” ECON 6070程序 写作、data课程程序 辅导Pset 2, ECON 6070A. Factor models.The data contains all firms traded from 1989-2015. This problem set is due on May18th.1. Read data from cleaned data.csv and FF-5 factors. match the dates from 1989on monthly basis. Drop those firms if there is any missing data.2. For each stock i and time t, consider the following factor regression:Rit = i + ift + it. Estimate the model using the first 80% of data (aka trainingsample )and leave the rest 20% as the testing data.Report the mean and standard deviation of across i = 1, 2, …, N, where N is thetotal number of stocks. Report the average in sample R2 and out of sample R2 over i.3. Consider the Markowitz optimal portfolio w =11(re), where e = (1, 1, …, 1)0is a N 1 vector of ones. Let = 2 and risk free rate r = 1%.Compute and from the training sample based on the factor model: i:= i +iEn[fit] for i = 1, 2, …, N, and V ar(Rt) = BV ar d (ft)B0+diag(21, …, 2N ), where V ar d (ft)is the sample covariance matrix of ft, and 2i:= 1T pPTt=1 2it, it := Rit i ift, andp is the number of factors.Report: (a) the return and volatility of the plug in optimal portfolio w := 1 1( re) in the training sample.(b) the return and volatility of the plug in optimal portfolio w := 1 1( re) inthe testing sample. Do you see any differences between (a) and (b)?B. Simulations and Black-ScholesConsider a law of motion of returns: rt+1 := + rt + t, where = 0.04, = 0.8,and t N(0, 2), = 20%. Initial price P0 = 100. Set r0 = 0.There is an call option with a strike price K and a maturity T = 10.Simulate M = 500 price paths from t = 0 to t = T and obtain 500 simulated priceat maturity P1T, …, P MT.Compute the NPV valuation of the option C(K) := 1M1(1+r)TPMi=1 max(0, PiT K).Report a table of C(K) with K = 100, 120, 140, 160, 180, 200.如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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