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 of the central concepts in finance is that returns above the risk-free rate are compensation for exposure to risks. Stocks have earned a premium above the risk-free asset because they expose their owners to their underlying risk factors. The capital asset pricing model (CAPM) can be thought of as the first theory of risk factors. According to the CAPM, the expected excess return on a risky asset is equal to the beta of the asset times the risk premium on the market portfolio. When asset returns are normally distributed, the CAPM correctly identifies the only risk factor to be the return on the market portfolio, and the measure of exposure of each stock to this factor to be its beta. By relaxing the assumptions of the CAPM, academic and industry researchers have extended the model, leading them to develop a long list of risk factors.18 Even though there is no consensus about the number of risk factors in financial markets, it is well established that the market portfolio is not the only risk factor in the market. The risk premiums earned by stocks and other traditional assets are indeed a combination of various risk premiums.
Our discussion of factor investing begins with three important observations detailed by Ang (2014):
1. Factors matter, not assets: The factors behind the assets matter, not the assets themselves. Assets are nothing more than means for accessing factors.
2. Assets are bundles of factors: Most asset classes expose investors to a set of risk factors; therefore, the risk premium offered by an asset class represents a package of risk premiums offered by factor exposures. Exposures of assets and risk premiums to factors can be used to estimate the risk premium that an asset should provide.
3. Different investors should focus on different risk factors: Asset owners differ in terms of time horizons, risk tolerances, objectives, and liabilities that should be funded. These differences require careful examination of factor exposures of a portfolio in order to ensure that the asset owners do not have too much or too little exposure to some factors.
If we consider the risk premium earned by each asset class to be a function of exposures to several risk factors, then several important questions arise:
These questions are addressed in the next six sections.
2.5.2 How Risk Factors Are Described
What is a risk factor? A risk factor represents a unique source of risk and risk premium in financial markets such that the observed risk and risk premium cannot be fully explained by other risk factors. In other words, risk factors are not supposed to be highly correlated with each other. In addition, risk factors should have a sound economic foundation, with rigorous academic and industry research supporting their presence. Finally, risk factors must show that their risk premiums are persistent over long periods.
Let us examine two well-known equity risk factors: momentum and value factors. To create the momentum factor, researchers examine the performance of equity prices through time. Then two portfolios are created at the end of each period (e.g., month). One equally weighted portfolio will contain those stocks that performed well during some specific period (e.g., past 12 months), and the other equally weighted portfolio will contain those stocks that performed poorly during the same period. This procedure is repeated every period and results in two return series. If one were to go long the portfolio of winners and go short the portfolio of losers, the return to this active strategy would be the return to the momentum factor. We can ascertain that this is indeed a new factor if the return to this strategy cannot be explained by other factors, such as return to the market portfolio.
The value factor is constructed the same way except that stocks are sorted based on the ratio of their book values to their market values. Stocks with high ratios of book value to market value are considered value stocks, and those will low ratios are considered growth stocks. Two equally weighted portfolios are created each period. One will consist of those stocks with above-average book-to-market ratios, and the other one will consist of those stocks with below-average book-to-market ratios. Again, a strategy will go long the first portfolio and short the second portfolio. The return to this active strategy will represent the return to the value factor. Exhibit 2.10 displays properties of these two risk factors.
It is important to note that the average returns reported in Exhibit 2.10 are for portfolios that, at least in theory, do not require any investment. This is because each factor consists of equal-size long and short positions. Therefore, the initial capital is available to be invested in the riskless assets, the market portfolio, or some combination of the two. For instance, if the capital were invested in the market, then the entire portfolio would earn the market portfolio plus the return on each factor. Of course, the resulting portfolio would be highly volatile because it would have a gross leverage of 300 %. Also, note that during the same period, the
