Does the choice of performance measure influence the evaluation of hedge funds, страница 8

*The rank correlations presented in the table are average values above different robustness tests.

For all these tests we find high rank correlations comparable to those presented in Section 3.2.^[12] Detailed results are available upon request.

4. Measuring performance when the fund represents only a portion of the investor’s risky investment

4.1. Data and methodology

To this point, we have looked at the performance of hedge funds in isolation, assuming a decision-making situation in which the fund under consideration represents the entire risky investment. Of course, this is an unrealistic assumption because most investors would not invest all their money in one fund; most investors would want only a small percentage of hedge funds in their investment portfolio. In this section, we consider this more realistic type of investor.

For our analysis, we use a representative investment portfolio (in the following also called reference portfolio) of a typical institutional investor, for example, a German insurance company. A typical German insurance company puts 20% of its assets in stocks, 60% in bonds, 10% in the money market, and 10% in real estate (for the weighting of the asset classes, see, e.g., Bundesanstalt fu¨r Finanzdienstleistungsaufsicht, 2004). Within these asset classes we divide up the assets in equal parts on the indices specified in Table 4.

We selected well-known market indices, which usually can be acquired over index funds at a small cost and are broadly diversified so that they are generally well suited for performance measurement (for the criteria to select representative benchmark indices, see Sharpe, 1992). For each of these indices, we extracted monthly returns between January 2000 and December 2004 from the Datastream database. In order to consider returns from changes in prices and dividend payments, we look only at performance indices. On the basis of the indices returns, we calculate the returns of the reference portfolio by weighting the indices’ returns with the asset allocation given in Table 4 and summing these values.

4.2. Findings

We analyze a decision-making situation in which exactly 1% of the investor’s wealth is shifted from the reference portfolio into one of the hedge funds considered in Section 3. To measure the performance with the Sharpe ratio, it is appropriate to calculate the Sharpe ratio for the new portfolio, which consists of the reference portfolio (99%) and one hedge fund (1%) (see Dowd, 2000). All other performance measures are calculated similarly, except for the Jensen measure and the Treynor ratio. The latter two measures are calculated by considering 100% hedge funds, whereas the market index is substituted by the investor’s reference portfolio without the hedge fund as described in Section 2.3.

Table 4

Modeling the reference portfolio