Monday, May 31, 2010

Estimating the fair price of ETF components

The essence of every arbitrage strategy (in any timeframe) is an estimator of a 'fair price'. Once you got that, the rest is easy: just buy the stocks that are too low relative to the fair value and sell the overpriced ones.
Now the hard part: how do we estimate the fair value? Solutions could be countless: linear regression, neural networks, kalman filter, weight in the index, mean value, ... you name it. And of course the ETF tracker itself.
In the example below I've taken a look at the old time favorite group of stocks : the XLE. The data  plotted is a cumulative return for 1 week history with 15 minutes sampling rate. Notice the fat lines: the blue one is just the mean return of the group and the red one is the return of XLE itself.

It turns out that the returns of XLE are almost identical to the mean of the group! A quick conclusion from this is that the ETF itself is as good estimator as just the mean value!. Another conclusion could be that one does not need a phd-rocket-science-chaos-theory sophistication to  design a descent arbitrage strategy.


  1. Nice. I agree, points to a number of strategies (assuming the above pattern holds true historically and beyond), amongst them:

    - observing that undeperformers and overperformers tend to have momentum in their respective directions (short spread or long spread to ETF)

    - various portfolio based approaches where one tries to outperform the ETF over a period, spread to ETF

  2. Indeed, looking at the chart I've thought about the momentum strategy, but for now I'm still focusing on a mean-reverter for this one.
    The reason for this: if you do a linear regresson y=beta*x+alpha , where y = stock return and x-etf return (for each bar), the offset factor alpha is incredibly small compared to beta. A momentum strategy would be based on this alpha, while a mean reverter works with beta. Beta should also be stable in time as opposed to alpha.