MSCI: Morgan Stanley Capital International, EMU: European Monetary Union, SDI: Sovereign Debt Index, JPM: J.P. Morgan, GPR: Global Property Research, PSI: Property Share Index, DIMAX: Deutscher Immobilien Aktienindex.
After measuring the performance of all portfolios, we again rank the measurement values and determine the rank correlations between the performance measures.[13] The performance measures under consideration are the 11 measures already used in Section 3 plus the correlation-based Treynor’s ratio and Jensen’s measure. The rank correlations between these performance measures are set out in Table 5.
We find that all performance measures except the Treynor ratio display a very high rank correlation with respect to the Sharpe ratio as well as in relation to each other. As expected, the rank correlation between the Sharpe ratio of the new portfolio and the Jensen measure of the hedge fund is equal to 1. In theory, this result must be true for marginal investments in the hedge fund (see Breuer et al., 2004, pp. 379–396). It appears that the 1% investment in the hedge fund is a good approximation for a marginal investment. Since we know from Section 3 that for single hedge funds the rank correlation between the Sharpe ratio and its alternatives are close to 1, we expect a similar result for our new portfolio consisting of 1% hedge fund and 99% reference portfolio. Table 5 confirms this expectation.
Furthermore, we find that the rank correlation between the Treynor ratio and Jensen’s measure is relatively low. A possible explanation for this might be the fact that hedge funds are often more leveraged than other investment vehicles. Given this low rank correlation between Jensen’s measure and the Treynor ratio and the high rank correlations
Table 5
Rank correlation based on different performance measures
|
Performance measure |
|
|
|
Sharpe ratio Omega |
1.00 |
|
|
Sortino ratio |
1.00 1.00 |
|
|
Kappa 3 |
1.00 1.00 1.00 |
|
|
Upside potential ratio |
0.93 0.93 0.93 0.92 |
|
|
Calmar ratio |
1.00 1.00 1.00 1.00 0.93 |
|
|
Sterling ratio |
1.00 1.00 1.00 1.00 0.93 1.00 |
|
|
Burke ratio |
1.00 1.00 1.00 1.00 0.93 1.00 1.00 |
|
|
Excess return on value at risk |
1.00 1.00 1.00 1.00 0.93 1.00 1.00 1.00 |
|
|
Conditional Sharpe ratio |
1.00 1.00 1.00 1.00 0.92 1.00 1.00 1.00 1.00 |
|
|
Modified Sharpe ratio |
1.00 1.00 1.00 1.00 0.93 1.00 1.00 1.00 1.00 1.00 |
|
|
Jensen measure |
1.00 1.00 1.00 1.00 0.93 1.00 1.00 1.00 1.00 1.00 1.00 |
|
|
Treynor ratio |
0.34 0.34 0.34 0.34 0.23 0.31 0.32 0.31 0.34 0.35 0.34 0.33 |
|
|
Average |
0.94 0.94 0.94 0.94 0.87 0.93 0.94 0.94 0.94 0.94 0.94 0.94 0.32 |
|
between Jensen’s measure and the remaining performance measures, it is clear that the rank correlations between the Treynor ratio and the remaining performance measures are relatively low as well. We conclude that the Treynor ratio is not appropriate for performance analysis in this context and exclude it from the following significance tests.
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