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Markowitz portfolio theory to balance option portfolio?
- Thread starter Gustaf
- Start date
Can you just use beta?
Quote from Gustaf:
"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?"
What do you really mean by this? There is tonnes of covered call stuff on google yet people discuss it overhere..
Br Gustaf
Gustaf:
I like what you are doing. Could I ask some questions:
1. Could you explain the objective function you are optimizing (the one mentioned above)?
2. What software do you use to calculate the covariance? Could you share the code/software?
3. You mentioned the formula you have for gain. Is it gain on underlying or gain on the option? Is it the gain anytime during the time period or gain measure at end of time period.
4. Someone mentioned the degree of freedom, which he may have meant with it the number of (possibly conflicting) objectives. But if degree of freedom are the variable over which you need to optimize, then there is never too much degree of freedom, and in fact the more freedom the better for what you are trying to optimize.
(I wrote this quick with No editing as I have to run to something now).
Quote from tradingjournals:
Gustaf:
I like what you are doing. Could I ask some questions:
1. Could you explain the objective function you are optimizing (the one mentioned above)?
A: Its about Risk / Reward.
Risk is this context is how much an asset fluctuates over time
Assets are correlated to eachother in variying degree
-1 The are mirrored
0 They dont move together at all
1 they move in sync
By combining different assets (in this case option contracts) we could minimize the TOTAL movements, since they statisticall cancel out eachother (hedge).
The goal objective then tries to minimize risk by producing the right mix, whilst also trying to maximize cash premiums recieved.
A variable mu controls how much emphasis there should be on risk tolerance.
2. What software do you use to calculate the covariance? Could you share the code/software?
A: I use AMPL software which is a modelling language for for example linear programs. You can quite easily calculate that in Excel to. But this software also optimizes.
www.ampl.com (free for evaluation with some problem size constraints)
3. You mentioned the formula you have for gain. Is it gain on underlying or gain on the option? Is it the gain anytime during the time period or gain measure at end of time period.
A: Its the probability of not hitting the strike price - premium recieved. Its using standard deviations and takes these inputs;
Underlying volatility (stock historical/estimated future volatility)
Timeleft in days
Strike price
Underlying price (stock price)
4. Someone mentioned the degree of freedom, which he may have meant with it the number of (possibly conflicting) objectives. But if degree of freedom are the variable over which you need to optimize, then there is never too much degree of freedom, and in fact the more freedom the better for what you are trying to optimize.
A: Well this works pretty well for stocks, as for options they are more complex having implied volatility and time and the Greeks.
Iam not sure at this point how this affects the correlation matrix but thats what experiments are for right.
Maybe we could use Beta as Eliot Housewater pointed out.
(I wrote this quick with No editing as I have to run to something now).
Iam happy to answer more questions.
Quote from Steven.Davis:
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?
Gustaf, I was wrong. My quick Google search found search-engine-optimized garbage. A better search "modern portfolio theory option heteroskedastic garch convex" results in at least a few papers touching on the subject.
Each academic paper that I found just eats at an edge of the problem. If there were any hope of a solution that a one-man outfit could implement, it would be described in Carol Alexanders books. Looking through the table of contents of her latest 4 book set find the subject again at most lightly touched. If she doesn't already know how to do it, then I don't have time to figure it out.
I was wrong to say, "Do you really expect someone at ET to give you a simple thumbs up?" I should have said, "Your question is better suited to the Wilmott forum."
Searching there did find a promising reference: "An LP Approach to Option Portfolio Selection" Advances in Futures and Options Research, JAI Pres, 1995.
I think what you are trying to do is dangerous as explained previously.
Good Luck
Quote from Steven.Davis:
Gustaf, I was wrong. My quick Google search found search-engine-optimized garbage. A better search "modern portfolio theory option heteroskedastic garch convex" results in at least a few papers touching on the subject.
Each academic paper that I found just eats at an edge of the problem. If there were any hope of a solution that a one-man outfit could implement, it would be described in Carol Alexanders books. Looking through the table of contents of her latest 4 book set find the subject again at most lightly touched. If she doesn't already know how to do it, then I don't have time to figure it out.
I was wrong to say, "Do you really expect someone at ET to give you a simple thumbs up?" I should have said, "Your question is better suited to the Wilmott forum."
Searching there did find a promising reference: "An LP Approach to Option Portfolio Selection" Advances in Futures and Options Research, JAI Pres, 1995.
I think what you are trying to do is dangerous as explained previously.
Good Luck
Yeah thats cool. Alot of garbage often comes up on google searches. Thanks for the link.
I was not aware of the Wilmott forum, thanks!
Did you also try optimization?
Br Gustaf
As far as optimization: Yes, I built my own continuous optimizer that did a good job of operating within the curved constrained "subspaces." When this comes up, I am often asked why I bothered since MatLab/SciLab/R could have saved me much development time. The answer is encapsulation. When you are writing blackbox components to be run on an untrusted hedge funds server, running through some third party both made my code look cheap and encourage prying eyes.
I am not a fan of integer optimization of this purpose. Rounding (not to one) and examining the marginal effects of risk and return can do alot to make sure that rebalancing fluctuations aren't just flutter.
There was something else I wanted to say. Modern Portfolio Theory is about optimizing risk vs reward based on a return model and a risk model. Whether there there is some closed-form component or not, I have found that good risk and reward model, even for stocks and futures to be, to be non-obvious and completely distinct tasks.
Once I started validating my models on historical data, I quickly found that the Markowitz era derivations were hardly even a starting point. Average monthly market price returns and their covariance are deceptively simple and should be used only for answering homework questions. I don't presume, Gustof, that you haven't been through the same experience yourself. I assume, for example, that you have integrated your option trading model with your expected return model and validated both.
After a couple of years of iterative reading/coding/testing, I understood much better why the academic literature focused on things like parameter estimation error (especially relative to the effects of autocorrelation), robust covariance estimation, model stability, non-linearity, heteroscedasticity, spurious serial correlation, leptokurticity, non-stationarity (jumps/breaks), asymmetric measures, conditional correlation, Bayesian methods, reducing dimension by sector/industry/PCA reframing, aggravation of sampling error effects when highly risk-averse, tail-risk/EVT and in the larger sense of portfolio analysis attribution, foreign exchange risk, and counterparty risk.
I am not a fan of integer optimization of this purpose. Rounding (not to one) and examining the marginal effects of risk and return can do alot to make sure that rebalancing fluctuations aren't just flutter.
There was something else I wanted to say. Modern Portfolio Theory is about optimizing risk vs reward based on a return model and a risk model. Whether there there is some closed-form component or not, I have found that good risk and reward model, even for stocks and futures to be, to be non-obvious and completely distinct tasks.
Once I started validating my models on historical data, I quickly found that the Markowitz era derivations were hardly even a starting point. Average monthly market price returns and their covariance are deceptively simple and should be used only for answering homework questions. I don't presume, Gustof, that you haven't been through the same experience yourself. I assume, for example, that you have integrated your option trading model with your expected return model and validated both.
After a couple of years of iterative reading/coding/testing, I understood much better why the academic literature focused on things like parameter estimation error (especially relative to the effects of autocorrelation), robust covariance estimation, model stability, non-linearity, heteroscedasticity, spurious serial correlation, leptokurticity, non-stationarity (jumps/breaks), asymmetric measures, conditional correlation, Bayesian methods, reducing dimension by sector/industry/PCA reframing, aggravation of sampling error effects when highly risk-averse, tail-risk/EVT and in the larger sense of portfolio analysis attribution, foreign exchange risk, and counterparty risk.
Quote from Martinghoul:
You have too many degrees of freedom to optimize over... That is, unless you introduce additional constraiints.
Actually, I take exception to that. When I took a class in Numerical Optimization, the professor said on the first day of class something similar, that the number of dimensions in the parameter space should be one less than the number of constraints. Since this had been an objection from a reviewer to a paper the previous year, I pressed the point as to why that would be. He couldn't come up with much of an answer.
I don't believe it.
Code:
min X^2 + Y^2
Code:
min X^2 + Y^2 + Z^2