1. The Standard&Poor\'s 500 (S&P 500) is a stock market index based on the marke
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Question
1. The Standard&Poor's 500 (S&P 500) is a stock market index based on the market capitalizations of 500 leading companies publicly traded in the U.S. stock market. If the monthly return on the S&P 500 is positive, there is a 61% chance that it will be positive in the subsequent month, and a 39% chance that it will be negative. If the monthly return is negative, it will be positive with probability 0.57.
(a) Assume this problem can be modeled as a Markov Chain. Define the states and the onestep transition probability matrix.
(b) Assume that the monthly return in October 2016 is negative. What is the probability that the monthly return in December 2016 is positive?
Explanation / Answer
Ans:
a) Transition probability matrix(one step),P=
b)Intial distribution in october a0=[0 1]
Probability distribution after two months(to time steps)
a2=a0*P2
first find out two step transition matrix P2=P*P
a2=[0*0.5944+1*0.5928 0*0.4056+1*0.4072]
a2=[0.5928 0.4072]
Hence,probability that the monthly return in december 2016 is positive is 0.5928.
positive negative positive 0.61 0.39 negative 0.57 0.43Related Questions
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