The premise for short gamma trades is that the options’ market consistently overprices the volatility of the underlying. This discrepancy can be interpreted as a risk premium that speculators demand from hedgers.
A simple test suggests that this hypothesis is true for the USD/INR options market. Also, this risk premium seems to be auto-correlated.
RESULTS FROM IMPLIED VERSUS REALIZED VOL TRADES
I took one-week implied vols and compared these with USD/INR’s realized volatility over the subsequent seven-days. I calculated the daily standard deviation of the exchange rate on a close to close basis (annualized by multiplying it with the square root of the number of trading days per year). Then I measured the difference between implied and realized vol over the period under consideration. Following are the results from this exercise for non-overlapping weekly periods (annualized):
Data: 1-week implied vols. from July 2003 to March 2009; USD/INR: Daily data from July 2003 to March 2009
Stdev: 3.5%
No. of trades: 294
Proportion of loss-making trades: 22%
Maximum: 18.7%
Minimum: -10.3%
THERE IS EVIDENCE OF MOMENTUM IN WEEKLY PERFORMANCE (VOL TERMS)
The serial correlation is about 0.52, suggesting the presence of momentum. Based on this result, I tested a historical scheme to go short gamma only if the last trade money. The results are the following (annualized):
Mean: 2.0%
Stdev: 3.3%
No. of trades: 228
Proportion of loss-making trades: 17%
Maximum: 18.7%
Minimum: -6.2%
Clearly, the performance improves on many fronts. The proportion of loss-making trades decline by 5% to just 17% and the maximum drawdown falls as well.
6 comments:
Interesting observation. I always thot this was the case but never took the effort to check.
I understand ur point on transaction cost but even in a non-dynamic hedging world, shorting gamma seems to make sense. Ofcourse the in-sample is different from out of sample world...
But is the trend the same in recent times (say last 6 mts)? I highly doubt it.
I have similar observation where implied vol was higher than historic vol, with annualized volatility calculated from daily returns (last 250 days)
Another interesting thing is this implied vol differs dramatically with the data used (open, close or day high)... all three were giving different values not just for USD/INR but accross indices.
Just was wondering what the results would be if u used low or high data instead of usual weekly close for your vols calculation ...
http://sharemarketindia.blogspot.com/2008/12/historic-volatility-calculation.html
Hi Mahesh,
The returns have increased over the last 1-year. If this phenomenon reflects some kind of risk premium, that is exactly what I would expect. Globally, risk premia - liquidity, term, credit etc - of all kinds remains bloated.
I am keen to know why you think that should not be the case.
Also, your point about things often not working out of sample is well taken.
Hi Shikhil,
Interesting observation. But I am not sure I understand what you are suggesting.
If we want to do this systematically, we would have to define a specific point of time because we know what the high of the day was ex-post but not ex-ante. It would be great to know what you think.
Shikhil,
Spoke too soon. I see your point.
I doubted because when I was pricing USD/INR options of late (say till a couple of mts back) the implied vol for USD/INR options were much lower than the realized vol for the same period
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