Optimal Design Of Risk Control Strategy Indexes
By Guido Giese

Conclusion
We have derived a model for the risk/return profile of strategy indexes that combine an investment into an equity index and a money market investment in a rules-based way. We have shown that using a rebalancing function that responds to the volatility of the underlying equity market is crucial to achieve a favorable risk/return profile.

In the context of our model, we have seen that existing leveraged indexes are suboptimal from both a performance and Sharpe ratio perspective, as they are not risk controlled in any way, i.e., they use a constant equity proportion in their portfolio allocation.

We have shown that incorporating a risk-control mechanism into the framework of leveraged indexes in the form of a response function that responds adversely to volatility leads to significant improvements in terms of absolute performance and Sharpe ratio.

Regarding target volatility indexes, we have shown that their long-run Sharpe ratio is always better than the Sharpe ratio of the underlying equity index as long as the target volatility level is chosen within reasonable boundaries. Further, it is interesting to note that in practical simulations, we have seen that the existing target volatility strategy comes very close to the optimal risk strategy we have derived in this paper in terms of risk and performance profile. We therefore argue that from a practitioner's point of view, existing target volatility indexes respond to volatility in an (almost) risk/return optimal way.

It is important to mention that the mathematical results we have derived are independent of the underlying equity index and money market, i.e., they are robust across different markets and market regimes.

Finally, this paper provides a clear recommendation to investors in passive equity strategies: In the long run, investors in equity indexes (e.g., in the form of index-tracking ETFs or certificates) can clearly improve their long-run Sharpe ratio by shifting their investment to a corresponding target volatility index that offers comparable equity returns at lower levels of risk.

Further, we have seen that the existing methodology of leveraged indexes can be improved substantially by incorporating a risk-control mechanism. We therefore propose index providers adjust their methodologies for calculating leveraged indexes to incorporate the risk-control mechanisms outlined in this paper.

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