Econ 393 Assignment 1

| August 14, 2017

I.ISP500 & XOM (Sep 16,2013 – Sep 14,2014)(30 pt)1. Download the last year daily close prices for SP500 index from yahoo financea. Download the last year daily close prices for ExxonMobil (XOM) from yahoo financea. Import daily close values into excel and computea. Log returnb. Expected returnc. Variance – mean zero theoretical formulad. Standard Deviatione. Covariance – theoretical formula and the COVAR excel functioni. Comment on the covariance you computedNote: When calculating above statistics, make sure your M (# of variables) is consistent with # of returnsi.e. if you have 10 daily close prices you will have 9 daily returnsIIUtility analysis and risk attitudesII.IA gamble based on a fair coin toss which pays $45 if the coin lands heads and $32 if the coinlands tails. ( fair coin toss i.e. probability of heads is 50% = probability of tails is 50%)(30 pt)1. Calculate the Expected value of this gamble2. Calculate Expected utility functiona. u(w) = 8w classify the risk attitudeb. u(w) = ln(w) classify the risk attitudec. u(w) = 2w2 classify the risk attitudeII.IIA risk averse agent, whose utility is given by u(x) = ln x and wealth is $50, 000 is faced with apotential loss of $10, 000 with a probability of p = 0.1. What is the maximum premium they would bewilling to pay to protect themselves against this loss? ( i.e. probability of earning 0 is 0.9 and probabilityof losing 10,000 is 0.1)(25 pt)1. Find expected value2. Find the expected utility (of wealth)3. Find the maximum premium to equate the two???? ? ??? = ??[???????]4. Compare the maximum risk premium (y) to the expected loss ( wealth – expected value)II.IIICalculate and classify the following utility functions according to the absolute and relative riskaversion(15 pt)1. u(w) =ln(w)2. u(w) = w-bw2

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