# Using indexes to manage risk

There are several different approaches to constructing indexes with risk management in mind. All follow systematic, transparent rules, but they have subtle differences. But how are these different indexes actually constructed – how are their components selected – to achieve the desired result?

Choosing the stocks that have proven the least volatile historically is one obvious way to attempt to manage index risk. Clearly, there’s no guarantee that these stocks will stay less volatile in the future. But studies have shown that there is some persistence in stocks’ volatility levels: for example, stocks from certain industry sectors (such as utilities or consumer staples) tend to have smoother return streams than those in other sectors.

Another approach is to construct an index from so-called low-beta stocks (beta measures the sensitivity of individual stocks to movements in the overall market, while volatility is an absolute measure of risk, calculated as the standard deviation of returns around the mean).

The stock selection methodology of both low-volatility and low-beta indices is often referred to as “heuristic”. It relies on a rule-of-thumb approach that is relatively easy to understand.

The weighting schemes used in such indexes are often also straightforward. For example, a low-volatility index may weight stocks by the inverse of their historical volatility: the less volatile a stock is, based on historical returns, the higher the weighting it receives.

By contrast with these rule-of-thumb indexes, minimum variance indexes use a mathematical algorithm called an optimization to arrive at the constituent list and constituent weightings.

The algorithm looks both at stocks’ past volatility and the correlations between individual stocks’ return patterns (including correlations makes for a more sophisticated approach than a simple low-volatility strategy). The algorithm then works out the combination of stocks that produces the lowest index-level volatility, based on historical data.

As an unconstrained optimization typically leads to a significant concentration in individual stocks and sectors, as well as negative stock weightings, index designers usually impose a series of constraints when producing a minimum variance index.

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