Project outline

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

1. Portfolioconstruction

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

• Start datefor the portfolio is March 1st
• Select 15-20stocks and collect daily prices over last 12 months (from March 1st 2014 to Feb28th 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 youcannot obtain historical data on S&P Futures by yourself, try the followingsource
• http://www.investing.com/indices/us-spx-500-futures-historical-data

• Constructyour portfolio according to the weights you have chosen. Now using theseweights you can calculate the daily value of your portfolio for the past year
• Calculatethe daily difference in value of the portfolio and the S&P 500 futuresprices i.e. ΔP and ΔF. Using these two difference series calculate thecorrelation between them and their standard deviations. Use the correlationcoefficient and the two standard deviations to compute the hedge ratio.

• Collectcurrent 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 yourportfolio on March 1st 2015
• Record thelevel of the S&P 500 index on March 1st2015 and the S&P futures price on March 1st 2015

2. HedgeImplementation

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

• Your hedgestarts on March 1st and ends on April1st.
• Since thehedge ends on April1st you will use May or later futures (i.e. futurescontracts that expire in May or later)
• Record thefutures price of the S&P 500
• Select thetarget Beta for your portfolio
• Compute thenumber of contracts you need to change your risk using the Portfolio Beta aswell as the hedge ration that you calculated
• Compute thenumber of contracts for a riskless hedge using the Portfolio Beta and hedgeratio you calculated.

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

3. Evaluate Hedgeperformance

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

• Record thefutures price, S&P index level and stock prices on April 1st.
• Use CAPM tocompute the expected return on the hedged portfolio
• Compute thevalue of your portfolio with and without hedging.
• Compute thereturns on your portfolio and compare to expected return
• You willalso need to compute the risk free return over this period. You must use the90-day T-Bill as your proxy for a risk free asset. Collect daily discount ratesfrom Yahoo finance. The ticker for the 90-day T-Bill is ^IRX and for theS&P500 index the ticker is ^SPX

4. Summary and Report

Summarize your findings and submit a report. Do not forgetto include the S&P 500 contract details (CME provides a comprehensivedescription of all its futures contracts). The contract value is $250 x IndexFutures Price.

Note: You will have to submit all your data and computationson an excel file. The report must be in MS Word of approximately 3-5 pages (12point font 1.5 line space). All returns must be in annualized. I will grade onclarity 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 onthe 90-Day T-Bill and compute the risk free rate. Refer to the notes on T-Billcomputations)

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

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

Portfolio Beta = 1.75 (You will compute the portfolio betaaccording 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 ofFutures 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 youlose 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% permonth

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 ofPortfolio - Loss on futures

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

After the hedge the Beta = 1.25, so compute the expectedvalue of the portfolio using this Beta, the value of the portfolio should beequal 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 yourportfolio to 1.25 by selling and buying stocks, then the portfolio value wouldbe $110,330,000. But you used futures contracts to get the same effect and yourportfolio is $107,570,000. The hedge did not work well. There could be severalreasons for this. First these figures are all nonsense but that will not be areason when you do the project. The reasons for the discrepancies could bebasis risk or that CAPM may not be accurate in pricing market risk. Perhaps,noise (inaccuracies) was introduced by errors in observations of the risk freerate. This is not your fault, it means that the 90-day T-Bill may not be a goodproxy for the risk free rate; the LIBOR may be better.