Project 2 Questions Summer 2023

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Florida State University *

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5935

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Finance

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Feb 20, 2024

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FIN 5935 – PROJECT 2 (12 Questions) SUMMER 2023 1. The Excel file Stock Price Data contains monthly price data for eight (8) stocks. a. Compute the monthly returns (using continuous returns) for each of the stocks. b. Compute the Matrix of Excess Returns for these stocks. c. Use the Matrix of Excess Returns to compute the Sample Variance-Covariance Matrix for these stocks. d. Use the Sample Variance-Covariance Matrix for these stocks to compute the Global Minimum Variance Portfolio (GMVP). e. Compute the expected return and standard deviation for this GMVP. 2. The Excel file Portfolio Bond Immunization Data contains information about three bonds. Coupons are paid annually. Use this data to: a. Compute the amount to be invested to meet the future liability noted in the data. This future liability is due in 12 years. b. Find a combination of Bond 1 and Bond 2 having a target duration of 12 years. c. Find a combination of Bond 1 and Bond 3 having a target duration of 12 years. d. Perform an analysis using a data table and an accompanying graph to determine which of the following options (i.e., a portfolio consisting of Bond 1 and Bond 2, a portfolio consisting of Bond 1 and Bond 3, or a portfolio consisting of Bond 1) would be preferred to attempt to immunize this obligation. i. Construct a data table by varying the yield to maturity that shows the value of each option at the end of 12 years. Use yield to maturity values ranging from 0% to 15% in 1% increments. ii. Based on your data table, construct a graph that demonstrates the performance of these 3 options. iii. Analyze each option’s performance in attempting to achieve immunization. 3. The Excel file Portfolio Manager Annual Returns contains returns realized last year by clients of two different portfolio managers. Based on this information what is the probability that Portfolio Manager A’s clients will realize a higher annual return in the upcoming year than Portfolio Manager B’s clients ? Use a resampling procedure with 80 simulations.
4. A stock is selling today for $125. The stock has an annual volatility of 45 percent and the annual T-bill rate is 12 percent. a. Calculate the fair price for a 15 month European call option with an exercise price of $118. b. Calculate how much the current stock price would need to change for the purchaser of the call option to break even in 15 months. c. Calculate the fair price for a 15 month European put option with an exercise price of $118. d. Calculate how much the current stock price would need to change for the purchaser of the put option to break even in 15 months. e. Calculate the level of volatility that would make the $118 call option sell for $30. f. Calculate the level of volatility that would make the $118 put option sell for $25. 5. On July 1, 2021 you purchased an option which will allow you to sell a commercial building on June 25, 2025 for $30 million. Your current estimate of the value of the building is $28 million. The annual volatility for the change in the building’s value is 25% and the annual T-bill rate is 8%. a. Calculate the value of the option to sell the building. 6. The Excel file Monthly Return Data contains return data for several stocks and the S&P 500. Use this data to determine the probability that INTC’s monthly return is likely to exceed MSFT’s monthly return. Run 75 simulations to determine this probability. 7. Demand for Coca Cola at a local restaurant is 125 bottles per day with a standard deviation of 10 bottles per day. a. Compute the probability that demand will exceed 5100 bottles during the next 40 days. b. Compute the number of bottles the restaurant should stock to have at most a 8% chance of running out over the next 40 days. 8. A stock sells today for $65. The price of the stock in a year is expected to be $70. The annual volatility of the stock is 30%. Assume stock prices follow a lognormal probability distribution. a. Calculate the probability that in four years the stock will sell for more than $80. b. Calculate the probability that in four years the stock will sell for less than $60. c. Calculate the probability that in four years the stock will sell for a price between $54 and $68. d. You are 80% confident the stock price in four years will be between what two values?
9. Explain the principle of immunization when used with a bond portfolio. a. What is bond portfolio immunization attempting to achieve? b. How is bond portfolio immunization achieved? c. Which bond risk components interact to make immunization successful? i. Explain how these bond risk components interact to immunize a bond portfolio. 10. A company forecasts it will sell 54 units of a product next year. Use the Excel file Sales Data to determine the probability that it will sell between 45 and 60 units of the product next year. 11. A stock is selling today for $30. The stock has an annual volatility of 50 percent, and the annual T-bill rate is 8 percent. a. Use Excel’s data table feature to construct a One-Way Data Table to demonstrate the impact of the stock price on both the price and intrinsic value for an 18-month European call option with an exercise price of $28. Use stock prices ranging from $10 to $80 in increments of $5. i. Based on your data table, construct a graph that demonstrates the impact of the stock price on both the price and intrinsic value of this call option. ii. How is the intrinsic value of the call option impacted as the stock price changes? iii. How is the time value of the call option impacted as the stock price changes? 12. The Excel file Moving Averages Data contains quarterly sales data. Use the Ratio to Moving Average approach (based on a 4 quarter moving average) to: a. Using all the data, forecast the sales for each quarter in 2009. b. Using data from 2006 & 2007, forecast the sales for each quarter in 2009 using a trend estimate.
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