maratikus Wrote: ------------------------------------------------------- > jg, you already got a lot of great suggestions but > I still don’t think you will get realistic > results. You are working on a difficult project. > I understand that you have to make simplifying > assumptions but I’m afraid you are > over-simplifying the problem. If I were you, I’d > play with historical data. For example, if you > analyze auto-correlations you will see > mean-reversion in credit spreads just as Mobius > pointed out (O-U process would be appropriate). > You can also find conditional heteroscedasticity > in equities. Even if you adjust for that, > standardized returns will be non-normal. I don’t > want to discourage you but I think your model will > have to be a little more complex in order to get > somewhat reasonable results. Good luck! I’m not too concerned about making adjustments for non-normality in the distribution of returns. I have what amounts to a disclaimer in all of my executive summaries that basically explains the problem with fat left tails and that extreme events will be expected to happen more often than predicted by the model. I also have a whole page worth of education on the different statistical pathologies that can be exhibited by these return series. The deliverable to the client is mostly designed to show the effects of adding more or less equities, and longer or shorter duration fixed income investments to the asset side of the equation. At the end of the day I just want to end up with a chart that shows the 95% confidence interval of funding levels either expanding or shrinking depending on the portfolio that they choose so that they can have a better idea how they would want to go. I’m not sure I need to be too concerned about getting the numbers exactly right. I just need them to be in the ballpark and confidence intervals going in the right direction…in other words as the duration of assets gets closer to the duration of liabilities my confidence interval will shrink. Does this make sense? At some point I would like to really clean it up and actually use the model for optimization but I guess I can live with some rough numbers as the first iteration of the product.
DarienHacker Wrote: ------------------------------------------------------- > maratikus Wrote: > -------------------------------------------------- > ----- > > If I were you, I’d > > play with historical data. > > I second that recommendation. Google “historical > simulation” – most hits will involve VaR, where > this technique sees a lot of use. If you have > Hull’s book he covers the basics. > > For better or worse, recent history includes a lot > of movements that, prior to 2007, might have been > thought extreme. So without needing to go too > far back in history you should easily be able to > generate a broad (conservative) distribution of > outcomes. I like this idea and will probably include a couple of historical examples for the client.
If I haven’t said so already, I really appreciate the discussion you guys are having with me on this. It never fails to amaze me how many great ideas I get every time I post a question on this forum.
jg1996business Wrote: I’m not sure I need to be > too concerned about getting the numbers exactly > right. I just need them to be in the ballpark and > confidence intervals going in the right > direction…in other words as the duration of > assets gets closer to the duration of liabilities > my confidence interval will shrink. Does this > make sense? It seems as if you are trying to explain ALM with some numerical results.
maratikus Wrote: ------------------------------------------------------- > > It seems as if you are trying to explain ALM with > some numerical results. In a way that is correct but as part of the deliverable we want to use the clients own information (portfolio values and liabilities) and our own thoughts on capital markets in the numerical results. Obviously if I can make the results cleaner through the ideas posted here then that would be an added benefit.