*Submitted by Salil Mehta via Staistical Ideas blog*,

Our last article, Volatility-product hitmen, provoked a number of enthusiastic comments about how it should be ** easy** to benefit from volatility exchange-traded products. The technical lingo in the counterarguments suggest they are likely from groping investment trading individuals. But how likely is it that these individuals are able to extract the divine trading signals, similar to what they have proposed? To answer this, we must first create a view for what fraction of the time these traders are able to implement any such "profitable signal" from the future curve (say in the past couple of years). Would a quarter of the time be sufficient to warrant having such a new-age, exchange traded strategy? We'll start with this assumption, and in this article below we'll debunk the conviction of these commentators - with two charts. Instead we show over the past 2 years that only

**of users of these derivative products, such as mass-market available volatility ETFs, would have earned a**

*less than 5%***profit from it (as opposed to from haphazard guessing). So at best, only 1 in 20 people.**

*skilled*First let's study the past two years of the VIX volatility index. We can see from the chart on the previous blog article link above, that the VIX was in a slight uptrend. It rose from about 14% in mid-February 2013, to about 15% in mid-February 2015. Also see this, Eruptions in market volatility note, about changes in volatility patterns along the way. So there should have been some opportunities for users of pro-volatility ETFs to benefit. While in the previous article we explored both the VXX, and UVXY, we'll be generous here and only explore further the less-leveraged VXX.

In the chart below we show the sampled distribution of 1-day returns for both the VIX, and the VXX. See the arithmetic returns first (**grey** for VIX, and **dotted blue** for VXX). The VXX distribution is less spread-out, and its typical value is ** slightly** negative (each day bleeding a fraction of a percent). Note that these are histogram frequencies with 5% units. So "0%" represents -5%, to 0%.

Returns on 1-day VIX versus 1-day VXX |

Now let's discuss the difference between the arithmetic return versus the geometric return. Say one had a financial product that produced the following return over two days:

*day 1 --> -25%**day 2 --> +25%** **adding (-25% +25%) = 0% **but this is misleading, since **total return --> (1-25%)*(1+25%) - 1 = (3/4)*(5/4) - 16/16 = -1/16 (or -6.3%)*

What we illustrate above is the flaw with studying arithmetic returns for more than a single period. Instead, we must use geometric returns instead for representation and convert all data to exponential form. So ** day 1** would convert to

**, and**

*ln(1-25%)=-29%***would convert to**

*day 2***. Now it's easy to see that**

*ln(1+25%)=22%***is more closely resembles the**

*-29%+22%***we seek.**

*-6%*For the chart above, for small values in a 1-day period, this difference is not noticeable with the naked eye. But the difference become greater when there are inevitably larger market swings over time. And another benefit from the exponential approach (as we see in the example above) is that one can more easily sum these returns over time.

So let's carry over our **1-day** geometric returns for the VXX. In the chart below we also show how the returns appear for different time frames. Say a **5-day**, **25-day**, and **125-day** period. Given the lack of serial correlation in the VXX returns (Durbin-Watson statistic of 2.0), we can interpret the ** n**-day statistics as any result of combining anyone's alleged "winning" signals together. The results would be the same that is, for someone who had 125

**single-day**signals in the past two years, as it is for someone with a 5 signals to hold the VXX for

**25-days**each.

Returns on n-day VXX |

What the results show are a few important, probability conclusions. The first is that the amplification of the subtle decay of the VXX (between 0%-1% daily ** loss**), even though the VIX rose over the course of the past two years. Notice for example that the

**125-day**distribution is about 5 times worse than the

**25-day**distribution?

Next, we notice that while the **1-day** returns were positive just under 50% of the time, the **5-day** returns were positive about 40% of the time, the **25-day** returns were positive about 35% of the time, and the **125-day** returns were positive about 10% of the time.

In other words, for anyone trading the VXX on signals they see about 25% of the days (or 125-130 days every bi-annual period), it is unlikely that they would be actually generating positive returns due to either luck or skill. The Bayesian math tools for this are shown here (and last year featured in a popular New York Times article). So there is somewhat less than 10% chance of someone being able to claim success here in being a skilled trader. Further, there is a high likelihood that on the "non-signal" periods that these same traders would be engaged in ** loss** trades due to their dominating and imperfect use of the product (this would not be attributed as haphazard guessing). From these two we have

**of seeing a skilled user of the product profit from these ETFs.**

*less than 5% probability* So at best, 1 in 20 users of these modern products such as VXX product over the past two years. And the odds worsen if we do any combination of these four things: (A) assume any futures curve trading signal is greater than 25% of the time, (B) we extend the time frame of trading beyond two years, (C) if we switch to other more levered products such as UVXY, or (D) if we inch closer to the assumption one is a ** typical individual** and not a purported skilled trader. Also if we assume the opposite of bullet (A) above and believe the trader is using VXX for less than 25% of their signals, then we must ask the equally damning question of whether any of this is worth anyone's time to begin with. Going from 25% to 15% for example, would give the small fraction of skilled traders (as opposed to anyone who claims to be a trader) the return distribution between the

**125-day**and the

**25-day**. And that's not great.