Download Engineering Economy – Stock Price Dynamics Homework | ISYE 6225 and more Assignments Systems Engineering in PDF only on Docsity! Stock Price Dynamics Homework 1. Let v1, v2, . . . , vn be positive numbers. The arithmetic mean and geometric mean of these numbers are, respectively, vA := ∑n i=1 vi n and vG := ( n∏ i=1 vi )1/n . (a) If r1, r2, . . . , rn are rates of return of a stock in each of n periods, the arithmetic and geometric mean rates of return are, respectively, rA := ∑n i=1 ri n and rG := ( n∏ i=1 (1 + ri) )1/n − 1. i. Suppose 40 is invested in the stock. During the first year the investment increases to 60 and during the second year it decreases to 48. Determine the arithmetic and geometric mean rates of return over the two years. ii. Suppose 100 is invested in the stock. During the first year the investment in- creases to 150 and during the second year it decreases to 100. Determine the arithmetic and geometric mean rates of return over the two years. (b) Which mean is more appropriate to describe investment performance? 2. A coin is flipped: if it comes up heads you win 0.25 and if it comes up tails you lose 0.25. The probability of the coin coming up heads is 0.60. (a) Determine the mean and variance of your earnings at the end of the game if you play the game 10, 100 and 1 million times. (b) Determine the probability your earnings will exceed 49,000 if you play the game 1 million times. 3. A stock price is governed by Geometric Brownian Motion with µ = 0.20 and σ = 0.40. The initial price S(0) = 1. Evaluate the following quantities: (a) E[lnS(1)] and the standard deviation of lnS(1). (b) E[S(1)] and the standard deviation of S(1). (c) The probability that S(0.25) ≤ 1.40. (d) The probability that the maximum value of the stock price over the next 3 months will not exceed 1.40. (e) The probability that it will take longer than 1 year for the stock price to double in value. (f) The probability an investor will make money on the following strategy: purchase 1 unit of the stock at time 0 and sell the stock at the first point in time at which either the price doubles or loses 50% of its initial value. 1
