I'm slowly grinding my way toward intuition and possibly action... I'm trying to stress-test a position. In this example, it is a bull call spread on SPY. Long 427 call expiring Dec 17, IV 18.9%, 59 delta Short 434 call expiring Oct 29, IV 16.7%, 49 delta I test 4 end-member cases (over 16 days): SPY falls from 434 to 420, vol flat SPY rises from 434 to 446, vol flat SPY flat, VIX drops from 20 to 17 SPY flat, VIX rises from 20 to 27 (I realize that in reality you can't decouple the price and IV, but still.) Here's the P&L of the 4 cases (dotted lines). The solid lines are the price curves corresponding to the same color P&L. Is there anything else, beside price and vol, I should be perturbing for this kind of analysis? Is this analysis even valid, in your view?
Not exactly. I assume you wanted both of these to be Oct 29, right? VIX is a 30-day moving average, so it's not very useful here. The expected move for that tenor in SPY is 16.84%/12.19; I'd say you're better off using that, maybe even figure out the 2SD move and run another pair of curves as well. By the way, I really like what you're doing here, and am following it closely. It's been one of the things on my own back burner for far too long, and I appreciate you kicking it off (the responses you've gotten are great, too!)
My bad. The long leg is indeed Dec 17 expiration. I was actually simulating a diagonal call spread. I'm not explicitly using VIX in the modeling. I had mental bounds on how far I thought the VIX could move in 2 weeks from its current level of 20. 17 to the downside (15% decrease), 27 to the upside (26% increase). Then I assumed that I could just scale the two options by 0.85 and 1.26 for the stress test. But from what you say, it sounds like that simple relationship might not hold! Your idea to use the IV to compute expected move sounds much more applicable. Sorry to be dense, but to compute the expected move, do you just multiply the IV by DTE/365 (or DTE/250)? And is this expected move an idealized (gaussian) 1 SD move? Thanks, I really appreciate it. It's been frustrating and embarrasing to start these threads and optimistically get one or two takeaways from them. People are generously conveying solid knowledge, but my brain just isn't ready to absorb. And then I go and re-ask the same question that was already answered. I guess I can take consolation that others are benefiting. Do you think I should also be testing an extreme change in vol skew? At my fledgling state of knowledge, I figured that it was a second order effect. However, @jamesbp made a good point in my "shitty trade" thread - what happens if the long leg IV goes to 10%? I thought, surely the long leg IV couldn't go to 10% with the short leg IV staying unchanged. But I think that was exactly his point. A large change in the skew could really skrew you. Or skewer you.
You'd also need to multiply the above by the stock price - i.e., S x σ x sqrt(t/365) - so for 15 days and an IV of 15% in SPY, you're looking at 435 x 0.15 x sqrt(15/365), or ~12.35. You can also find it on the option chain in your trading software, or just price the ATM straddle for that tenor (if you believe in the efficient market hypothesis, the latter should be more accurate. ) Brother... you ain't alone. And I say that with a whole lot of feeling behind it. I'm doing the same thing as you - trying to build an intuition for it on a base of solid knowledge - and absorbing all this stuff makes me feel like a drooling moron on a more regular basis than anything else I've ever learned in my life. I must be a masochist, 'cause I keep coming back for more. I'd love to know enough to answer that, but I don't - yet. I've been playing with skew quite a bit the past few months, putting on lots of flys... but no satori as yet. I've seen a fair bit of skew reversion, but outside of some insight into vega and volga, I can't claim to have any sort of a solid grip on it; not even a certainty that I know what I'm doing with flys. Good thing they're cheap.
Thank you, OP, for coming up with this analysis. I'm wondering what's the advantage of your type of analysis comparing to the risk profiles plotted by brokers? If it's for just learning, by all means play with it. But I think you made assumptions about the paths of stock prices over a period of time in your analysis: they go up, down, or unchanged linearly, which is not true in practice. That's also why I think the risk profiles offered by brokers are more useful (PnL vs. stock price): they don't assume the stock price path to be any form and just show the PnL give a stock price at a particular time.
Couple of quick points 1. Both methods ( Spot x Vol x Time or Straddle ) of estimating the Implied Move are rough approximations that are only useful when Time < 90 days / Vols < 40% 2. If using the ATM Straddle method then better approximation of implied Move is Straddle x 1.25 as ... Implied Move = Spot x Vol x SqrtTime ... ATM Straddle = Spot x Vol x SqrtTime x 0.80 ... ATM Straddle x 1.25 = Implied Move 3. If using the TastTrade platform ... be careful ... ... as they calculate Implied Move < ATM Straddle ( error approx 50% ) ... as they do not 'finesse' the calculation when Time > 90 days / Vols > 40% For example ... say Time = 365 days / Vols = 100% ... TastyTrade reckon that the implied move for 1 year is +/- 100% ( so what's the 2 standard deviation move ? )
I think you commented on this in a previous post, but this options game is notable for the magnitude of disconnect between "book knowledge" and real-world success. I mean, in any field, you don't let academics put the rivets in the fighter jet, but man, options is crazy. That (futile) "best options book" thread was telling. I guess the only conclusion was: traders can't write, academics can't trade? Though I suppose herein lies the angle - options is a relatively small pond, and the skill differential between the average punter and the pro is immense.
That last is a useful addition - thanks! I knew it was a rough approx, and it makes sense that things go non-linear as vol gets high. I've seen all sorts of fiddle factors here... e.g., TastyTrade says it's the ATM straddle x 0.85. But based on what I've seen over time, the actual move (in SPY, at least) tends to be closer to what you're saying - something over 1, at least. https://www.tastytrade.com/definitions/calculating-expected-move Heh. It's a bit surprising, actually; they've got some fairly smart quant kids on board these days. I guess they just haven't gone back to fix all that crude, normal vs. log-normal stuff they built in the early days.
I do know one guy - a retired trader/MM who can put words together pretty well - who has written a book; I reviewed it for him. The problem is, he keeps fiddling with the damn thing because it's "not perfect", and, well, putting something that's not perfect out into the market is something he's incapable of doing. I hope he manages to break through that wall at some point... Regarding that disconnect, Taleb said it quite well: For us practitioners, theories about practice should arise from practice or at least avoid conflict with it. This explains our concern with the "scientific" notion that practice should fit theory. Option hedging, pricing, and trading are neither philosophy nor mathematics, but an extremely rich craft rich with heuristics with traders learning from traders (or traders copying other traders) and tricks developing under evolution pressures, in a bottom-up manner. It is technë, not ëpistemë. I'm enough of an engineer by training, practice, and preference, that this definitely strikes a spark. You need theory to get you most of the way there - but after that point, you've got to do some sweating in the trenches.
It's a bit more work to make these "typical" P&L graphs, but I agree with you that I should do it. That is probably the most intuitive way to visualize.