Quantitative Methods for Finance and Investment Essay

University of Bristol – School of Economics, Finance and Management QUANTITATIVE METHODS FOR FINANCE AND INVESTMENT (EFIMM005) Review Questions Question 1: Concepts a. Deï ¬ ne a stochastic process. Give an example in Finance of a quantity that can be modelled as a stochastic process. b. Deï ¬ ne a stationary stochastic process. c. Consider a stochastic process {Yt , t = 1, .., T }. Deï ¬ ne the partial autocorrelation function (pacf) associated to this process. d. Explain the diï ¬â‚¬erence between estimator and estimate. e. Let {Ut , t = 1, .., T } be a mean zero white noise process. What is the value of pacf at lag 2 for the process Yt = .5Yt−1 + Ut ? f. Explain the diï ¬â‚¬erence 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 + ÃŽ ²j (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 coeï ¬Æ'cient ÃŽ ²j is the CAPM beta for security j. Suppose that you have estimated ÃŽ ²j 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 closely follows the market, in the sense that security j is equally risky, on average, to the market portfolio. Perform a 5% signiï ¬ cance level test of hypothesis to determine whether data support the analysts claim. b. Are hypotheses tested concerning the value of ÃŽ ²j or its estimated values? Question 3: Techniques Consider the moving average process: Yt = ÃŽ µt + ÃŽ ¸1 ÃŽ µt−1 + ÃŽ ¸12 ÃŽ µt−12 with {ÃŽ µt }T a mean zero white noise process with variance ÏÆ' 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 ÃŽ ¸12 ÃŽ µt−12 capture? 1