I'd like to give here a real interview question that I was posed when I interviewed for a quant role. I will try to recall the context of the question, and the wording of the question as accurately as possible. Please _do not_ ask me about the interviewing institution/ interviewers/ exact nature of role etc. I don't want to cross any lines with regard to confidentiality.Interviewers: Please give the equation for the evolution of a stock price according to the Black-Scholes modelMe: dS/S = mu*dt + sigma * dWInterviewers: [General positive feedback -- this seemed to be the answer they wanted.]Interviewers: Hmmm, so how would you find out the value of mu?I found this second question interesting. Before discussing my response and their reaction etc., I thought it might be fun and more interesting to throw this question out to the forum for initial responses. What are your answers to this latest question?Paul Epstein

I dont mean to sound arrogant but isnt this a question from finance 101 ie basic??

But what is your answer?

One way is to use CAPM.If so,mu = rf + Beta * (rm-rf)(Maybe, the next question would be: How to find Beta? -- There are many ways, many based on running statistics on historical data).

Interesting response, Bhutes. This was not similar to the interviewers' "intended answer." (This is not to say that they would not have liked that answer. I have no idea how they would have responded to the CAPM answer.)I will wait for a few more responses before giving the interviewers' intended answer. Since Senior Member, Player knows that the question is extremely basic, and that I must be stupid for not knowing the blindingly obvious answer, I'm absolutely sure Player's answer will match the answer the interviewers were expecting.Paul Epstein

Usually, the evolution of the stock price process is used to evaluate the price of derivatives, with the stock as the underlying.In that case, mu is never needed to be evaluated."mu" obtained from CAPM, is useful for predicting stock returns themselves, but hardly ever used in the black-scholes context.(Though, the same "mu", as CAPM, (i.e. asset growth rate) is being referred to in the differential equation).In practical use, a risk neutral evolution of the stock price process is assumed (though, it's not real life), and the functional form of BS is:dS/S = r*dt + sigma*dWOne doesn't need to calculate "mu"

mu in the RN measures or the RW measure??

to answer their second question: the starting point is the market price of risk, lambda = (mu - r)/sigma. This price can be derived (and shown to be common for each asset) through an application of risk-neutrality (see page 484, hull5).then a change of measure W_P = W_Q - lambda.t we seedS/S = (mu.dt + sigma.dW_P) = (mu.dt + sigma.(dW_Q - lambda.dt)) = (r.dt + sigma.dW_Q)hence mu = r in the RN (W_Q) world.

A far better question would be why mu (RW measure) isnt included in the BS model..Explaining this in a clear concise manner is far trickier than it seems

All of these are interesting answers, and I am very familiar with all this theory that's been discussed.The reason I opened the thread is that these answers (and my answer) are very different from the interviewers' what-we-wanted-to-hear answer. (Which is not to imply that these other answers would not have impressed the interviewers -- I can't know.)Intended answer: "You can tell mu from the stock dividends."Paul Epstein

QuoteOriginally posted by: playerA far better question would be why mu (RW measure) isnt included in the BS model..Explaining this in a clear concise manner is far trickier than it seemsYou could use mu (RW measure) in the BS model for the evolution of the stock price process.You could calculate the future payoff on a derivative, assuming the above (i.e. RW - mu) BS model.BUT, you would need to discount such payoff, under a risk-weighted discount rate. (which would be a hassle, almost at big as computing the RW-mu).Therefore, for practical use, BS under a RN-mu is used, and the payoff can be discounted at the known risk-neutral rate.While nothing is to be gained by using a RW-mu in BS and accordingly using a RW-discount rate, there is no theoretical argument against using it. If somebody wants to do all that (unnecessary) computation, feel free from any theoretical restrictions. They don't exist.

QuoteOriginally posted by: pauldanepstIntended answer: "You can tell mu from the stock dividends."Paul EpsteinNo. Capital appreciations are an important means of returns on a stock (Dividends only tell a part of the story).mu = return on the entrire stock = Capital Appreciation + Dividend yield

QuoteIntended answer: "You can tell mu from the stock dividends."Can we have an explanation on this?..You're telling me that the real world mu (average return on stock) can be told by dividend??...I'm with bhutes on this...

Player, I'm not telling you that at all. What I'm telling is that the interviewers said something like: "Actually, the stock pays a dividend, and these dividends give you the value of mu."The whole point of my opening of the thread is that I was taken aback by the interviewers' intended answer. Admittedly, I didn't record the interviewers' words. But my memory for this type of thing is excellent, and they certainly didn't mention capital appreciation.Paul Epstein

But did they give an explanation.....???even interviewers get things wrong sometimes....