Quantitative Methods for Finance and Investment Essay

University of Bristol School of Economics, pay and Management QUANTITATIVE METHODS FOR FINANCE AND investment funds (EFIMM005) Review Questions Question 1 Concepts a. Dene a stochastic process. Give an example in Finance of a quantity that net be modelled as a stochastic process. b. Dene a unmoving stochastic process. c. Consider a stochastic process Yt , t = 1, .., T . Dene the partial autocorrelation operate (pacf) associated to this process. d. Explain the dierence between estimator and estimate. e. Let Ut , t = 1, .., T be a incriminate zero sporty noise process. What is the value of pacf at lag 2 for the process Yt = .5Yt1 + Ut ? f. Explain the dierence between the autoco naval division function and the sample autocovariance function.Question 2 Application The capital asset determine model (CAPM) can be written as E(Rjt Rmt , Rf t ) = Rf t + j (Rmt Rf t ), where Rjt is the net return 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 of import for security j. Suppose that you have estimated j by ordinary least squares and found that the estimated value was 1.37 with modular deviation 2.6. based on 3665 observations. a. A city analyst has told you that security j closely follows the market, in the sense that security j is equally risky, on average, to the market portfolio. Perform a 5% signicance take 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. Calculate 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 dependence can the term 12 t12 capture? 1