Erwin, welcome to the WIND thread. I like your entry. I apologize for this late response, but I was away once again.
I very much like your suggestions about indexing content on the thread. One democratic way this could be done would be start a new Wind River Index thread, and post abstracts that contain links to multiple past posts on the main thread that rightfully group together. Any volunteers?
I applaud your attempt to extend my simple closed-form asset allocation model through simulation. You correctly perceived that I believe simulation is the easy tool for adding real-world complications. The algebra quickly gets out of hand when trying to keep the solutions in closed form.
I will make a couple of comments about your observations and modeling now, and then suggest that we pursue details off line, for fear of boring most participants. Perhaps later, you might want to post any changes that might result from our collaboration.
>In my profession, I have come across many asset allocation models for
>pension fund portfolios.
What is your profession?
>I have always questioned the validity of using past experience in making forward
>projections in an economy and market place that is changing constantly.
You are in good company. Many deep thinkers have expressed major doubts about statistical extrapolations of financial market data.
>I would not feel comfortable with using a linear 1-to-1 function even
>at the lower end of the wealth spectrum.
That is your choice, and I suspect the correct choice for your wealth situation. However, it is easy to conjure up practical situations where an appropriate utility function is perfectly linear. I solved the linear case for theoretical completeness and to demonstrate the role of curvature in the utility function, not because I favor linear utility functions.
>In your straight application of the Gambler's Ruin approach,
>there are only two results: win or lose.
The art of making a simple but practical model is to focus on the essence of the problem. To lose all may seem extreme, but the practical ramification of this assumption is merely to bias the model away from the gambler's ruin, i.e. toward a conservative solution. This means that any optimum solution to the model is robust relative to the possibility of ruin.
>No sensible investor is going to hold on to an investment that is
>tanking until the value of the investment is zero.
Would that that be true! The fact is that many a sensible investor has held steady to his/her beliefs and watched an investment zero out completely. Traders presumably never succumb to this embarrassment (they say), but others, certainly including most amateurs, do. It turns out that the resistance to closing out a transaction at a loss is so universal that it causes legitimate concerns about the legitimacy of axioms underlying so-called rational behavior. While I am the last person to suggest that WIND might zero out, nevertheless, I don't believe this assumption is so extreme as to invalidate the usefulness of the model.
That being said, I agree that a less dramatic downside would be useful in situations where the investor understands that the downside cannot be violated.
>With a stock like WIND, there is a definite possibility that the stock will
>more than double in value over a period of time.
You are correct, and including that possibility is a nice extension. Again, however, excluding the possibility merely bias the model toward not gambling excessively.
>Whether he/she realizes it or not, an investor is intuitively making decisions
>based on certain criteria, e.g., not to end up with a portfolio that is less
>than 50% of the current size.
So what? The optimum solution maximizes the expected utility of the return resulting from the investment allocation, period. There are no other criteria that need be considered. Believe it or not, all the concern about loosing more than 50%, or anything else, is all incorporated in the investor's utility function - so choose your utility function with care!
>Most investors are likely to have more than one favorite stock. The math
>of course becomes a lot more tedious, if not impossible.
Only tedious, but sufficiently tedious to keep me from solving the equations. Adding additional companies is a very good reason to turn to simulation.
Unfortunately, I haven't had time to fully appreciate your simulation results, but I can make a couple of observations. First, your 30% maximum compares to my 10% maximum for a candidate quadratic utility function. This is in keeping with my model guarding strongly against ruin. In other words, your "refined" approach (assuming your calculations are correct and you only maximized expected utility of return) is much more venturesome than my simple model.
Second, adding additional companies begs for formal consideration of the co-variance of return between the two companies - especially if the companies happen to be picked from the same sector. At a minimum, you might strongly suggest that the two companies should have a history devoid of correlation, positive or negative.
Third, I suggest that you verify your calculations by temporarily disconnecting all your refinements and simulating the quadratic cases I presented without any change whatsoever. You can use my examples to establish the number of simulated realizations needed for statistical accuracy, and to make sure your simulation duplicates the closed-form solutions. If you fail to duplicate my results, email me and we can resolve the differences.
Allen |
