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Stock behavior random variable
- Thread starter simplekid
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If we were to model random behavior of stock, whether the stock generates a positive daily return of 10%, which random variable would best depict this phenomenon? I was thinking a uniform random variable (continuous)?
What are your thoughts?
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Is this a mathematical exercise or are you trying to model the 'real world'. If a mathematical exercise then first, you would need to answer a couple of questions about the return. For example, are you saying that the mean (average) return of the stock is 10%? Is there a given standard deviation for the value or is this just a one parameter random variable? In other words, describe the problem better.My thought is that it may be a continuous random variable? As the return on stock may yield a percentage which is not countable and thus not discrete. However, could it be a Bernoulli random variable? Because there are two outcomes, one is that the stock gives a return in excess of 10% in a given single day (which is a success) or that it doesn't produce a return in excess of 10% which is a failure. Also, these events are mutually exclusive as if one happens, the other doesn't. Am I on the right track?
If you are trying to model the real world, then you probably have some reading to do about the myriad indicators used in technical modeling of the financial market, learning about moving averages, moving average convergence divergence (MACD), relative strength index (RSI), directional movement indicator (DMI), Bollinger Bands, and quite a bit more.
Yes, I think the Bernoulli distribution would be most appropriate. Yes/No type questions are typically binomial distributions and the Bernoulli distribution is a binomial distribution for a single trial, i.e. in a given day.The question just merely asks, if you were to model random behaviour of stock, whether or not it gives a return in excess of 10% in a given single day, what random variable would be the most appropriate for this phenomenon.
The question also asks, if you were to use the binomial distribution to explain this phenomenon for trade activity over 1 year (only including weekdays), then what assumptions would you have to make and are these reasonable?
What im thinking is that in order for this to be a binomial distribution, the assumptions would be that n = 260 (260 weekdays) and that a p success occurs when the return of a stock exceeds 10% and a failure occurs when this does not happen and rather it is less than 10%. I would say that the binomial distribution is not reasonable to use due to the large value of n and when computing specific values, our actual equation would contain huge numbers. Am I on the right track with this?
My approach: The binomial distribution for n=1 is the Bernoulli distribution. As you said, you are being asked to consider the period for 1 year [a nominal 52 * 5 = 260 days], i.e. n=260. Now, with modern moderately sophisticated computers (handheld or otherwise), handling the values coming out of this distribution is no problem although it would be somewhat painful doing it by hand.
However, from there, the only other variable we have at our disposal is p. But just what is this p? The simplest answer is that we are up with probability p and not up with probability q=1-p. Can we make a 'reasonable guess' for a value p? Even if we could, is that something we could trade on?
You might have other meanings for p, i.e. the probability that you were up that day. But this would lead to even further assumptions which, on the face of them might seem unreasonable, i.e. each 'up' would have to be the same as every other 'up and each individual down would have to be the same as an individual up otherwise you get into something other than a binomial distribution. Also, from that binomial distribution, you would have to have more 'ups' than 'downs' to be up overall which is totally different than the simple binomial distribution for trading.