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August 13, 2010

Do Weekly Options Have Too Much Risk?

I read a blog post today about the weekly options and how the risk was too high. The article was trying to explain that the wings are not priced correctly, which I agree with. The problem was the statement about risk vs time was incorrect.  To quote part of the article:

“…the July weekly in 25% of the time has a standard deviation that is over 1/2 the size of the month out.  For those that would think the expected movement of the weeklies would be 1/4 or less this is a big burst to your bubble.  This basically says the trader is taking on over 50% of the risk in a trade that has only a week to develop.  Many do not realize standard deviation is not linear!”

The assertion that standard deviation is non-linear is correct; however, to say that this relationship proves risk is too high just because of the time to expiration doesn’t make sense to me.Watch movie online The Lego Batman Movie (2017)

He compared a monthly option to a seven day option.  The seven day option was about 50% of the risk of the 30 day trade in 25% of the time.   He was comparing 25% to 50% and saying it’s too much risk!

Horse feathers

Horse Feathers

Horse Feathers

The author forgot to look at the equation for time decay as it is a square root of time function.

Just a quick refresher… the square root of 4 is 2 and the square root of ¼ is ½.

So applying it to this idea of time decay,  comparing ANY two options that have a ratio of 1:4 days to expiration will have a 1:2 ratio of time decay.  So:

7 days  vs  28 days

30 days vs 120 days

90 days vs 360 days

These are all 1:4 ratios so the risk should be 1:2 for all of them.  If so, then the pricing models are fair and work for ALL option time frames.  There’s no black hole where weekly option are mis-priced.   If they were, they would be arbitraged back to the fair price right?  That’s the argument Market Makers make to defend how the markets are priced fairly.  You can’t have it both ways.  Markets can’t be fairly priced for only part of the market right?

OK.. so let’s get back to our example.  Let’s use AAPL and look at different 250 Call prices. Unfortunately we don’t have exactly 1:4 ratios of time, but we can still estimate the predicted price vs the actual market price to see if the relationships hold across all time frames.

Expire Days to
8/21/2010 8 $5.175
9/18/2010 36 $10.65
10/16/2010 64 $14.975
1/22/2011 162 $25.175
1/21/2012 526 $48.50

Square root of (8/365.25) divided by square root of (36 / 365.25) = 47.1%

Therefore I would expect the 47.1% of the 36 day option to be roughly the 8 day option:

47.1% times $10.65 = $5.02 predicted price vs $5.175 actual price

Applying this same math to the rest of the combinations we find:

Dates Ratio Predicted
8 days vs 36 day 47.1% $5.02 $5.175 8 days
36 days vs 64 days 75.0% $11.23 $10.65 36 days
36 days vs 162 days 47.1% $11.87 $10.65 36 days
64 days vs 162 days 62.9% $15.19 $14.975 64 days
162 days vs 526 days 55.5% $26.92 $25.175 162 days

Of course this assumes constant volatility and no interest or dividends, which is NOT real world; however, it’s close enough for our purposes.  The longer term options are affected proportionately more for these factors so we would expect more error with them.

Overall I think it’s clear the markets are fair FOR ALL TIME FRAMES, INCLUDING WEEKLY OPTIONS! If you used my friends logic, you would only trade the farthest out in time LEAPS.  Weekly options are fairly priced from what I can see.   I’m not a Market Maker so perhaps I’m missing something.  Please let me know what you think in the comments section.

I wrote an article on the benefits of weekly options.  I was going to write the dangers of weekly articles next but I saw that post on another site and I had to add my $0.02.  The dangers of weekly options will be next… I have it mind mapped already 🙂

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Tom Nunamaker

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