I am a relative newbie to stochastic processes, so please bear with me. If we look at standard Brownian motion model:
dS = μdt + σdX
Would I be remotely correct to state that the drift parameter above (μdt) is what can represent systemic component of return that can be described by any of the pricing models out there that relate systematic risk to fair return (CAPM, APT etc) and the last component representing non-systematic risk that is stochastic?
I do realize that the last last component affects the walk path of the price but the central deterministic tendency is still "dominated" by the drift component.or am I completely off here?
I will be grateful for any feedback you guys could offer.
what a terrible day to be able to read
The ability to speak does not make you intelligent
I don't think so. If you take the average of had n assets S_i, then the drift will be the mean drift, but the stochastic component will go to 0 (since in your model the dX represent non-systematic/independent risk). But by definition systematic risk can't be diversified away.
Usually in these models, the drift is related to the beta = cov(asset return, mkt return) / var(mkt return) (and risk free rate), and the stochastic component represents both idiosyncratic risk and systemic risk, perhaps via 2d BM. A great, rigorous reference on models like CAPM is the book "Financial Markets in Continuous-Time" by Rose-Anne Dana and Monique Jeanblanc.
Yes, I concur.
IB VP moment
Can you add more meat to this?
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