1. Spreadsheet Demonstration Investment Simulation

2. 2 Investment simulation Winston 12.4  Mary Higgins is a freelance writer with enough spare time on her hands to play the stock market fairly seriously. Each morning she observes the change in stock price of a particular stock and decides whether to buy or sell, and if so, how many shares to buy or sell. We will assume that on day 1, she has $100,000 cash to invest and that she spends part of this to buy her first 500 shares of the stock. From that point on, she follows a fairly simple “buy low, sell high” strategy. Specifically, if the price has increased three days in a row, she sells 25% of her shares of the stock. If the price has increased two days in a

3. 3 Investment simulation Winston 12.4 (cont’) row (but not three), she sells 10% of her shares. In the other direction, if the price has decreased three days in a row, she buys 25% more shares, whereas if the price has decreased only two days in a row, she buys 10% more shares. She wants to simulate how this strategy will do over a period of 75 trading days.

4. 4 Investment simulation Winston 12.4 (cont’)  Price change distributions for investment example ProbabilitiesFollowing Price ChangeDecreaseIncreaseNo Change -$20.200.100.15 -$10.250.150.20 $00.30 +$10.150.250.20 +$20.100.200.15

5. 5 Stock market investment simulation Basic problem  Investor wants to develop buy/sell strategies for trading in the stock market  Stock prices vary randomly from day to day  We’ll simulate 75 trading days to see how the strategy works  Investor wants to develop buy/sell strategies for trading in the stock market  Stock prices vary randomly from day to day  We’ll simulate 75 trading days to see how the strategy works

6. 6 Stock market investment simulation Uncertainties  Stock price change each day is random  Model chosen uses a different discrete distribution depending on whether previous change is negative, zero, or positive  Probabilities used tend to make negative follow negative, positive follow positive  Other types of dependence could be used  Stock price change each day is random  Model chosen uses a different discrete distribution depending on whether previous change is negative, zero, or positive  Probabilities used tend to make negative follow negative, positive follow positive  Other types of dependence could be used

7. 7 Stock market investment simulation Buy/sell strategies  This model illustrates a buy low/sell high strategy  Sell 10% following 2 straight up days, sell 25% following 3 straight up days  Buy 10% more following 2 straight down days, buy 25% more following 3 straight down days  Any other strategies could be modeled  This model illustrates a buy low/sell high strategy  Sell 10% following 2 straight up days, sell 25% following 3 straight up days  Buy 10% more following 2 straight down days, buy 25% more following 3 straight down days  Any other strategies could be modeled

8. 8 Stock market investment simulation Initial conditions  Investor starts with $100,000 and no stock  Buys 500 shares at the end of day 1 at the going price  Investor starts with $100,000 and no stock  Buys 500 shares at the end of day 1 at the going price

9. 9 Developing the spreadsheet model (See Excel “Step 1” sheet)  Step 1: Enter all inputs, including:  Initial cash  Probability distributions (with cumulative probabilities) of price changes  Step 1: Enter all inputs, including:  Initial cash  Probability distributions (with cumulative probabilities) of price changes

10. 10 Developing the spreadsheet model (See Excel “Steps 2-5” sheet)  Step 2: Enter day numbers (1 to 75)  Step 3: Generate a random number (with RAND) for each of the days  Steps 4, 5: Generate random changes in price, and the corresponding prices, using the VLOOKUP function  Assume day 1 follows a “no price change” day  Step 2: Enter day numbers (1 to 75)  Step 3: Generate a random number (with RAND) for each of the days  Steps 4, 5: Generate random changes in price, and the corresponding prices, using the VLOOKUP function  Assume day 1 follows a “no price change” day

11. 11 Developing the spreadsheet model (See Excel “Steps 6-8” sheet)  Steps 6-8: Based on buy/sell strategies, calculate:  How many shares are owned at the beginning of each day  How many shares are bought each day  How many shares are sold each day  How many shares are owned at the end of each day  Steps 6-8: Based on buy/sell strategies, calculate:  How many shares are owned at the beginning of each day  How many shares are bought each day  How many shares are sold each day  How many shares are owned at the end of each day

12. 12 Developing the spreadsheet model (See Excel “Steps 9-11” sheet)  Steps 9-11: For each day calculate:  The investor’s cash at the beginning of the day  Cash inflow or outflow from selling or buying shares  Cash after transactions  Current worth of shares owned  Cumulative gain or loss (relative to initial cash)  Steps 9-11: For each day calculate:  The investor’s cash at the beginning of the day  Cash inflow or outflow from selling or buying shares  Cash after transactions  Current worth of shares owned  Cumulative gain or loss (relative to initial cash)

13. 13 Developing the spreadsheet model (See Excel “Steps 12,13” sheet)  Step 12: Create a data table to replicate the simulation  Keep track of the cumulative gain or loss after 75 days  Step 13: Calculate summary measures from replications, including:  Average of gain/loss after 75 days  Fraction of replications investor ends up ahead  Step 12: Create a data table to replicate the simulation  Keep track of the cumulative gain or loss after 75 days  Step 13: Calculate summary measures from replications, including:  Average of gain/loss after 75 days  Fraction of replications investor ends up ahead

14. 14 Developing the spreadsheet model (See Excel “TimeSeries” sheet)  Based on a single replication, create a time series graph of the investor’s cumulative gain/loss  This is “live,” so press the F9 key to see how many random patterns are possible  Based on a single replication, create a time series graph of the investor’s cumulative gain/loss  This is “live,” so press the F9 key to see how many random patterns are possible

15. 15 Developing the spreadsheet model (See Excel “Histogram” sheet)  Create a frequency table and corresponding histogram of cumulative gain/loss after 75 days  These are based on data table of replications  This is also “live,” so press the F9 key to see how the fortunes of the investor can depend on randomness  Create a frequency table and corresponding histogram of cumulative gain/loss after 75 days  These are based on data table of replications  This is also “live,” so press the F9 key to see how the fortunes of the investor can depend on randomness

16. 16 Stock market investment simulation Other buy/sell strategies  The histogram shows that investor is ahead more often than not  Is this due to a good strategy or just luck?  Try building in other strategies (buy high/sell low??) and see whether they do as well  The histogram shows that investor is ahead more often than not  Is this due to a good strategy or just luck?  Try building in other strategies (buy high/sell low??) and see whether they do as well