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PROBLEM SET 1 Solution

Problem 1 (10)




Let rt be a log return. Suppose that r1; r2; : : : are i.i.d. N( ; 2).




a) What is the distribution of rt(3) = rt + rt1 + rt2 .




b) What is the covariance between rt(k) and rt(k + l) for some integer t; k and l.







Problem 2 (20)




Suppose you bought an asset at initial price P0 = 20 and the asset price follows a lognormal geometric random walk where




Pt = P0 exp(rt + rt1 + + r1)




and ri are i.i.d. N(0:03; 0:0052).




Simulate the annual price of the asset for the next 10 years i.e. (P1; P2; : : : ; P10) and plot it against time.



Simulate P10 2000 times and estimated the expected value i.e E[P10].



Compare your simulated result with the actual expected value of P10 .












Problem 3 (10)




Suppose in a normal plot that the sample quantiles are plotted on the vertical axis, rather than on the horizontal axis as in our lectures.




What is the interpretation of a convex pattern?



What is the interpretation of a concave pattern?



What is the interpretation of a convex-concave pattern?



What is the interpretation of a concave-convex pattern?



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Problem 4 (20)









































































Problem 5 (20)

















































Problem 6 (20)























































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