 qinnanjoshua
Topic Author
Posts: 1
Joined: September 2nd, 2013, 2:42 pm

### A probability question

Two analysts make prediction of the movement of a stock separately. Analyst A have an accuracy of $p_1$, which means his prediction is correct at the probability of $p_1$, while analyst B have an accuracy of $p_2$. Now given that both analysts predict the stock price will rise tomorrow, what is the probability for the stock price to rise tomorrow? What if A predicts rising and B predicts falling? (Assuming the stock either rise or fall but won't stay the same tomorrow.) QuantOrDie
Posts: 36
Joined: June 2nd, 2011, 2:23 am

### A probability question

Insufficient information. For example, it could be that analyst 1 is from Goldman and analyst 2 is from UBS. The UBS analyst has stolen the Goldman excel model which makes these predictions, so the predictions are the same except for the 20% of the time that the UBS analyst gets the sign wrong on the model's output. In this case the probability is p_1 because you gain no additional information from the second prediction.On the other hand, if we assume that the accuracy of the analysts' predictions are independent then you get a trivial probability question - the probability is simply the conditional probability of two independent events given that they either both happen or both do not, i.e. p_1 * p_2 / (p_1 * p_2 + (1 - p_1) * (1 - p_2))  