Time and Volatility have similar effects on an Option position. Time moves in one direction [save one special exception] while Volatility can increase, or decrease.
If a trader has a position that is positive gamma, then by definition he is negative theta.
A Credit spread [written position] is short gamma, and long theta.
Taking one of the posted examples we can analyse the position; Let's look at FD
Sell PUT
Expiry February 17 2007
Strike $37.50
Common @ $40.22
#Contracts = 10
Credit = $0.30
Buy PUT
Expiry February 17 2007
Strike $35.00
Common @ $40.22
#Contracts = 10
Debit = [-$0.10]
Net Credit = $0.10 = $100.00 [less brokerage]
Net Risk = $2,500.00
Return on Capital at Risk = 4%
Now the first point is; no-one will be satisfied with a $100/month return, therefore just as a back of the envelope calculation, assuming that this is an *average* trade, then to return $2000.00 per month, we will be risking;
2,500 * 20 = $50,000.00 = 5% return on capital/month or 60% per annum.
That 60% looks alluring, seductive almost, but you are risking $50K * 12 = $600,000.00
That is the capital really required to implement this strategy.
Moving on;
Historical Volatility = 26.26% [High = 50.76% Low = 6.72%]
IV = 28%
Fair value = $0.20
Sell @ $0.30
delta [-16.9]
gamma 7.9%
vega 0.029
theta [-0.013]
rho [-0.005]
Immediately we can see that Implied volatility is pretty much the Historical volatility aggregated, however, there is quite a bit of potential in the worst case scenario. The 2% margin of sold IV to the Historical aggregate is too low in my opinion for a rational write strategy, especially when you look at your reward to risk, viz. 1:25
We have a high gamma, a 7.9% jump in delta can seriously damage your position.
theta bleed at $13/day is not really compensation for this high a gamma position
This trade was placed last Friday, as of todays prices @ $39.90 we can re-evaluate the position. The DJIA had a nasty day falling, and FD fell with it.
delta = [-19.5]
gamma = 8.7%
vega = 0.031
theta = [-0.014]
rho = [-0.006]
delta has picked up already with a very small price fall; $40.22 - $39.90 = $0.32
gamma has increased along its curvature, and can hurt this position maximally through the strike price.
theta has picked up 0.001.........hardly anything that is going to help you if this price action continues.
Looking now at the probability calculations;
In-the-money probability = 18.7%
Probability to expire worthless = 81.3%
Probability Price > $38.00 = 76.4%
Probability Price will be between $38.00 - $37.51 = 4.8%
Probability Price < $37.51 = 18.8%
Extrinsic Value = $0.30
Intrinsic Value = $0.00
The probabilities, based on a 100 position diversified holding, would see you with 19 trades/100 trades losing.
19 * $2,500 = $47,500.00 loss
81 * $100 = $8,100.00
Net Loss = $39,400.00
$47,500/$600,000.00 = 0.079% loss on capital
Thus the *hedge* serves its purpose, and keeps the trader in the market, but, can you call this a true *edge*?
jog on
d998
