Gustaf, Why do you think that it will work well for covered calls against your stock portfolio? I would argue that it will not work well for portfolios that contain material option exposure (puts or calls). Example: How many one-delta puts with 1 penny of edge do you think your Markowitz Optimizer wants to sell? Quite a few, is my guess. Why is that? Well the puts aren't going to increase the variance of the portfolio that much, since they are only 1 delta. Should you keep on selling them? Also, the problem isn't just with selling tail risk. How many at-the-money straddles will Markowitz have you buy if you don't effectively model the vega risk? kps
Well, I might be wrong, but I think it would work well because not all stocks would go in the bad direction at once, at least thats what i see with my current portfolio, for example: a bad day index goes down 1.5% my portfolio is down 0.6% etc. The optimizer would pick lets say I allow it to sell for a certain amount (margin based on strike), it would pick a bunch of different contracts that statistically would go well together. Iam have not though about any vega re-balancing yet, just initial "go well" contracts.
Oh yes, they might. And that's the very situation you want to avoid, however infrequently it occurs. Instead, consider using your option trading to modify total portfolio risk. Long deltas here, short deltas there, vol attributes, etc. It's an easy way to step out of the all equity-long delta world if you're of a mind anyway to put the effort into options.
You have too many degrees of freedom to optimize over... That is, unless you introduce additional constraiints.
Made a draft of the optimization, 63 samples (9 days x 8 hours) (All I could get at the moment) Hardcoded that 4 puts must be written with a max amount of 1 per contract. Notice how variance goes down.. which is what i wanted.. I will try to make some delta/gamma optimization later, need to read up on Nathenbergs book again. Br Gustaf
I have worked on Modern Portfolio Theory for Futures and Equities, but not options. When the market is falling apart, it is will understood that short-term correlation rises. For this reason, exposure is monitored closely with frequently updated short-term GARCH estimates, and risk analysis includes shock matrices. For options, there are so many risk dimensions that tend to all go wrong together. Without having a really elaborate and thorough model, I think that you putting yourself at great risk by using mean-variance optimization. Your optimizer will nicely find combinations which according to your model have little risk so you trade larger. When things go wrong, your optimizer neatly changes its mind, and you are left with an untenable basket and real market slippage. A quick Google search shows that there are quite a few papers on the topic. Do you really expect someone at ET to give you a simple thumbs up?
Let me start by noting that I really don't understand what you are doing. You started by saying you were running a Markowitz optimization, then you said you were calculating probabilities of winning. Thats fairly inconsistent. There are two inputs to a markowitz optimization, a vector of expected returns and a covariance matrix. The "probability of winning"(though I don't even really know what that means) will affect the results of the optimization, but only to the extent that it affects the two inputs. Classically, there is no need to calculate it for the purpose of Markowitz optimiazation. Perhaps you are using it as an additional constraint? Now, if you actually do mean Markowitz optimization, the problem is not that there are too many degrees of freedom. You could do the optimization, but you will probably end up with very strange results. You would then need to add more constraints to give you a less weird solution. This is usually what happens with MV in practice, you get a shitty solution so you put on more constraints to clean it up. It doesn't have anything to do with not being able to do the optimization. So, to do this, effectively you would treat every traded option that you are potentially willing to add to your portfolio as its own asset(this includes options written on the same stock). You would then estimate expected returns and covariances, run the optimization, and out pops your "optimal" portfolio. The biggest trouble here in my opinion is estimating expected returns. First of all, it will be a pain in the ass to collect the data and do the calculations(and the results will be pretty sensitive to how you do so, mostly with respect to what time horizon you choose). Second, estimates of expected returns are typically very very noisy(as a sidebar, this is why risk-neutral pricing is rather elegant). All in all I think this is a pretty poor idea that will not work very well. Your results would be a lot more interesting if you could clarify what type of optimization you are actually doing and how you are getting your estimates.
Okay thanks for the input. Iam trying to picks stocks that doesnt go in the same direction at the same time, its not true Markowitz since right now Iam only trying to minimize the variance and maximize premium. Here is the AMPL modelling goal objective. minimize linear_combination: mu*sum{i in T} (sum{j in A} Rtilde[i,j]*(x[j]))^2 / card{T} - sum{j in A} premium[j]*x[j] ; I dont expect or trying to get a "thumbs up" Iam just sharing my experiments, thats what the forums are for right? As I wrote earlier in the thread, I have been running a stocks portfolio with optimization that has had lower risk than index but still offering a good return. Anyways Iam happy you point out the flaws in my method. Please continue to give feedback! Not all my experiments succeed! Br Gustaf