Monday, February 23, 2009
Measuring ETF Decay
First visit - More On ETF Decay.
So how much do levered ETFs actually decay? I ran a few examples on paper, then computed the formula.
Say we have an underlying A, that is trading at 27.00 while it's double short Z is trading at 100.
Consider the example of a two day move in A where it drops 2% and then the next day retraces completely back to 27.00.
On that move, Z, the double short, will first rise to 104.00. Then the following day, it should theoretically close at 99.755.
So, a 2% drop and retrace (note the up move is greater than 2%) will *decay* the levered short by .25% - which isn't too bad.
Let's now consider a larger drop-and-retrace. A 10% drop on A would bring its price down to 24.30 - and obviously the retrace would bring it back to 27.00.
In that case, Z, the double short, would rise to 120.00 on day one - and then fall to 93.33 on the underlying's retrace. So after a two days of net-flat trading, the double short has just gotten hammered, losing 6.66% of its value.
Here's the formula:
Lemma - Given an underlying A and its daily compounding double inverse Z, a drop of R-percent which retraces fully the following day will DECAY Z by:
6*R2 / (1 - R)
when .3333 > R > 0
In other words, the initial drop can't be greater than 33%. Taylor will explain why in the comments.
Let's test my examples.
6*(.022) / (1 - .02) = .0024 which correlates to the 99.75 price we *retraced* to.
6*(.102) / (1 - .10) = .0666 which correlates to the 93.66 price the double inverse Z *retraced* to the second example.
Conclusion - The last thing a levered ETF holder wants is rapid, large price retracements!
Time for homeschool to open. This discussion will be continued later.