# session 9a

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Session 9a. 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 - PowerPoint PPT Presentation

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Session 9aDecision Models -- Prof. Juran1Decision Models -- Prof. Juran2OverviewFinance Simulation ModelsForecastingRetirement PlanningButterfly StrategyRisk ManagementIntroduction to VaRCurrency RiskUsing Historical Data in SimulationsParametric ApproachResampling Approach Decision Models -- Prof. Juran2Decision Models -- Prof. Juran3Example 1: Retirement PlanningAmanda 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.

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Decision Models -- Prof. Juran4Decision Models -- Prof. Juran5The 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 Amandas simulated investment performance either with cell F5 (simply =D35, the final amount in Amandas 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 didnt). 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. Juran5Decision Models -- Prof. Juran6

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It looks like Amanda has about a 48% chance of meeting her goal of \$1 million in 30 years.Decision Models -- Prof. Juran12Decision Models -- Prof. Juran13Example 2: ButterflyThe 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. Juran13Decision Models -- Prof. Juran14Avant 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 at 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. Juran14Decision Models -- Prof. Juran15We are considering investing \$100,000 in the S&J index over the next month, based on our estimation that the S&Js 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. Juran15Decision Models -- Prof. Juran16

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Put in quantities bought and sold, according to the analysts proposalDecision Models -- Prof. Juran17Decision Models -- Prof. Juran18

Figure out how much cash is going out, in D10:D17Decision Models -- Prof. Juran18Decision Models -- Prof. Juran19

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. Juran19Decision Models -- Prof. Juran20

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. Juran20Decision Models -- Prof. Juran21

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. Juran21Decision Models -- Prof. Juran22

In B19:B20, calculate how many shares of the index are being purchased.Decision Models -- Prof. Juran22Decision Models -- Prof. Juran23

In E10:E17, calculate the amount of cash coming back in at the end of the month.Decision Models -- Prof. Juran23Decision Models -- Prof. Juran24

In D2:F2, calculate the P/L from the index.Decision Models -- Prof. Juran24Decision Models -- Prof. Juran25

In D3:F3, calculate the P/L from the options.Decision Models -- Prof. Juran25Decision Models -- Prof. Juran26In D4:F4, calculate the total P/L.

Decision Models -- Prof. Juran26Decision Models -- Prof. Juran27In F6 calculate the difference between the two strategies (with and without the options).

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An old Excel trick:DataTableDecision Models -- Prof. Juran33Decision Models -- Prof. Juran34Select A24:B55, then Data Table

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Decision Models -- Prof. Juran36Decision Models -- Prof. Juran373. Evaluation of Hedging StrategiesIt 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. Juran37Decision Models -- Prof. Juran38Specifically, 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. Juran38Decision Models -- Prof. Juran39Unfortunately, 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. Juran39Decision Models -- Prof. Juran40(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&Ks revenue from these three countries over the next 12 months? What is the probability that C&Ks 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&Ks revenue from these three countries over the next 12 months? What is the probability that C&Ks revenue will be less than \$2,087,700?Decision Models -- Prof. Juran40Decision Models -- Prof. Juran41

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Converting prices into returns:Decision Models -- Prof. Juran43Decision Models -- Prof. Juran44Here 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) :

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Decision Models -- Prof. Juran45Decision Models -- Prof. Juran46Distribution fitting: Checking to see which Crystal Ball distribution be