Hedging a Stock Portfolio with S&P 500 Futures Contracts

For this project, you will gain understanding of how a financial institution could use futures contracts to hedge against general market-level equity risk for their stock portfolio holdings, over a given period of time. You will also gain familiarity with futures contracts. Finally, you will refresh your statistical and Excel skills, because the exercise will require you to perform an OLS regression in Excel in order to estimate the hedge ratio. For the purposes of this assignment, we will ignore the discreteness in your hedge position, based on the size of futures contracts. Rather, we will assume that you can take a position in any dollar amount for your futures position. This project will evaluate the 2019-2020 timeframe as an interesting period historically with several instances when VIX was very elevated, even exceeding 60% briefly in March 2020.

Due Date: The due date is by 11:59 pm on Monday, April 25; files submitted to the Blackboard Assignment. See page 3 for details on the deliverables for this project. I would encourage you to complete the project during the preceding week, but am allowing for this later due date to give you maximum flexibility. After the due date, I will post a document with answers and some comments, to close the loop on this project.

Hedging a Stock Portfolio with S&P 500 Futures Contracts

This project will feature the posted SP500_FuturesData Excel spreadsheet. This spreadsheet contains daily returns that represent returns you would have approximately earned from holding a position in S&P500 futures contracts over 1/2/2019 to 12/31/2020 (Filename: SP500FutPric2019- 20.xlsx). January 2, 2019 is the first trading day of the year.1

1. For our hypothetical stock holdings, we will use the ETF on the Russell 2000 to represent a hypothetical small-cap stock portfolio that an institution might hold. The Russell 2000 is a small- cap equity index that is widely used as a benchmark for small-cap mutual fund performance (see additional information on the Russell 2000 on the last page of these instructions). To illustrate the concept of hedge mismatching (in terms of your operational holdings not aligning exactly with the underlying of the futures contract), we will use this small-cap index. Go to Yahoo Finance and select the price history from 12/31/2018 to 12/31/2020 for the ticker IWM (which is the ETF for the Russell 2000) and then download the data to an Excel spreadsheet. Then, use the adjusted closing price (Adj Close) to calculate the daily returns for this ETF stock fund for each trading day over 2019-2020 to match with the daily returns of the S&P futures. (With this download and calculation, you should end up with 504 daily returns, dating from 1/2/2019 to 12/30/2020.) It is

1 Note that the futures return is really the percentage change in the price of the futures contract; rather than an actual return because there is no initial outlay when you enter into a future contract.

1

recommended to compute and work with percentage return units (rather than decimal), for ease of review.2 Then, merge the stock-fund returns and the S&P 500 Futures returns together, by date, in a single worksheet for statistical evaluation.3

2. To evaluate whether the S&P 500 futures contract appears to useful as a good hedge against equity-market risk for your stock fund, graph the S&P 500 futures return (as the x-variable) against the stock-fund return (as the y-variable) using a scatter graph from Excel, with an included linear regression line over the 2019 evaluation period only (so do not graph all your data, but just that over 2019. Include this graph as an appendix in your deliverables for this assignment.

3. Next, assume that you are a hedge fund and you have a broad small-cap oriented stock portfolio (represented by the IWM fund) that you might periodically wish to hedge against general stock market risk. For the purposes of the hedge exercise, assume that the beginning value of your stock portfolio is $150 million. In this exercise, you will evaluate how a stock hedge would have performed over 2020, based on a hedge ratio estimated with 2019 daily data. Specifically:

a) In terms of the timing for this hedge, pretend that it is the end of 2019 and you just received the stock returns for your portfolio over 2019 (as calculated from the Yahoo IWM prices). Then, to determine the hedge ratio for your hedge going forward, regress the daily percentage returns of the S&P 500 futures contracts (as your explanatory x variable) against the daily returns of your stock fund (as the dependent y variable) over 2019 only. Include a copy of this Excel regression as an appendix in your deliverables for this assignment.

b) From your regression above over the 2019 period, what proportion of the variance of your stock- fund returns are you able to explain based on the S&P 500 futures returns? Based on your estimated Beta, what should be your dollar position (exposure) in the futures market to appropriately hedge your stock portfolio, going forward?4

c) Next, assume that you are going to set up your hedge at the beginning of 2020, using the hedge ratio determined in a) above and with a starting value of a $150 million stock portfolio at the beginning of each trading day over 2020.5 Given these return outcomes over 2020, use Excel to determine: Without the hedge, what would have been the standard deviation of your daily dollar gain/loss (or change in the value of your portfolio in dollars) ? With the hedge, what would have

2 You can either format the cells to %, or multiply the decimal returns by 100, so that the number indicates a

percentage return.

3 Recommend using Excels VLookUp function to merge the two return series.

4 Forthisapplication: Nf (indollars)= NS(indollars)*futures_spot wherethebetaisfromaregression

of the futures return as the x-variable versus the spot return as the y-variable. This is an application of the minimum variance hedge ratio discussed on pages 355-360 in the Chance textbook, as we derived in class. 5 Thus, these instructions assume that your daily holdings are consistently about $150 million, but if this hedge was actually put into place there would be day-to-day fluctuations in the funds value.

2

been the standard deviation of your daily dollar gain/loss? Without the hedge, what would have been your greatest daily dollar loss over this period? With the hedge, what would have been your greatest daily dollar loss over this period? Include a copy of this Excel spreadsheet where you did these calculations as a separate file for your deliverables for this assignment (Hint: Do not forget to review the example spreadsheet from the in-class demonstration.)

Deliverables: Your report should include: 1) Header Information: Project title, class, & date. 2) Name; 3) A summary written report, in the spirt of an Executive Summary, that concisely summarizes the problem assignment and your work and findings. The summary report should briefly address the embedded questions in the above instructions. (See http://en.wikipedia.org/wiki/Executive_summary for a review of Executive Summaries). 4) The requested spreadsheet, regression output, and graph that are asked for in the instructions should be included as appendices that are referred to in the written report. See the demonstration file as an example format for your spreadsheet. 5) Report Due: Due date is by 11:59 pm by Monday, April 25.

Your deliverables should be submitted through the Blackboard assignment. For the graph and regression output; you can paste the required parts into MS Word and submit as a Word file (or .pdf file) that contains the Executive Summary and the answers for the project, with the graph and regression output as appendices to the Executive Summary. But, dont forget to also submit your supporting spreadsheet as a second file. Make sure to name the files so for clarity. (For example: FIN403_Project2_Hedge_Jones.doc and FIN403_Project2_Hedge_Jones.xlsx) ____________________________

About the Russell 2000 Index, from Investopedia