According to the National Bureau of Economic Research (NBER), since 1945 to 2009 (extremes included) there has been approximately 11 business cycles. Assume that on average contractions (c) last 10.24 months while expansions last 53.76 months and define normal times (n) as 60% of the expansion months, characterizing the residual months as booms (b). Furthermore, suppose the expected return on the US market conditional on contractions to be -17%, i.e. um(c) = -0.17, during normal times to be 1%, and overall to be 8%. Characterize both analytically and graphically: A The probability distribution function (pdf) of the market return m B The cumulative distribution function (cdf) of the market return m hint: first compute the probabilities of the states of the world, then check if you have all the associated expected returns (if not calculate the missing one(s)), finally refer back to the notes where we introduced the pdf and cdf for discrete random returns According to the National Bureau of Economic Research (NBER), since 1945 to 2009 (extremes included) there has been approximately 11 business cycles. Assume that on average contractions (c) last 10.24 months while expansions last 53.76 months and define normal times (n) as 60% of the expansion months, characterizing the residual months as booms (b). Furthermore, suppose the expected return on the US market conditional on contractions to be -17%, i.e. um(c) = -0.17, during normal times to be 1%, and overall to be 8%. Characterize both analytically and graphically: A The probability distribution function (pdf) of the market return m B The cumulative distribution function (cdf) of the market return m hint: first compute the probabilities of the states of the world, then check if you have all the associated expected returns (if not calculate the missing one(s)), finally refer back to the notes where we introduced the pdf and cdf for discrete random returns