Fin485 Derivatives Project Paper

The six stocks that I used to create my portfolio included Altera Corporation, Cabot Oil & Gas Corp., Dominion Resources, FMC Corporation, Chevron Corporation, and Nike Inc. Each of my stocks had weights, which I distributed for my \$100,000. 20% of the \$100,000 went towards Altera Corp., 15% to Cabot Oil \$ Gas Corp., Dominion Resources, and Nike Inc. Finally I allocated 10% towards FMC Corp. and 25% towards Chevron Corporation.

The stocks that I chose were intended to make my portfolio as diversified as possible so that I could receive high returns. I found that Dominion (D) Resources was the most steady and reliable investment from the six stocks in the portfolio. Altera (ALTR) was the one of the smaller investments with the smallest daily returns out of the six stocks, it performed consistently, however, was the only stock in the portfolio that finished the time period with a smaller daily return compared to a year prior (3/1/12).

To begin my project I first found the daily prices for my 6 stocks from March 1st 2012 – March 1st, 2013. To find these I used the Bloomberg Terminal as a search engine and then also found the S&P 500 historical futures prices for the same period as for the 6 stocks. After finding these daily returns I then allocated my weights dividing them up throughout my \$100,000 of capital.

After allocating my weights I then calculated my number of shares for each stock by dividing the 3/1/2013 stock price to the amount of capital that was divvied up through the weights given. For example, if the weight for Altera Corp. was 20%, that would mean that 20,000,000 was invested. From that 20,000,000 Altera’s stock price on 3/1/13 is divided by the \$20,000,000 leaving me with 573,221 shares purchased.

After I did this calculation for all 6 of the stocks, I found the value of my portfolio through multiplying each number of shares purchased for each stock by its individual initial stock price on March 1st, 2013. After finding my portfolio value I then calculated my futures value. I did this by multiplying the S&P 500 futures price on 3/1/13 by \$250. The “\$250” is the multiplier for the S&P 500 historical futures, which opened on April 21st, 1982. Using the betas for each of my stocks that I found on the Bloomberg Terminal I calculated the beta of my portfolio.

The beta for my portfolio was 0.97, which means that my portfolio was not as risky as the market return. To keep away from not making it any more risky than it was, I made my target beta 0.84. Using the target beta, portfolio beta, portfolio value and futures value I found that my portfolio was short 34 contracts. My portfolio had a \$6,791,170.95 gain while having a value of the futures contract at \$379,550.00 on March 1st and a \$350,076.54 loss on the futures position for the month. The return on the S&P 500 Index was 3.07% while the S&P 500 Annual Dividend Yield was 2.13% and monthly came to 0.18%.

The risk free rate was 0.11, which was used to calculate the Treasury Bill Price, which came to \$97.25. The 3-month return was calculated through subtracting the Treasury Bill Price from \$100 of par. This 3-month return brought us to the calculation of the monthly Risk Free Rate to be 0.93%. These calculations brought me to finding the unhedged Return on the Portfolio of 2.73%, which hence gave us the Expected Value of the Portfolio

If you were to move to “Sheet 2” on my portfolio spreadsheet on excel you would see how I ended up finding the Hedge Ratio. My first step began with finding the daily price on the Bloomberg Terminal for each stock in my portfolio from March 1st, 2012 – March 1st, 2013. Along with the daily price I found the daily amount of each stock from the same date range. To find the daily amount of each stock I multiplied the close price for that day by the number of shares purchased for each stock.

After doing the same calculation for each stock I then found my Portfolio Daily Value through throughout the same date range. After finding the Daily Portfolio value I calculated the Daily Difference of the portfolio for each day. I then found the S&P 500 Futures prices for the same dates through the Bloomberg Terminal. This step was a bit tricky because I had to find the days of the futures prices only on trading days so they could match the days the close prices were given for each stock. With that information I found the S&P 500 Daily Difference Value.

I then found the Correlation Coefficient by finding the “CORREL” of the portfolio daily difference and the S&P 500 daily difference. I calculated the Correlation Coefficient to be 0.82. After finding the Correlation Coefficient I calculated the standard deviation of the portfolio to be 0.0102 and the standard deviation of the futures to be 0.0087. Finally with these three last calculations I found the Hedge Ratio of the portfolio. The Hedge Ratio was calculated through multiplying the Correlation Coefficient by the number the equals the Standard Deviation of the Portfolio divided by the Standard Deviation of the Futures. The Hedge Ratio of my portfolio was 0.95.

After finding all the calculations and numbers in my portfolio that I needed, I finally found the hedge ratio, as I stated in the above paragraph. Through this process I found that it was impossible to have a perfect hedge because I had to round out the number of contracts that I needed to short from 34.41 to 34. This meant that I was always going to be short .41 contracts from perfectly hedging my portfolio. However, using the Capital Asset Pricing Model I found the Expected Return on the portfolio using my target beta and the actual beta of the portfolio. We used a 90-Day Treasury bill right while calculating the Index Dividend per month.

This was eventually a problem because while finding the risk free rate we used short-term government debt. To have an accurate reading we would have had to have used a fixed variable since the 90-Day Treasury bill is constantly changing. This is an issue because it would cause our number of contracts that need to be shorted to change, in order to meet our target beta.

This was the only interesting issue that I found that could have been looked at as a problem of the portfolio. Overall this portfolio did teach me a lot about hedging. As we know Hedging is making an investment to reduce the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting position in a related security, such as a futures contract. My goal was to find the hedge ratio so that I could reduce the risk of adverse price movements. In conclusion, the project did bring up interesting points about my stock. I am happy that I learned this process.