lever up low volatility portfolios to generate attractive returns and that, as a result, low volatility stocks and portfolios are underpriced. While leverage increases risk and excess return by the same factor, under some conditions it might be possible to create portfolios with higher Sharpe ratios by applying leverage to low-risk portfolios. As an example, consider the two portfolios depicted in Exhibit 2.7.
While the expected rate of return on the RP portfolio may appear unattractively low to some investors, those who are willing and able to acquire funding at attractive rates can lever up the RP portfolio and earn a superior risk-adjusted return compared to the MV portfolio. In particular, a portfolio with 60 % leverage will produce (11.6 % = 1.6 * 8 % − 0.6 * 2 %) return and (16 % = 1.6 * 10 %) volatility.
EXHIBIT 2.7 Two Hypothetical Portfolios
The important question is why the low volatility portfolio should provide a higher Sharpe ratio in the first place. The leverage aversion argument is that because many investors are not allowed to use leverage, demand for low-risk stocks is low, and therefore they are undervalued. For example, if a mutual fund manager wants to overweight stocks he judges to be undervalued but still track a broad equity benchmark with some degree of accuracy, the manager cannot afford to overweight low volatility stocks. Although low-risk stocks may offer attractive risk-adjusted returns, the mutual fund manager will not be able to lever up their low raw returns to match the overall market return; as a result, the fund will underperform its benchmark in terms of raw returns. The idea that low volatility stocks are underpriced and therefore offer higher expected risk-adjusted returns is known as the volatility anomaly.16 According to this anomaly, portfolios consisting of low volatility 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.
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
See Frazzini and Pedersen (2014) and Schneider, Wagner, and Zechner (2016).
