Optimal Design Of Risk Control Strategy Indexes

August 17, 2012


Strategy indexes that invest in a frequently rebalanced portfolio of equity and fixed income have become very popular in recent years across equity markets and have led to the issuance of numerous financial products such as ETFs and certificates. Currently, there are two basic types of strategy indexes that are based on an equity investment and a money market investment:

  • Pure return strategies such as leveraged equity indexes that borrow in the money market to offer leveraged equity returns for risk-seeking investors
  • Target volatility index strategies for risk-averse investors that shift part of the equity investment into the money market in volatility markets to protect the investor from serious losses

The objective of this paper is to analyze the risk and performance characteristics of existing strategy index concepts—in particular, existing methodologies for leveraged indexes and target volatility indexes—and to show that these existing index concepts can be improved significantly by incorporating a risk-control mechanism into the index methodology in the mathematically optimal way.

In the following, we assume an equity investment in the form of a liquid equity index to ensure the index scheme can be replicated and traded in a cost-efficient way. Further, we allow the equity investment and money market investment to be either long or short to allow leveraged, de-leveraged and short index strategies.

This paper aims to show the benefits of indexes that are risk controlled in the sense that the size of the equity investment and money market investment is determined as a function of the prevailing level of market risk, where we will use equity volatility as the basic risk measure. The reasons for using equity volatility to determine the index composition are twofold:

  1. Using equity volatility as an allocation factor has become common practice even in active portfolio management, mainly due to the empirical fact that there is a strong negative correlation between the performance of equities and equity volatility, i.e., falling equity markets typically coincide with rising levels volatility and vice versa.
  2. It has been shown (see Despande, Mallick and Bhatia 2009; Cheng and Madhavan 2009; Giese 2010) that frequently rebalancing investment schemes composed of an equity and a fixed-income investment results in the portfolio suffering from rebalancing losses that are proportional to the variance of the underlying equity index, as we will also show later in this paper. Therefore, using the volatility of the underlying equity market as an input factor for the asset allocation is essential to minimize the adverse effects of rebalancing.

Rules-based investment schemes that invest in equity and fixed income have been analyzed in finance literature before in several different contexts. The first and influential contribution of Merton [1971] was based on the assumption of an investor who maximizes a predefined utility function on a fixed time horizon, which resembles the decision problem of an investor saving for his retirement.

Further, the basic idea to shift the portfolio investment between the risky equity market and a less risky fixed-income investment has led to the development of portfolio insurance investment models (see Perold and Sharpe 1995) that rebalance the portfolio to ensure a certain minimum capital protection level.

However, this paper analyzes rules-based strategy indexes from a pure expected return and expected Sharpe ratio perspective, without referring to an arbitrary utility function or time horizon or capital protection level. The article's research is intended to assist in the creation of investment schemes that can easily be tracked and issued in the form of retail investment products that aim to optimize the performance or the risk/return profile.



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