The purpose of the project is to use the S&P 500 index futures contract to hedge portfolio risk and subsequently evaluate the hedge performance.

1. Portfolio construction

Assume you manage an all equity portfolio worth $75 to 150 million (you choose your capital level between these boundaries). You must first select a portfolio of 15-20 stocks. You must then allocate the capital across these stocks that you have selected.

• Start date for the portfolio is March 1st
• Select 15-20 stocks and collect daily prices over last 12 months (from March 1st 2014 to Feb 28th 2015). You can collect the data from Bloomberg, yahoo or CRSP. Also, collect the daily S&P 500 futures prices for the same period. (If you cannot obtain historical data on S&P Futures by yourself, try the following source
• http://www.investing.com/indices/us-spx-500-futures-historical-data

• Construct your portfolio according to the weights you have chosen. Now using these weights you can calculate the daily value of your portfolio for the past year
• Calculate the daily difference in value of the portfolio and the S&P 500 futures prices i.e. ΔP and ΔF. Using these two difference series calculate the correlation between them and their standard deviations. Use the correlation coefficient and the two standard deviations to compute the hedge ratio.

• Collect current Betas of the stocks from Value line, Morning Star or some such source. Compute portfolio Beta using your allocation of weights.
• Calculate the exact value of your portfolio on March 1st 2015
• Record the level of the S&P 500 index on March 1st 2015 and the S&P futures price on March 1st 2015

2. Hedge Implementation

You will use the S&P 500 Futures contract to hedge your portfolio risk.

• Your hedge starts on March 1st and ends on April 1st.
• Since the hedge ends on April1st you will use May or later futures (i.e. futures contracts that expire in May or later)
• Record the futures price of the S&P 500
• Select the target Beta for your portfolio
• Compute the number of contracts you need to change your risk using the Portfolio Beta as well as the hedge ration that you calculated
• Compute the number of contracts for a riskless hedge using the Portfolio Beta and hedge ratio you calculated.

Note that you have two hedging strategies one using Portfolio Beta and one using your own hedge ratio.

3. Evaluate Hedge performance

Once you have closed the hedge on April 1st, you will evaluate the hedge performance

• Record the futures price, S&P index level and stock prices on April 1st.
• Use CAPM to compute the expected return on the hedged portfolio
• Compute the value of your portfolio with and without hedging.
• Compute the returns on your portfolio and compare to expected return
• You will also need to compute the risk free return over this period. You must use the 90-day T-Bill as your proxy for a risk free asset. Collect daily discount rates from Yahoo finance. The ticker for the 90-day T-Bill is ^IRX and for the S&P500 index the ticker is ^SPX

4. Summary and Report

Summarize your findings and submit a report. Do not forget to include the S&P 500 contract details (CME provides a comprehensive description of all its futures contracts). The contract value is $250 x Index Futures Price.

Note: You will have to submit all your data and computations on an excel file. The report must be in MS Word of approximately 3-5 pages (12 point font 1.5 line space). All returns must be in annualized. I will grade on clarity of thinking and presentation of your findings.

Example:

Data at time t = 0 i.e. on Feb 1st

S&P 500 Index Level = 1200

S&P 500 Index Futures Price = 1250

Do not confuse Index level with Index futures price.

Risk free rate = 2% annualized (you can find the discount on the 90-Day T-Bill and compute the risk free rate. Refer to the notes on T-Bill computations)

Dividend Yield on S&P 500 index = 1.2% (You can get this from Bloomberg)

Portfolio Value = $100 million (This will be the figure you have chosen as your initial capital)

Portfolio Beta = 1.75 (You will compute the portfolio beta according to your capital allocation)

Target Beta = 1.25 (You want to reduce risk)

Calculations:

Value of Futures Contract = 250 x 1250 = $312,500

Number of contracts = (β* - β)*(Value of Portfolio/Value of Futures Contract) where β* and β are the target and current Betas respectively.

Number of contracts = (1.25 - 1.75)*(100 million/312,500) = - 160. The negative sign means you short 160 S&P 500 futures contracts.

Data at time t = T i.e. on March 1st

S&P 500 Index Level = 1300

S&P 500 Index Futures Price = 1375

Gain/Loss on Futures Position:

Remember you shorted the futures contracts, therefore you lose money as futures prices rise. You agreed to sell at 1250 by going short. Now to close the position you need to go long (i.e. buy) at 1375

Loss = (1250 - 1375) * Number of contracts *$250 = - $5,000,000

The gain/Loss on the S&P 500 Index:

The index rose from 1200 to 1300 i.e. a gain of 100/1200 = 8.3333 % (in one month)

However the index also pays a dividend = 1.2/12 = 0.1% per month

Total Return on Index = 8.3333 + 0.1 = 8.4333% per month.

Risk free rate = 2/12 = 0.1667% per month

Expected Return on Portfolio (unhedged) according to CAPM

RP = 0.1667 + 1.5(8.4333 - 0.1667) = 12.57% per month.

Expected Value of Portfolio = 100 million * (1+ 0.1257) = $112,570,000

Expected Value of hedged Portfolio = Unhedged Value of Portfolio - Loss on futures

= 112,570,000 - 5,000,000 = $107,570,000

After the hedge the Beta = 1.25, so compute the expected value of the portfolio using this Beta, the value of the portfolio should be equal to the above value if the hedge was perfect

Expected Return on Portfolio (unhedged) according to CAPM

RP = 0.1667 + 1.25(8.4333 - 0.1667) = 10.33% per month.

Expected Value of Portfolio = 100 million * (1+ 0.1033) = $110,330,000

This means that if you actually altered the beta your portfolio to 1.25 by selling and buying stocks, then the portfolio value would be $110,330,000. But you used futures contracts to get the same effect and your portfolio is $107,570,000. The hedge did not work well. There could be several reasons for this. First these figures are all nonsense but that will not be a reason when you do the project. The reasons for the discrepancies could be basis risk or that CAPM may not be accurate in pricing market risk. Perhaps, noise (inaccuracies) was introduced by errors in observations of the risk free rate. This is not your fault, it means that the 90-day T-Bill may not be a good proxy for the risk free rate; the LIBOR may be better.