Essay About Variance C And Risk-Return Trade-Offs

Econ 424
ECON 424SPRING 2015Lab#2  Lei, Tao #1263559Exercises1. X is normally distributed random variable, with mean 0.05, variance c(0.10)2.Pr(X>0.10): 1-pnorm(0.10, 0.05, 0.10)= 0.3085Pr(XPr(-0.051% quantile: qnorm (0.01, 0.05, 0.10)= -0.18265% quantile: qnorm (0.05, 0.05, 0.10)= -0.114595% quantile: qnorm (0.95, 0.05, 0.10)= 0.214599% quantile: qnorm (0.99, 0.05, 0.10)= 0.28262. X ~ N(0.05, (0.10)2) and Y ~ N(0.025, (0.05)2).(a) Plot the normal graph[pic 1](b) Comment on risk-return trade-offs for the two stocks.[pic 2]According to the graph, the Microsoft stocks has a higher mean and a higher standard deviation. This tells us that Microsoft stocks possibly has a higher expected return, and at the same time, higher risk. 3. Value at Risk Calculations with simple monthly return(a) 1% quantile:w0 = 100000w0*qnorm (0.01, 0.04, 0.09) = -16937.13(b) 5% quantile: w0 = 100000w0*qnorm (0.05, 0.04, 0.09) = -10803.68There’s 1% probability that there’ll be a loss of $16,937 next month, and there’s 5% probability that the loss will be $10,803 next month from the initial investment. 4. Value at Risk Calculations with cc return(a) Using Excel functions, 1% quantile: $-15,580.46.     5% quantile: $-10,240.55. When cc return is normally distributed, there’s 1% probability that there’ll be a loss of $15,580 next month; there’s 5% probability that there’ll be a loss of $10,241. (b) If annually invest with cc returns, we just times the mean and the standard deviation with 12 months. Mean= 0.04*12= 0.48Standard deviation= [pic 3]Apply the two changes in Excel functions, 1% quantile: -$21,751.895% quantile: -$3,228.34.There’s 1% probability that $21,752 or more next year from our initial investment, 5% probability that the loss will be $3,228.5. Chi-square and student’s t-distribution Using r-studio, code as follows:x.vals = seq(0, 20, length=100)ub = max( c(dchisq(0, df=c(1,2,5,10)), dnorm(0)) )plot(x.vals, dchisq(x.vals, df=1), type=”l”, lwd=2, ylim=c(0,1), ylab=”pdf”, xlab=”x”)