Читать книгу Alternative Investments - Black Keith H. - Страница 53

The portfolio in Exhibit 2.5 would have performed very well over the past 20 years because the portfolio was allocated heavily to fixed-income assets, and fixed-income assets outperformed equity assets on a risk-adjusted basis during that period. However, selecting strategies based solely on successful historical performance, even spanning 20 years, runs the risk of unsuccessfully chasing historical performance. Chasing historically superior risk-adjusted performance is futile in an efficient market.

In theory, it is difficult to find any reason why a risk parity portfolio should be optimal. For example, if asset returns are normally distributed and financial markets are perfect, then there are sound economic reasons why investors should select portfolios that plot on the efficient frontier. In other words, it would be difficult to come up with sound economic reasons supporting the risk parity approach in perfect financial markets. In addition, it is not immediately clear how and why market imperfections should make risk parity portfolios more desirable compared to, say, mean-variance efficient or even equally weighted portfolios. Therefore, the case for the risk parity approach must be built through careful analysis of its properties.

As was previously shown and as demonstrated by other studies, the risk parity approach creates low volatility portfolios where low-risk assets are overweighted. Under what conditions, then, would low-risk portfolios become optimal for some investors? One obvious answer is that if an investor has a very high degree of risk aversion, then a risk parity portfolio could be optimal for him. However, a low volatility portfolio can also be constructed using the mean-variance framework. For example, one can create a minimum volatility portfolio using the mean-variance approach (see Exhibits 2.5 and 2.6). It turns out that the most compelling arguments that can be put forward in support of the risk parity approach also support the use of low-risk portfolios, including the minimum volatility approach.

The economic rationale for low volatility portfolios is that because of market imperfections, many investors are unable or unwilling to use leverage. This is referred to as leverage aversion. The leverage aversion theory argues that large classes of investors cannot 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.