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## Session 9a

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**Overview**• Finance Simulation Models • Forecasting • Retirement Planning • Butterfly Strategy • Using Historical Data in Simulations • Parametric Approach • Resampling Approach • Risk Management • Introduction to VaR • Currency Risk • Securities Pricing • Black-Scholes • Electricity Option • Miscellaneous • Intro to Retailer • Dynamic vs. Static • Monte Carlo vs. Latin Hypercube • Review of Binomial Decision Models -- Prof. Juran**Example 1: Retirement Planning**Amanda has 30 years to save for her retirement. At the beginning of each year, she puts $5000 into her retirement account. At any point in time, all of Amanda's retirement funds are tied up in the stock market. Suppose the annual return on stocks follows a normal distribution with mean 12% and standard deviation 25%. What is the probability that at the end of 30 years, Amanda will have reached her goal of having $1,000,000 for retirement? Assume that if Amanda reaches her goal before 30 years, she will stop investing. Decision Models -- Prof. Juran**The annual investment activities (columns A-D, beginning in**row 5) actually extend down to row 35, to include 30 years of simulated returns. The range C6:C35 will be random numbers, generated by Crystal Ball. We could track Amanda’s simulated investment performance either with cell F5 (simply =D35, the final amount in Amanda’s retirement account), or with F4 (the maximum amount over 30 years). Using F4 allows us to assume that she would stop investing if she ever reached $1,000,000 at any time during the 30 years, which is the assumption given in the problem statement. Cell H1 is either 1 (she made it to $1 million) or 0 (she didn’t). Over many trials, the average of this cell will be out estimate of the probability that Amanda does accumulate $1 million. This will be a Crystal Ball forecast cell. Decision Models -- Prof. Juran**It looks like Amanda has about a 52% chance of meeting her**goal of $1 million in 30 years. Decision Models -- Prof. Juran**Example 2: Butterfly**The S&J index is a measure of overall equity value in the software publishing industry. Shares of a “tracking” mutual fund (a fund that tracks this index) are available from Avant Garde Investments, Inc. Shares in the mutual fund are currently available at a price of $605. Decision Models -- Prof. Juran**Avant Garde also sells 1**- month call options on the S&J index, with current prices as follows: Strike Option Bid Price Option Ask Price 580 $25.54 $25.64 585 $22.84 $22.94 590 $20.33 $20.43 595 $18.01 $18.11 600 $15 .79 $15.89 605 $13.95 $14.05 610 $12.09 $12.19 615 $10.60 $10.70 (A call option gives its holder the right to purchase one share on the expiration date at the strike price. For example, if we buy one call option at the 600 strike price, and the S&J is a t 620 on the expiration date, we can exercise the option and buy one share at 600 and immediately sell it for a $20 gross profit. The net profit would be $20.00 – $15.89 = $4.11, which is a ($4.11 / $15.89) = 25.9% gain.) Decision Models -- Prof. Juran**We are considering investing $100,000 in the S&J index over**the next month, based on our estimation that the S&J’s level one month from now is a log-normally distributed random variable with a mean of 605 and a one month standard deviation of 30. An analyst proposes that in addition to investing the $100,000 in the S&J index, we take some positions in call options. He suggests selling 200 options contracts (1 option contract is an option to purchase 100 shares) at the 605 strike price, and buying 100 option contracts each of the 600 and 610 strike prices. What do you think of this scheme? Does it have any advantage over simply investing all the money in the index? Assume that there are no transaction costs. Decision Models -- Prof. Juran**Put in quantities bought and sold, according to the**analyst’s proposal Decision Models -- Prof. Juran**Figure out how much cash is going out, in D10:D17**Decision Models -- Prof. Juran**Cell A5 will be an assumption; the ending price of the**option in one month. Put cell references to A5 into H10:H17. Decision Models -- Prof. Juran**In I10:I17 enter a formula to calculate the payoff for**options bought, as a function of the random ending price of the index. Decision Models -- Prof. Juran**Similarly, in J10:J17 enter a formula to calculate the**payoff for options sold, as a function of the random ending price of the index. Decision Models -- Prof. Juran**In B19:B20, calculate how many shares of the index are being**purchased. Decision Models -- Prof. Juran**In E10:E17, calculate the amount of cash coming back in at**the end of the month. Decision Models -- Prof. Juran**In D2:F2, calculate the P/L from the index.**Decision Models -- Prof. Juran**In D3:F3, calculate the P/L from the options.**Decision Models -- Prof. Juran**In D4:F4, calculate the total P/L.**Decision Models -- Prof. Juran**In F6 calculate the difference between the two strategies**(with and without the options). Decision Models -- Prof. Juran**An old Excel trick:**DataTable Decision Models -- Prof. Juran**Select A24:B55, then Data - Table**Decision Models -- Prof. Juran**3. Evaluation of Hedging Strategies**It is July 1, 2002, and international entrepreneurs Clifford & Kearns (C&K) are concerned about volatility in the exchange rates between U.S. dollars and certain European currencies. C&K have incurred costs in dollars to develop, produce, and distribute merchandise to Norway, Switzerland, and Great Britain, for which they expect to realize revenues in 12 months. Decision Models -- Prof. Juran**Specifically, they expect to earn 1 million units each of**British pounds, Swiss francs, and Norwegian kroner. Based on current exchange rates, this should result in $2,337,700 in revenue (see current rates below). Decision Models -- Prof. Juran**Unfortunately, it is possible that one or more of these**currencies could devalue against the dollar in that one year, causing C&K to realize a smaller total revenue (in dollars) than expected. C&K has turned to their investment bank, Nuccio, Noto, and Rizzi (NNR) for advice. NNR has recommended buying 1.3 million 1-year Euro put options with a strike price of $0.98, for $0.0432 each. NNR claims that this hedging strategy will substantially decrease the risk of a large loss due to exchange rate fluctuations. Decision Models -- Prof. Juran**(a) Create a simulation model to study the “unhedged”**distribution of revenue for C&K, using the historical exchange rate data in Exhibit 2. Make a histogram and report summary statistics. What is the 5% value at risk (VAR) for C&K’s revenue from these three countries over the next 12 months? What is the probability that C&K’s revenue will be less than $2,087,700 (i.e., a $250,000 loss or worse)? (b) Create a simulation model to study the “hedged” distribution of revenue for C&K. Make a histogram and report summary statistics with the policy recommended by NNR. What is the 5% VAR for C&K’s revenue from these three countries over the next 12 months? What is the probability that C&K’s revenue will be less than $2,087,700? Decision Models -- Prof. Juran**Here are summary statistics for each of the currencies’**returns against the dollar, including a t-test to see if the means are significantly different from zero (they are not) : Decision Models -- Prof. Juran