor investing were developed by academic researchers over the past 30 years. However, only in recent years have these ideas been synthesized and presented in practical form by the investment industry.

      2.5.1 The Emergence of Risk Factor Analysis and Three Important Observations

      One

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