maratikus Wrote: ------------------------------------------------------- > jmh530 Wrote: > -------------------------------------------------- > ----- > > If you’re doing this strictly for daily loss, > than > > it wouldn’t make much sense to regress Japanese > > stocks against a US index or factor score or > > something. This can help avoid the time > > inconsistency issue. Just do the regressions > with > > the data available for that market at that > time. > Let’s say I invest in a market-neutral manager who > is beta neutral and trades US vs Japan. I am not > very concerned for his position if markets move > 10%. However, if I calculate his beta using > settlement daily prices, I would be way off. What > do you mean by doing the regression with the data > available for that market at that time? Since I > work with portfolios of thousands different > instruments, I have to automate the process. I guess I’m still having some trouble understanding the issue here. You have a portfolio of some thousands of US and Japanese stocks. Do you regress each against both the Japan index and the US index to get the betas in a multi-factor model or do you just use a single-factor model depending on whether it is the one country or the other (or alternately a multi-factor model with n factors that are the same always and a stock index that changes depending on the country)? So long as you use one country’s index when you calculate the beta for the stock, there should be no issue with time inconsistency. Then just create a vector of the betas for US and Japan and incorporate it into your optimization constraints. If you did go with the factor model that incorporates multiple countries, I would guess that the beta for the foreign countries would be low and the home country beta would be similar to the single-country approach. However, you would have to test it both ways to check.
jmh, very simple and yet general example. You go long 1 million dollars worth of S&P 500 futures, go short 1 million dollars worth of Dax futures. How would you estimate what would happen to your position in case the stock market dips again?
For the sake of simplicity, I am ignoring the impact of currencies, but you should make sure to make the appropriate corrections when you do the analysis. I also ignore other obvious things like the adjustments for risk-free rates, the betas for the futures vs. the indices, and putting things in percentage changes. So far as I can tell there are three ways to gather the betas: 1) Use whatever is in your data provider as the daily close, regress the Dax and US indices against the MSCI world’s close 2) The same as 1 except use weekly data 3) Use the historical intra-day bar data from Bloomberg to obtain the close the MSCI world at the time of the close of each respective market so that instead of having one series of MSCI world, you have two. Regress the index against the respective MSCI World index. Alternately since the Dax and S&P500 are open at the same time you could take everything from the close of the Dax. This might be a better approach, but it is not generalizable to Japanese stocks or some market that doesn’t overlap. You can do these through time easily in Matlab or excel when you have data and collect a vector of the betas. After obtaining the betas you can test whether they are statistically different using standard tests. I would probably constrain alpha to 0 when performing the regressions also. If there are no statistically significant differences, you can use the betas in 1 since it might be the easiest. Otherwise, you might have to look at the results and see which way is best. Your portfolio weights are w=[1 -1] and the returns of the portfolio can be effectively modeled as r=w*B*MSCI World +e where B is a vector of betas and e is some error. Converting to dollar returns would be R=1,000,000*r. You could also do this within the confines of VAR by using the factor covariance and idiosyncratic variance into the whole covariance matrix. Note that the 1,000,000 long/short isn’t market neutral, it’s dollar neutral. If you want it to be dollar neutral, you could long 1,000,000 of the S&P500 and short 1,000,000*B_SNP/B_Dax of the Dax so that w*B=0.
jmh, thanks for sharing your thoughts. I understand that dollar-neutral position is different from beta-neutral. That’s why I gave an example of a position that’s probably not market-neutral. I agree that currencies can be ignored because we are dealing with futures. Your approach is theoretically sound and probably a very good one for VaR calculations. For stress testing purposes, I wonder whether I should just assume that betas are proportional to volatilities since correlations are very close to 1. What are your thoughts on that?
There’s a big literature on stress testing (a start would be Jorion’s Value at Risk). I’m by no means an expert on some of the advanced methods. If the correlations are assumed to be 1 (not necessarily true) and you’re regressing against some sort of world market index, then the betas are just the variance of the individual market divided by the variance of the world market. If you’re instead using betas such that beta=Sw/(w’Sw), where S is the covariance matrix of the assets you’re looking at and you assume the correlations between the different assets are equal to 1 are equal to 1, then you might be able to say that the betas are proportional to the volatilities and the weights in the portfolio. For instance if the standard deviation of the asset you’re long is 10% and the asset you’re short is 20%, then your betas by that formula are 0.2 and -0.8. (and if you set the short position to -25% instead of -100%, then the betas sum to 0 like the formula I mention above). Personally, I would rather do it with poorly estimated correlations than making an unreasonable assumption about them. Even if they were 1 for some markets, if you expand to look at other ones, then these ones might not be 1 and you’ll have to rewrite the program anyway.
jmh, I understand your perspective and I appreciate your feedback. Stress testing is a very general term. Even though there are a few typical techniques, underlying assumptions make a huge difference. In a lot of ways stress testing is more of an art than a science. bchadwick and jmh, I’m going to a fun workshop in New York. It seems as if you might enjoy going there. It’d be fun to meet there: http://www.baruch.cuny.edu/math/arpm/
I was planning on attending, but got side-tracked by a family reunion that weekend.
Maratikus, I did Atillio’s workshop last August and found it useful. It does go at warp speed and I was only really able to get the big picture. You do get a copy of Attilio’s book, which is a good reference book for delving deeper after you’ve gotten the overview. Overall, I found the course useful, although I have issues with some parts of the methodology he uses, which I’ll be happy to share after you’ve done the course. It’s also kinda trippy, because it’s basically 6 days of portfolio management with pretty much zero economics and zero financial theory. Every asset is a statistical distribution, nothing more. If I’m in town that week (pretty sure I am), I’d be happy to catch up for a drink or something after the class one day.
bchadwick Wrote: > If I’m in town that week (pretty sure I am), I’d > be happy to catch up for a drink or something > after the class one day. bchadwick, could you shoot me an email at maratikus.maratikus@gmail.com and then I will reply from my personal email. It would be great to meet in person.