Hi all,I am working on how to forecast the beta of stocks. Does anyone know any good or effective models ? Any help is appreciated.oengier

i thought they usually do it for portfolios, stocks have too much idiosyncratics risk

QuoteOriginally posted by: oengierHi all,I am working on how to forecast the beta of stocks. Does anyone know any good or effective models ? Any help is appreciated.oengierThe beta of a firm is defined as the expected return on equity minus the risk-free rate, the whole thing divided by the market risk premium. As you can see, there are more unknowns than knowns. For example, what is the risk free rate and how do you define the "market" risk premium? Acceptable proxies for these are: (1) for the risk-free rate you can use the treasury rate at some practical maturity (2) and for the market risk premium you use the return of some broad index averaged over the same maturity period. For the "expected" equity return, I guess you could either refer to analyst reports or you can use your own guess, if you have some justification for it.The beta itself further depends on the firm's leverage (Hamada's equation). This is another story!

jawabean: yes, portfolio is my final aim. thank your comment.rcohen: thanks for your clear explanation. what I want to know more is about how future beta of portfolio changes and then i can take the corresponding measures in advance. Could you recommend some papers about it? thanks.oengier

QuoteOriginally posted by: oengierwhat I want to know more is about how future beta of portfolio changes and then i can take the corresponding measures in advance. u can regress your portfolio' beta on some exogenous parameters, like book-to-market ratio and other stuff (interest rate models) . then forecast these parameters using something like vector autoregression, then predict beta of portfolio.

QuoteOriginally posted by: jawabeanQuoteOriginally posted by: oengierwhat I want to know more is about how future beta of portfolio changes and then i can take the corresponding measures in advance. u can regress your portfolio' beta on some exogenous parameters, like book-to-market ratio and other stuff (interest rate models) . then forecast these parameters using something like vector autoregression, then predict beta of portfolio.thanks a lot. which beta does your "portfolio' beta " mean? historical estimated beta? or calculated by other methods?

Hi all,I would recommend looking at the work the guys do @ Barra.In short they estimate a beta (in light of the discussion I think an equity beta) based on a set of market and fundamental indicators.Pioneered by Barr Rosenberg, try looking for some of his original papers.I think you will find the attached "cook book" rather interesting...Regards,MichalPS add a"." for adobe to recognise this...

QuoteOriginally posted by: oengierthanks a lot. which beta does your "portfolio' beta " mean? historical estimated beta? or calculated by other methods?historical. get the daily return, adjust with dividends. then get the daily "market" from Fama's data library. compute annual beta. regress it on something like mean book-to market and stuff. predict your explanatory variables somehow, like IR models for treasury yields or autoregression on other stuff; predict beta using regression on explanatory variables

type this into excel, and you'll get as good an estimate as is possible=NORMINV(RAND(),1,0.25)

if you have no faith in your economic intuition(market cycles, growth, management & all fundamental stuff) then use analysisof historical data and GARCH. you might use that as beta is after all determined by variance/covariance of market and stock.

Regarding GARCH, i do not know which G model r u thinkin, but vanilla one for beta modelling assumes RHO=CONSTANT, which is certainly ... disappointing (i.e. hi,j = RHO * hi,i * hj,j )im working on this also so... please helpp.s.> murtin1 , i cannot download your barra file, can u re post it? tnx

Yes, if anyone has that Barra file, can they please repost a link? This one doesn't work.

I don't know why you want to forecast the beta. It is usually assumed constant. From what I've played with financial time series, it seems that it is a assumption that holds most of the times.But, if you still want it, I think you can forecast the coefficient with state space models. I'm not sure about this. You'll have to go through the bibliography to confirm it. Regarding software, Eviews 4.1 (or higher) can handle them.You can also do this with a markov switching model, but the forecast will be the probability of being in each beta coefficient (each state) given a k state model, switching on the beta. Its close to what you're trying to do, but forecasting probabilities, not the coefficient itself.I've writen a matlab code that can do this easily. If you want I can pass you the link.

QuoteOriginally posted by: jawabeanQuoteOriginally posted by: oengierthanks a lot. which beta does your "portfolio' beta " mean? historical estimated beta? or calculated by other methods?historical. get the daily return, adjust with dividends. then get the daily "market" from Fama's data library. compute annual beta. regress it on something like mean book-to market and stuff. predict your explanatory variables somehow, like IR models for treasury yields or autoregression on other stuff; predict beta using regression on explanatory variablesThis post by jawaben will work too. But I'll would be cautious about it. The final forecast in this case can be very uncertain.For instance, lets say you model Y (betas) as Y=f(X)+e1, where X is a vector (one explanatory variable) and e1 a normal error variable with zero mean and std given by the model's standard error.Now you forecast X with an autoregressive component where X(t+1)=f(X)+e2. With expectation operator we can see that E(X(t+1))=E(f(X)), which is the basic equation for forecasting an autoregressive model.The final forecast of the Beta (vector Y) will than be:Y(t+1)=f(X(t+1))+e1substituting:Y(t+1)=f(f(X)+e2)+e1Its possible to see that the forecast will have another stochastic component given by the standard error of the autoregressive model from the vector X. Once you have the standard error from both models (beta and autoregressive), you can use monte carlo by simulating those normal errors and getting the actual distribution of the forecast.Unless e2 has zero variance, which probably won't happen, the bounds of the forecast can be very high, which is natural considering both uncertainties about the models.