Beta Weighting (index weighted beta hedging)

Beta is used to measure the volatility of an asset against the volatility of an index. If a stock moves the exact same percentage as the index during the observation period, then the stock will have a beta value of “1”. If the stock moves less than the index the beta value will be less than one. If the stock moves more than the index, then the value will be higher than 1. A stock with a beta of 1.5 is thus 1.5 times, or 150% as volatile as the index.

Beta weighting is the name given to the process of ascribing a beta value to individual assets, or portfolios for the purposes of measuring and managing risk, relative to a benchmark.

A portfolio containing different asset classes and different currency denominations might not lend itself easily to making comparisons between the individual positions. For example, consider a portfolio consisting of single stock Asian equities, US ETF’s, options and futures. How would you look to understand the risk of your holdings in Google stock relative to your long-dated Google call options? How would you compare the long-dated call options to your Singaporean REIT holdings?

Beta allows you to standardize the measure of risk (volatility) in the context of a chosen benchmark. For most investors investing heavily in US equities, this benchmark (the index or single stock being benchmarked to) will be the S&P500 index (SPX). The benchmark  should be appropriate given the nature of the asset or portfolio being observed. For example, a US tech-heavy portfolio might be benchmarked to the NASDAQ rather than the S&P500. Appropriate selection will give the investor a reading of the systematic risk of the portfolio relative to their chosen benchmark. This can be used to hedge systematic portfolio risk.

Mr. Client has a large stock portfolio consisting of US and EU equities, with the majority of positions in US stocks, denominated in USD.

His wealth manager beta-weights his portfolio to SPX and the portfolio has an index-weighted beta of 0.82.

As the portfolio is geographically diversified outside of the US, and Mr. Client does not hold many high-beta US stocks, the index-weighted beta being less than 1 is no surprise.

With this step complete his wealth manager can go about hedging the portfolio, based on Mr. Clients risk tolerance and irrational belief that the upcoming month, May, will be bad for the stock market (…”sell in May and go away”).

Knowing that the PV of the portfolio is 9,256,000 USD, and that its index weighted beta is 0.82 the wealth manager determines that (9,256,000 x 0.82) 7,589,920 USD of SPX futures need to be sold to remove systematic risk from the portfolio for the hedging period.

With the current price of the index at 4,280 USD, and the futures contract size being calculated as 250 USD x the index price (4,280 x 250) each contract lot has a value of 1,070,000 USD.

The wealth manager sells the corresponding number of contracts to offset the systematic risk of the portfolio:

9,256,000 USD portfolio / 1,070,000 USD lot size = 8.65 lots

Because his wealth manager is lazy, rather than using E-Mini contracts to hedge the exact dollar amount, with the permission of Mr. Client the wealth manager sells x9 lots and overhedges. For the month of May Mr. Clients portfolio has reduced its systematic risk. (Note: index-weighted beta hedging may not necessarily nullify market risk entirely for a number of reasons).