Friday, March 20, 2009

FAZ Decay

Above find historical prices for RIFIN - which is the underlying index for FAZ - that *triple-short* financials ETF I've been trading. It's also the underlying for FAS - the *triple-long*.

I've discussed, at length, the concept of ETF decay. Here I will try to quantify precisely how badly FAZ decayed during this recent bear market rally. [The S&P 500 has rallied from 666.80 to 803.00 in the past two weeks.]

The first whammy was on March 10th where the underlying (RIFIN) rose 13.75%

Then on March 12th it rose 10.62%.

On March 17th it rose 5.05%

And the final dagger (hopefully) was March 18th when it rose 9.79%.

Let's call up that formula I derived:

Lemma - Given an underlying A and its daily compounding triple inverse Z, a drop of R-percent in A which retraces fully the following day will DECAY Z by:

12*R2 / (1 - R)

when .25 > R > 0

Plugging in .1376 for R tells us that on that first upward move, March 10th's rise, the FAZ decayed by a whopping 26.34%.

Allow me to clarify.

Using March 9th and March 10th closing prices, the FAZ dropped from 99.17 to 61.50.

Now, IF on March 11th, the RIFIN did a complete *retrace* the FAZ would only have risen back up to 73.05 - a far cry from the penultimate close of 99.17.

Now note that these numbers are only theoretical and approximate. The initial 13.76% rise in RIFIN should have sent the FAZ to 58.26 - on paper. But it closed officially at 61.50. And my math projecting a *retrace* to 73.05 by necessity presumes it went to 58.26.

In other words, none of you would-be Captious nerds out there need waste your time trying to poke holes in my Kevlar analysis.

By extension, the three other large *up* moves in RIFIN also induced substantial decay into FAZ.

March 12th's 8.98% up-move shaved 10.62% off FAZ.

March 17th's 6.28% up-move shaved 5.05% off FAZ.

And March 18th's 8.63% up-move shaved 9.79% off FAZ.

So what exactly should I do with these numbers? How should I aggregate their collective decay?

I don't well know.

A straight up compounding via multiplication yields:

98.50 * (1-.2634) * (1-.1062) * (1-.0505) * (1-.0979) = 55.92

That means that roughly and theoretically speaking, a complete retrace of the squeezing FAZ underlying would only get that ETF back to about 56.00 - a far cry from it's value of 98.50 with the underlying at the same exact level.

Let's test my hypothesis more directly.

On March 18th, the RIFIN closed at 510.24. In order for it to drop all the way back to March 9th's nadir of 357....

It would have to decline by 30.00%.

In that case, the FAZ should rise by three times that magnitude - it should rise by 90%.

Since the March 18th close of FAZ was 26.35, let's multiply that by 1.90 to see where a one day 90% rise would theoretically take it:

26.35 * 1.90 = 50.06

So by utilizing both methods, we can safely presume that the new backward-looking high for FAZ is somewhere between 50.00 and 56.00 - a sufficient guestimate for our purposes.

What does this mean?

It certainly doesn't mean that FAZ will never rise above 60.00 or eclipse its recent acme of 115.50.

That is still 100% possible. We'll just need much lower lows in Goldman Sachs, JP Morgan, Wells Fargo, and a sufficient number of other financials for it to occur.

It also means that those simpletons on xTrends comment threads drawing all sorts of lines on FAZ charts are complete Morons.

And, lastly, it means anyone sitting on a recently acquired high-cost-basis FAZ position ought to at least reduce their expectations accordingly.

Related posts:

ETF Daily Compounding

More On ETF Decay

Measuring ETF Decay

Leveraged ETF Risk

ETF Leverage - Test Case


Taylor Conant said...


Anonymous said...

What are the odds that this leaked memo at citi will be nonsense? How much wealth changed sides on this manuever. Out of all the news, the american public is fussing over $165 million in bonuses to aig, while dc continues to pull rabbits from their hat destroying the long term viability of the republic.

auntulna said...

So, are you back to considering selling a put and a call on FAZ?

CaptiousNut said...

No, not now - and that *paper trade* straddle was in its little brother - SKF.

Which I deftly took off for a profit!

Anonymous said...

I don't understand how when you used your equation, entering .01376, you computed 26%. Your calculator must be in utter distress. You are supposed to use .1376 as, 13.76% is equal to 13.76*.100. See, when there is a % and you want to bring it into decimal form, you must multiply the % by .100. Just thought I would bring you into the light.

CaptiousNut said...

Thank you for catching that *typing* mistake. I've corrected it.

Pat yourself on the back. Thousands have read this post and you were the only one to catch the extra zero.