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Has anyone looked at the Bakshi-Chen-Dong model (see link below) as a possible source of alpha? Better yet, anyone implemented it or interested in working through it with me (I've already made significant progress)?http://www.yorku.ca/mdong/papers/stkmodel.htm

I haven't gone through the whole paper yet, but am already suspicious of this BC model after reading the first section.The Bakshi and Chen (2001) model seems to use the following data: book value of equity, historical earning streams, and instantaneous (stochastic) interest rate.The main aim seems to be to apply "a stochastic pricing kernel which makes the model arbitrage-free and takes into account the risk aversion of the agents, in the Harrison-Kreps (1979) sense."Maybe it's just bad writing but these seem to be inconsistent aims. Also, in what sense is the valuation "arbitrage-free"? After all, there is no 'underlying', apart from the stock price itself, as the earnings process(es) itself is not directly tradable.The "average in-sample pricing error [is] within 1%"... well naturally, if you discount the future cash flows at a stochastic discount rate you can get any value you like. They find an out-of-sample error "within 9%" - I'd like to know the out-of sample period as I think the model should have more limited predictive power.However before I criticise further I should go back and read the rest of the paper...

First, let me say that I'm not making any claims yet on the validity of this as a theoretical model... For right now, I'm more interested is the predictive power of it's mispricings. As far as the notion of "arbitrage-free", I think the actual argument is to balance the expected return on the stock with the risk-free return. One concern I have from the orignial Bakshi and Chen (2001) paper is, when they discuss the comparative statics, they claim higher kappa_g => higher P/E. But when I implement the valuation formula for their example (bascially just calculating the integral), it seems to me that higher kappa_g => lower P/E. ??

Very difficult to test the practical aspects of the model since there are a large number of parameters to be estimated. Especially with regard to the earnings and earnings growth processes, but also in specifying pricing kernel {M(t)} (sigma_m? how are you supposed to calibrate this, in fact what is it?).No kappa_g notation in the original paper but I assume you mean the speed of mean reversion of earnings growth. I think kappa_g increasing should imply P/E increasing where utility is concave. Which integral are you calculating?

GM, you're right-- by kappa_g, I mean speed of mean reversion for expected earnings growth. And by original paper, I mean the paper at http://papers.ssrn.com/sol3/papers.cfm? ... 20Download (Bakshi Chen 2001)I also agree that the model is somewhat difficult to test emprically.. that's why I'm looking to others for help. I have tried to use a combination of randomized algrorithms and least-squares optimization, but the parameter estimates do not seem very robust. So as a sanity check, I thought I would check the comparative statics discussed in (Bakshi Chen 2001) on page 10. There, they basically calculate the integral from formula (17) for the P/E ratio for a fixed parameter set, and vary one of the parameters such as kappa_g. Their results are also depicted at the end of the paper in Figure 3. But when I use Matlab to try to reconstruct the plots, I see something quite different for the speed of mean reversion plots-- namely, they have the opposite effect. Stronger mean reversion in R => a lower P/E ratio. I'm wondering if someone else did this simple test, if they would see the same thing.Thanks for the interest.

Ah, I was looking at their previous paper Bakshi and Chen (1997), hence the confusion.Their plot of kappa_g does seem to be wrong. In fact, the range for kappa_g included in the graphs violates their transversality condition, given the other parameters. If I had to guess, I'd say they might have plotted 1 - kappa_g in [0,1] for some reason. I also find that the integral (for S(t)/Y(t)) is decreasing in kappa_g, and that this integral only converges for a limited range of kappa_g. Economically neither of these two results make much sense, and I'm struggling to see how they arise from the model specification.Any idea how they derived the solution from the PDE in (9)? They claim to derive it in the appendix, but there they just re-state it! Can you use mathematica or a similar package to deal with it? They only seem to specify one boundary condition, that is the time (t+tau) payoff.If you want to discuss further you can PM me.

I have tried fitting this model, I seem to get local minima very dependent upon starting pointand a large number of useless minima which is surprising given the number of free parametersvs the number of data points; it should be "easy" to get a good fit. What upper/lower parameterboundaries are you guys using?

I assume you are not modelling the PDE directly but are trying to fit some data to the solution.I was assuming their solution was correct and just computing the integral as given in Bakshi Chen (2001) to replicate their comparative statics graphs. I used the parameter values given in their paper initially.I have a suspicion that in fitting this model the parameter estimates will not be robust. Perhaps this is because earnings and earnings growth are modelled as dependent stoch processes so it could be easy to get conflicts between the free parameter values?

Exactly - I am actually trying to fit the solution to a model by Dong to minimize MSE on price instead of P/Ebut its virtually the same - my results are as you suggest "not robust". It is a complex system with manyparms but there seemed to be enough "order" there to maybe force a single solution. Dong talks about using a "random" search which doesnt seem feasible with 8 parms, (the commoninterest rate parms Kr Ur and Sr are fixed) and 2 constraints unless some pretty tight bounds are set.

After 3 long years did you get any progress on the subject ? I´m interest in quant approachs to general equity valuations....

QuoteOriginally posted by: msardelichAfter 3 long years did you get any progress on the subject ? I´m interest in quant approachs to general equity valuations....trust me, great equity valuation models are hard to come by.