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02-11-2009, 06:03 PM   #1

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I wanted to start a discussion on this topic of thinking about the intraday high to low range of the S&P futures and the level of the VIX. I am not an options expert by any means -- but have spoken to some option market makers about this and here are some thoughts. Any options experts that would like to chime in would be great for discussion.

1. VIX and range should be related

VIX is 30-day implied volatility of returns. The term 'returns' implies that it is measuring the 'closing price to closing price' volatility. So there is a difference here -- 'close to close' is different than 'range' (ie, the high vs the low). Nevertheless, the ranges will likely be affected by the same things that are causing 'close-to-close return volatility'.

2. VIX Math Basics: VIX is stated as an annual percentage

To convert an annual VIX percentage to a single day percentage, the math is to take the square root of the number of trading days in a year. ie 252^(1/2). Divide VIX by this number (~15.9).

example, a 30 VIX equates to a single day return volatility of 30 / (252^0.5)

=~1.89%
This would be the expected average daily % change over the next 30 days.

You can re-arrange this formula and ballpark an implied volatility from daily returns. For example, if price has varied by 1.89% -- then you have"
(252^0.5) = ~15.9

.0189 x 15.9 = 30

Note, VIX is a weighted average of the current month and next month options volatility. This calculation is done every day such that you are always comparing apples to apples (ie, if you used only the near-term contract then it wouldn't be a consistent 30-day-forward looking calculation).

3. How does VIX do at predicting the forward 30-day close-to-close return volatility?

I am not going to go into this as this is a lengthy discussion for which I am not fully qualified. But basically, it does a fair job.

4. How does VIX do at predicting the NEXT DAYS range?

I am not going to present all the data here but here are some highlights:
over the last 7 years:
the S&P futures have achieved the implied range of the previous days closing VIX 54% of the time. In 2008, a year of ever rising VIX, this figure was 65%. The lowest year was 2007 at 42%.

Now, let me be clear that this is just a 'thought piece' and not supposed to be used for hard and fast rules. A few ideas:

Expect the market to do a range that falls between 0.7 and 1.3x what VIX is implying much of the time.

About 5% of the time, the range has been > 2.0x what VIX implied (these are the outliers).

About 30% of time, market will do 1.4x or more what VIX implied for a range.

(these numbers are based on historical 7 years and should not be thought of as precise forecasts of the future).

I have done some quick EasyLanguage code to present a working idea for an indicator for using this concept (note you input the previous days closing VIX -- or some estimate of what you think is the 'right' forward VIX estimate is --- and it spits out the projections to track against the developing high-to-low range):

EL Code:

inputs: VIX(46);

value1=squareroot(252);
value2=(VIX/100)/value1;
value3=closed(1)*(value2* 1.0);

value4=highd(0)-lowd(0);

value10=closed(1)*(value2 *1.0);
value11=closed(1)*(value2 *0.7);
value12=closed(1)*(value2 *1.3);

if time > 934 then
Plot1(value4,"+Range");

if time > 934 then
Plot2(value10,"1.0");

if time > 934 then
Plot3(value11,"0.7");

if time > 934 then
Plot4(value12,"1.3");

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Last edited by Frank; 02-11-2009 at 06:13 PM.

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02-12-2009, 05:44 PM   #2

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Re: S&P Intraday Range and VIX

Review for today:

After the large 46pt range from tuesday was followed by low range on Feb 11, was expecting a better high to low range today and we got that.

I saw 45 VIX and thought this might mean 20-30 pts of range. Final range was 31.25 pts.

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02-12-2009, 09:30 PM   #3

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Re: S&P Intraday Range and VIX

Recent Data:

The ratio listed represents the relationship between the actual range relative to the projection based on the previous closing VIX.

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03-06-2009, 08:44 AM   #4

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Re: S&P Intraday Range and VIX

Did some more work on this topic.

As previously stated, the VIX is essentially a forecast by market participants about the near-term return volatility. But as I look at the data for the past 7 years, you can see the relationship in the red bars below.

Red bars are calculated as follows.

Project the close to close volatility (absolute return) based on the previous days close and closing VIX. Then take the actual return and create a ratio of actual vs implied. Do this every day over past 7 years and show: on how many days does it close where VIX implied (absolute so either up or down). This is a frequency distribution --- so what this implies is that the market has lots of 'recovery' days back towards previous days close --- (since median ratio is much less than 1.0). Thus, it also implies that despite the many recovery days that only get 1/2 as far as VIX would imply, you get a small number of LARGE moves that go more than VIX implies. You won't see this in a frequency distribution because frequency is not going to calculate that. Frequency is good for intraday traders because you don't care so much about the outliers (if you are just short-term trading and you use stops). You care more about taking pieces out of the market on all those days where it does what the odds say it will do.

I like to think about this like an options trader might. An options trader gets a premium to take 'fat tail' risk. So, once the market has done its range (the move away from previous days close), you can think of it as an options trader selling options premium at inflated prices and playing for the recovery (as it does on majority of days). The problem for option traders comes when you get those small number of days with very large moves -- then the options go in the money and trader loses all those accumulated profits.

The way to think about this conceptually is -- figure out your directional bias -- but be wary of late reversals back towards the previous days close once the market gets extended. ie, expect the 'range' to get hit and don't be afraid to go for big win when all lines up --- but at some point, get out -- odds are that on many days, your gains will evaporate if you attempt to hold on until the close.

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03-06-2009, 12:26 PM   #5

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Re: S&P Intraday Range and VIX

Hi frank nice observations.
I am an option writer, but I trade in Indian markets not much in s & p ..but option market is somewhat same. I use VIX and OI PCR( open interest put call ratio ) in my trades. what I do is, i divide open interest put call ratio by VIX which gives directional bias of the underlying price moves, rising vix is indirectly proportional to price movements in this case s&p500 and oi pcr is directly proportional to price moves.
OIPCR rises when there is comparatively higher put writing than call writing, very few times vix rises and oipcr rises, then net change of vix/oipcr is almost zero and so filter out the noise without getting delay, but most of the time there is more put writing happens when vix is falling and so oipcr rises, on rising vix there is comparatively more call writing happens indicating weakness in markets, and for option writer, writing call option is safer bet than writing put option as probability model skewed towards fall, speed of fall is more than speed of rise in prices…
Hope to get other interesting ideas on vix from other known members and pardon me for such a long post.
Alex

Last edited by alex_laxya; 03-06-2009 at 12:46 PM.

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03-06-2009, 01:48 PM   #6

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Re: S&P Intraday Range and VIX

alex, can you post a chart or two of that?

also, how do you time this indicator into a trade?

thanks for the interesting post.

03-06-2009, 03:13 PM   #7

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Re: S&P Intraday Range and VIX

Quote:
 Originally Posted by Frank » alex, can you post a chart or two of that? also, how do you time this indicator into a trade? thanks for the interesting post.

It was just sample chart, not my trade setup, in first window is nifty, NIFTY is same as s&p500, most liquid index derivative contract, in second window its vix ( mathematical formula of nsevix is same as cboe vix ) in third window is oipcr
By arrow i suggested the practical use to get directional sense.
While there r other things as well, instead of depending completely on it i try to put this data in overall context and also there r few things like oipcr has historical resistance at 169-1.75 zone ( in this one year old so called bear cycle )also need of smoothing the data to reduce the noise without getting delay response etc..to make a more reliable and logical combination, more i posted here
scroll down to post 29,later half of the section, posted the chart over there for trading setup.
Attached Files
 vix_comp_meth.pdf (146.5 KB, 587 views)

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03-06-2009, 07:55 PM   #8

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Re: S&P Intraday Range and VIX

today a good example of what 'fits' the general concept I was trying to relay. The market traded a wide range and recovered late towards the previous days close.

Using a VIX of 50 and Thursdays Closing Price of 686.50, a 'normal' day would be a range of 21.5 points and a close back towards the previous days close off the afternoon high or low. Conceptually, this is what happened as from an option traders view, you got paid to sell puts after doing a lot of range.

686.50 Previous Days Close
688.50 Final Close
+ 2pts Final Change after trading as low as 665.75 (Low of Day)

Last edited by Frank; 03-06-2009 at 08:01 PM.

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