Quantitative Methods for Finance and Investment Essay Example for Free

Quantitative Methods for Finance and Investment EssayUniversity of Bristol School of Economics, Finance and Management QUANTITATIVE METHODS FOR pay AND INVESTMENT (EFIMM005) Review Questions Question 1 Concepts a. Dene a stochastic process. Give an example in Finance of a quantity that can be modelled as a stochastic process. b. Dene a stationary stochastic process. c. Consider a stochastic process Yt , t = 1, . ., T . Dene the incomplete autocorrelation function (pacf) associated to this process. d. Explain the dierence between estimator and estimate. e. Let Ut , t = 1, .., T be a mean nothing white noise process. What is the order of pacf at lag 2 for the process Yt = .5Yt1 + Ut ? f. Explain the dierence between the autocovariance function and the sample autocovariance function.Question 2 Application The capital asset pricing model (CAPM) can be written as E(Rjt Rmt , Rf t ) = Rf t + j (Rmt Rf t ), where Rjt is the net make of security j at period t, Rmt is the return on a market portfolio proxy, and Rf t is the return on a risk-free proxy. The coecient j is the CAPM beta for security j. Suppose that you have estimated j by ordinary least squares and found that the estimated value was 1.37 with standard deviation 2.6. based on 3665 observations. a. A city analyst has told you that security j about follows the market, in the sense that security j is equally risky, on average, to the market portfolio. Perform a 5% signicance level test of hypothesis to determine whether data support the analysts claim. b. Are hypotheses tested concerning the value of j or its estimated values?Question 3 Techniques Consider the moving average process Yt = t + 1 t1 + 12 t12 with t T a mean zero white noise process with variance 2 0. t=0 a. take care the mean of Yt . b. Calculate the variance of Yt . c. Calculate the autocovariance function of Yt T . t=a T =120 d. Assume that yt t=1 represents the monthly tons of ice cream sold in the UK between Oct. 2001 and Oct. 2012. What type of colony can the term 12 t12 capture? 1