Visitors Now:
Total Visits:
Total Stories:
Profile image
By Quantum Blog (Reporter)
Contributor profile | More stories
Story Views

Now:
Last Hour:
Last 24 Hours:
Total:

Guess what, leveraged etfs don't decay!

Tuesday, October 25, 2016 6:24
% of readers think this story is Fact. Add your two cents.

(Before It's News)

While writing the previous posts and doing the math I still had a feeling that something in my reasoning was not quite right. I could not put a finger on it, but with the help of the author of OnlyVix blog, I seem to have figured it all out.
Let me start with an old problem of 50/50 chance of winning 1% every timestep. Here is a puzzle from E.Chans blog (and book):

Here is a little puzzle that may stymie many a professional trader. Suppose a certain stock exhibits a true (geometric) random walk, by which I mean there is a 50-50 chance that the stock is going up 1% or down 1% every minute. If you buy this stock, are you most likely, in the long run, to make money, lose money, or be flat? Most traders will blurt out the answer “Flat!”

…And they would be right. To prove this, let's write down a binomial tree for this case. I'll use 10% step to simplify the math:

B4INREMOTE-aHR0cDovLzQuYnAuYmxvZ3Nwb3QuY29tLy02aVliRGtsVG1lVS9UZEdETmFGek5iSS9BQUFBQUFBQURFWS9DblFBQmdBTU85cy9zMzIwL2Jpbm9taWFsX3RyZWUucG5n



Here we start with initial 100$. Every branch has 50% probability. Notice that the expected value at each time step is exactly 100$. However, on the third timestep the most probable value is 99$ .


To double-check it, I've run a Monte-Carlo simulation of the above problem. Here is the result:

B4INREMOTE-aHR0cDovLzIuYnAuYmxvZ3Nwb3QuY29tLy1KSWozUXExYURNRS9UZEdCWnBHTV9NSS9BQUFBQUFBQURFVS9hM2g5b1pXZTBEdy9zMzIwL21jX3NpbmdsZV8xLnBuZw==

The average value is 0, while the median is -0.5% for 100 steps or -0.005% for one step.

The case for 5% change per timestep looks like this:

B4INREMOTE-aHR0cDovLzEuYnAuYmxvZ3Nwb3QuY29tLy1YdU5tVzBsRU5ZNC9UZEdGbTJsUlJWSS9BQUFBQUFBQURFYy82RTZzWlRzbUFFay9zMzIwL21jX3NpbmdsZV8yLnBuZw==

The distribution shifts to the left, bu again, average value is zero, and median is -0.1176.

So the answer to above puzzle is indeed 'flat'.

Now returning to a leveraged pair like FAS&FAZ, here is a Monte-Carlo simulation of a leveraged pair:

B4INREMOTE-aHR0cDovLzEuYnAuYmxvZ3Nwb3QuY29tLy1sbi1scnlEWFQ5RS9UZEdJTGQyRTJKSS9BQUFBQUFBQURFZy9XcUVGMzYwYUNzUS9zMzIwLzN4X3BhaXIucG5n

Here I've used a normal distribution for returns of the underlying with sigma = 1%. Once again, the average return over 100 periods is zero, while most of the occurrences are negative.


This means that leveraged etfs don't decay over time, they just look like they do, because that is the most likely outcome.
So here we go, contrary to common belief, the leveraged etfs don't decay after all!

Report abuse

Comments

Your Comments
Question   Razz  Sad   Evil  Exclaim  Smile  Redface  Biggrin  Surprised  Eek   Confused   Cool  LOL   Mad   Twisted  Rolleyes   Wink  Idea  Arrow  Neutral  Cry   Mr. Green

Top Stories
Recent Stories

Register

Newsletter

Email this story
Email this story

If you really want to ban this commenter, please write down the reason:

If you really want to disable all recommended stories, click on OK button. After that, you will be redirect to your options page.