Is there a chicken-and-egg problem with RBSA?
The textbook says, regress the stock’s returns vs various categories like (for example) large-cap value, large-cap growth, small-cap value, small-cap growth.
My question is, how do you construct these categories in the first place without resorting to a holding-based analysis? If you don’t know where a stock goes, how would you what stocks are in (say) the large-cap growth category?
Holdings based analysis is based on the Holdings you (investor/institution) has ON THEIR CURRENT PORTFOLIO.
Large Cap Value/Growth etc. is based on “classification” by which the stock is placed in particular indices provided by providers.
Understood, but consider the providers. How did they arrive at value vs growth, small-cap vs large-cap classification? They could not have used RBSA. So when you’re looking at your stock returns, why should you?
Concrete example: I have 5 stocks, 2 large-cap growth and 3 small-cap value stocks, as defined by the providers, equal-weighted. You don’t want to go into details of my holdings or you are skeptical of my claims that that’s what I have, so you regress my aggregate returns against all 4 classes and find (for some reason) that my style is small-cap growth. Of what use is this information? My portfolio is not going to track small-cap growth no matter what the current correlation is. Eventually my portfolio and small-cap growth index will part ways anyway.
I agree that in the first place you couldn’t use RBSA to identify the style of the benchmarks. But once those benchmarks are in place, and are well-known as value or growth, regressing your returns against the benchmarks can get close to identifying the style of your holdings without having to undertake a detailed holding-by-holding analysis. I think the primary benefit of RBSA is “its less intense data needs”. Further, the text says that it might be performed first, to see how close (coeff. of determination) you are to a given style, and then analyze the individual holdings as a second step.
Hi ,
There is something I don’t really get with RBSA.
It is look like it is not just a rolling multi linear regression. I did an analysis with excel R lm and with excel using Linest function, however I don’t have the same results.
if it would be only a multi linear regression, excel would do that quickly , so where is the subtility ?
Thanks
You simply grab a set of mutually exclusive (and, ideally, collectively exhaustive) indices and use those.
The point is that the regression will use whatever indices you choose. If you include an index whose returns have an extremely low correlation with the returns of the portfolio, you’ll likely get a very small coefficient on that index.
In short, as long as they’re mutually exclusive, you can choose as many indices as you want: the more, the merrier.
are you referring to reading 23 - exhibit 13? to me this style chart is impossible to produce.
the chart is quite spikey, so i doubt it is using a moving average type of calculation. if you take the bast case that it uses daily returns of 4 indexes, v.s. the portfolio, using 1 month (20 trading days) of data, then you are getting a huge margin of error.
the fact that all the indexes are highly correlated to begin with… and i say it’s a BS chart.
I believe it’s a constrained regression, where:
each coefficient is constrained to be >0
and
the sum of all coefficients = 1
With that in mind it’s easier to understand the interpretation, which is that the coefficients are your % exposure to each market represented by an index. In the 5 stock example given, theoretically you would expect to see a beta of .4 on the LCG index and .6 SCV with a beta of 0 for SCG.
In reality the results are going to be much noisier (possibly modeling a high allocation to SCG), but as long as you take it for what it’s worth and don’t read too much into it it can be a quick, easy way to get an idea of style and style drift with minimal data.
That chart is most definitely not BS. I make these types of charts all the time at work, there are tons of providers that offer RBSA software to produce charts exactly like this. Same goes for holding-based analysis. It doesn’t matter if the indexes are highly correlated, as long as they’re mutual exclusive as s2000 pointed out, RBSA should provide a close approximation for underlying style exposures. If you don’t include enough indexes, however, you could get a faulty result. For example, for a domestic all-cap manager you would want to use r 2000 growth, r 2000 value, r mid cap growth, r mid cap value, and r top 200 growth, r top 200 value.
so… what happens if you put in half a dozen indexes, and regress against a single stock fund- say GE or something? then you see some non zero EM exposure for the fund?
you then explain it away by saying GE has operations in singapore…
to me it’s tea leaves.
let say the correlation is 1, then you are screwed. you will just get random garbage.
here is the original paper (ref 41)
https://web.stanford.edu/~wfsharpe/art/sa/sa.htm
the “pretty picture” is generated using a trailing 60month data set, vs 12 indexes (in 1992 I’d guess much lower correlation than today). going back to exhibit 13 - we see a 10% jump in 2003 - does this mean the allocation was changed? Impossible. if you told me it is the R3000 getting regressed it would not suprise me…
I’m still not sure how to interpret this LOS. for me it needs long rolling series and uncorrelated indexes.
If they have a strong (positive or negative) correlation, you’ll have a multicollinearity problem in your regression: recall your Level II multiple regression.