Yates – Fall 2013FI 4240Project3 – Page 1 of 3

Project 3Instructions

Note: This is an individual assignment, and you are expected to work on your own. If you have questions, you should consult with me only.

Overview

You have been hired as a portfolio manager for Cookie Doe, who just turned 44 years old. Cookie has $100,000 in a tax-free account and has been putting a lot of thought into portfolio strategies lately. She would like you to help her evaluate three unique strategies.

Strategy One

Cookie will invest in a mix of the optimal risky portfolio and 30-year treasury bonds. Specifically, based on a rule of thumb she read online, she will use her age to determine the percentage of her portfolio that will be invested in bonds. For example, while she is 44 years old, 44% of her portfolio will be invested in bonds. Based on an analysis that you performed previously for her, you have found that the ORP has an annual expected return of 12% and an annual standard deviation of 23%.

Assuming that continuously compounded annual returns on the ORP are distributed normally with the mean and standard deviation calculated above, you simulate 1,000 possible portfolio future values on Cookie’s 70th birthday. For the return on treasury bonds, you will use the spot yield on 30-year treasury bonds.

Strategy Two

Cookie will invest all of her money in a series of a unique derivative product offered by a large investment company. For every two-year period, the product offers the following returns:

  • If the two-year return on the S&P 500 index is positive, then the product will provide a return equal to the minimum of:
  • twice the two-year S&P return, or
  • 11%.
  • If the two-year return on the S&P is negative, then the product will provide a return equal to:
  • zero if the two-year return on the S&P is greater than – 10%, or
  • the two-year return on the S&P plus 10% if the two-year percentage change is less than – 10%.

Cookie likesthis product, since it offers some downside protection when the market return is negative for a two-year period, but she would like you to further investigate its merits.

To begin, you download the monthly closing prices for the S&P 500 index (^GSPC) for the entire data history available on Yahoo. From the closing prices, you calculate the annual continuously compounded returns as:

From this time series of returns, you calculate the monthly mean and sample standard deviation of the returns.

Next, you simulate 1,000 possible series of two-year S&P returns over the next 26 years.[1] For your simulation, assume that continuously compounded two-year returns on the S&P are distributed normally with mean and standard deviation consistent with the values from your monthly historical data.[2]

Finally, you use this simulated return data to calculate 1,000 possible portfolio future values on Cookie’s 70th birthday, assuming that Cookie invests all of the money in her account into one of these derivative products every two years.

Strategy Three

Cookie will invest all of the money in the S&P 500. Every month she will check her portfolio value, and if the value ever reaches $1 million, she will immediately shift all of her assets into 30-year treasury bonds.

To evaluate this strategy, you will simulate monthly portfolio values from now until Cookie’s 70th birthday using a bootstrap technique. First, for the entire monthly history of S&P prices, you calculate the monthly returns. Then, you simulate monthly returns going forward by taking random draws, with replacement, from the set of historical monthly returns.

You perform 250 trials of simulated portfolio future values on Cookie’s 70th birthday. For the return on bonds, you use the monthly spot rate on 30-year treasury bills.[3]

Analysis

For each of the three strategies, calculate the following statistics based on your simulated future values:

1)Expected value

2)Standard deviation

3)Probability of loss

4)VaR

5)Probability future value > $1 million

If Cookie’s largest concern is making sure that she has $1 million dollars by her 70th birthday, which of the three strategies would you recommend? Why?

If Cookie is interested only in maximizing her expected future wealth, which strategy would you recommend? Why?

Deliverables

You will be responsible for emailing an Excel file and hand-delivering an answer sheet.

Your Excel file should be named FI4240_Proj3_Lastname_FirstName.xlsx (or .xls) and must be emailed to prior to the start of class on December 5th. Please ensure that your file contains descriptive sheet names and organizes all of your findings in a professional, attractive manner. Required output should be easily found and clearly marked. Any formulas used in Excel should be contained in the sheet, so be careful that if you paste from one sheet to another, you retain the formulas you used to get your numbers.

Helpful Hints

  • When simulating portfolio values based on normally distributed, continuously compounded returns, remember to subtract off ½ the variance from the mean in your simulation.

[1] Thus, for each of the 1,000 trials, there will be a sequence of 13 simulated two-year returns.

[2]Recall that if a return is ~ over one period, then its distribution over T periods is ~

[3] For simplicity, you may simply divide the annual yield by 12 to get the monthly yield.