Quantitative Methods for Finance and Investment
University of Bristol - School of Economics, Finance and Management QUANTITATIVE METHODS FOR FINANCE AND INVESTMENT (EFIMM005) Review Questions Question 1: Concepts a. Define a stochastic process. Give an example in Finance of a quantity that can be modelled as a stochastic process. b. Define a stationary stochastic process. c. Consider a stochastic process {Yt , t = 1, .., T }. Define the partial autocorrelation function (pacf) associated to this process. d. Explain the difference 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 difference 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 + βj (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 coefficient βj is the CAPM beta for security j. Suppose that you have estimated βj 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% significance level test of hypothesis to determine whether data support the analysts claim. b. Are hypotheses tested concerning the value of βj or its estimated values?
Question 3: Techniques Consider the moving average process: Yt = εt + θ1 εt−1 + θ12 εt−12 with {εt }T a mean zero white noise process with variance σ 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
Question 2: Application The capital asset pricing model (CAPM) can be written as E(Rjt |Rmt , Rf t ) = Rf t + βj (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 coefficient βj is the CAPM beta for security j. Suppose that you have estimated βj 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% significance level test of hypothesis to determine whether data support the analysts claim. b. Are hypotheses tested concerning the value of βj or its estimated values?
Question 3: Techniques Consider the moving average process: Yt = εt + θ1 εt−1 + θ12 εt−12 with {εt }T a mean zero white noise process with variance σ 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