Читать книгу Alternative Investments - Black Keith H. - Страница 55

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.