Sunday, December 29, 2013

Daily price data underestimates stock beta

Those who manage market neutral equity portfolios spend a great deal of time estimating betas (see definition) of individual holdings. The goal is to measure the amount of index-equivalent exposure needed to offset the "market-sensitive" component of each stock's volatility. This often becomes more of an art than a science, with dozens of different (and often proprietary) approaches. These include splitting the measure into the "up-side" and the "down-side" beta based on observations that some companies' share price responds differently to rising vs. falling markets. Another approach used by some risk managers is to look at "stress beta" - a measure of how a stock responds to extreme movements in the market.

There is however one overriding mistake that many portfolio managers make in their estimates of beta. For those who have holding periods of longer than a day, it probably does not make sense to use daily movements in stock prices to estimate beta. Daily data contains a significant amount of noise that tends to dampen the relationship between a stock and the overall market. Daily responses to news about a particular company are sometimes exaggerated, and adjust within the next few days to trade more in tandem with the overall market. On days when the overall market has little direction, stocks of some companies temporarily decouple from the market. All this could lead to erroneous results in measuring beta.

Let's look at an example. In the chart below, the y-axis represents the daily returns for Alcoa Inc., a large US firm focused on aluminum products (website). The x-axis shows the daily returns for the S&P500 index (here we are using SPY because many managers trade this ETF as a liquid proxy for the S&P500). The red line is the regression fit to this scatter plot. The classical way of estimating beta is simply using the slope of this red line, resulting in a measure of 1.63. This means that on average Alcoa shares will move 1.63 times as much as the S&P500. The company by its nature is cyclical and carries a significant amount of leverage, resulting in share price movements that are higher than the index (sometimes referred to as a "high-beta" stock).

In theory if someone is long $10 million worth Alcoa shares and decides to short $16.3 (10 x 1.63) million worth of S&P500 against it, the market exposure should be "hedged". That means the long/short position should exhibit the lowest possible volatility one could achieve by hedging with S&P500.

But most portfolio managers don't hold stocks for just a day. Using weekly as opposed to daily price data results in a beta of 2.05, a materially different outcome (see chart below). It means that in order to minimize the volatility over several days, one needs to short $20.5 million worth of S&P500 against $10 million worth of Alcoa - not $16.3 . The "daily beta", represented by the red line below would have resulted in higher losses during large market corrections than the weekly measure (green line).

Weekly data is based on each Thursday's close

Portfolio managers have numerous options for beta calculations. But one key factor for those who do not turn over their holdings daily is making sure to avoid using daily returns data for these measurements. Betas derived from daily stock prices could significantly underestimate the overall market exposure of a stock portfolio.
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