If you want an equity hedge for the portfolio, don't look at other equity markets. The major asset classes for diversification are bonds, currencies, and commodities. These are also the big three for managed futures and global macro. A hedge fund that stays in this space will be in good shape with respect to any diversification benefit.
The long bond has been the "great diversifier" in the post Financial Crisis period. This has not always been the case, but bonds have done better than most other asset classes as a mechanism for hedging equity risk.
Looking at correlations across asset classes against equities since 2009 shows a wide difference between high and lows especially for bonds, currencies and commodities. All three have moved between positive and negative numbers. These asset classes offer diversification but the value can be highly variable.
Using these asset classes as diversification tools may require active adjustment based on the changes in correlation.
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