Consider the following simple model for stock prices: Pt = P* +It P* + 1 +1 With probability 1 (buyer initiated) It IID -1 With probability (seller initiated) Here, P.;* is the fundamental value of the security, and s is the bid-ask spread. (3) a) Assume that P = P* is fixed through time. Derive expressions for the variance, autocovariance, and autocorrelation of successive stock price changes. [6 marks] b) Now assume P* is serially uncorrelated, and independent of It, and has increments with variance expressed as o2(AP*). Derive a new set of expressions for the variance, autocovariance, and auto- correlation of successive stock price changes. [6 marks] c) What is this effect known as? Explain whether (and why) this might lead you to erroneous conclusions when estimating whether stock prices are weak-form efficient. [8 marks] Consider the following simple model for stock prices: Pt = P* +It P* + 1 +1 With probability 1 (buyer initiated) It IID -1 With probability (seller initiated) Here, P.;* is the fundamental value of the security, and s is the bid-ask spread. (3) a) Assume that P = P* is fixed through time. Derive expressions for the variance, autocovariance, and autocorrelation of successive stock price changes. [6 marks] b) Now assume P* is serially uncorrelated, and independent of It, and has increments with variance expressed as o2(AP*). Derive a new set of expressions for the variance, autocovariance, and auto- correlation of successive stock price changes. [6 marks] c) What is this effect known as? Explain whether (and why) this might lead you to erroneous conclusions when estimating whether stock prices are weak-form efficient. [8 marks]