Derivative Securities and Portfolio Management Project

The second part of the project involved following options prices of the stock I picked. Options give the holder the right (not obligation) to buy or sell stocks within a period of time at a specified price. To obtain the option prices of the company, I used the website of Chicago Board Options Exchange. I entered Delayed Option Chain section, and then entered JPM ticker symbol which provided me numerous options contracts. As we are supposed to pick a contract that expires after the semester is done, I chose an options contract with a strike price of $45, and with an expiration date of 08 January 2008. There was no particular rational behind picking a contract with a strike price of $45.

The third part of the project involved Futures. Futures are a financial instrument that requires a buyer or seller to purchase or sell an asset at a predetermined price at a specified time. For this part, I chose CME S&P 500 futures, with an expiration date of 07 December 2007. As this was the only contract which had an active open interest near the end of the semester, I decided to use it. I obtained the futures price from Wall Street Journal, in its Commodities and Futures Section of Markets Data Center.

Risk-Adjusted Return on the Portfolio

For my first portfolio, I had a total return of -0.58% along with a standard deviation of 4.06%. The stock portfolio saw its highest return in Week 2 with a rise of 5.01%, and its biggest drop in value on Week 11, when the portfolio lost as much as 7.59% of its value. The Options Hedge portfolio also saw a drop in its value. The portfolio dropped by -0.14%, and had a standard deviation of 4.25%. The Futures Hedge on the other hand rose by 0.04%, along with a standard deviation of 3.76%.

Securities

The risk free rate for the 12 weeks of the project was .69%, and the return on the portfolio was a negative 7%. JP Morgan had an "alpha" of .273%. An "alpha" tells us how much a portfolio outperformed a benchmark index, and in this case - S&P 500. An alpha of 0.273% means that my securities portfolio outperformed S&P 500 index by 0.273% on a risk-adjusted basis, which is the excess rate of return than was expected. During the 12 week period, the instability in the market was in full swing, with financial stocks and the market as well rising one day, and falling the other day drastically. The market as a whole took a beating, but financial sector was further affected due to numerous losses attributed to sub-prime mortgage. A positive alpha shows us that even when financial stocks were expected to drop, the rate of return of JP Morgan was higher than expected.

Options

The objective of the hedge ratio was to figure out how many shares were needed to be sold, or the number of calls that were required to be sold short in order to minimize the risk or make the hedge risk-less. The options portfolio beta should have been 0, taking the risk-free rate into account. This risk-free rate is return you would expect that guarantees those returns without any risks attached to it. The return on the Options portfolio should have been the same as the risk free rate return. As such, the return on the Options portfolio should have been .69%.

Futures

As the market dropped, the hedged futures portfolio worked, and the beta of the hedge should be as close to zero as possible. As in the options, the return on the futures hedge should be the risk free rate of return.

Variability of your 3 portfolios' rates of return

During the first 6 weeks of the project, the un-hedged securities provided higher returns than both the hedged securities or had greater losses than the hedged securities. In Week 7, the futures hedge provided a larger return than the un-hedged portfolio, while the options hedge provided lower return. In week 8, the options hedge had an abnormally large rise in its value, but its value plummeted in the following week along with both hedged futures, and un-hedged securities. During 11th and 12th week, the options return stabilized, while hedged portfolio provided greater returns than un-hedged securities. As the financial sector wasn't performing well, a hedge consisting of S&P 500 futures performed better throughout the 12 weeks.
A hedge protects against unexpected drop in value of a stock, it doesn't protect against regular fluctuations in the market movement. If a stock price dropped due to more sellers than buyers in a normal business day, a hedge is not intended to protect you from that, but if a stock drops drastically due to depressing future performance of a company, a hedge will help minimize the losses. Futures hedge seems to provide a better hedge compared to options hedge. A hedged future would definitely be a better option compared to options hedge. Although the negative return on options hedge was almost negligible, the hedged futures and un-hedged securities have performed better at the conclusion of 12 weeks.

The e* (hedging effectiveness) for Securities and Options is -.087 (4.06^2-4.25^2/4.06^2). For the hedged futures, the hedging effectiveness was .142(4.06^2-3.76^2/4.06^2)

Return Standard deviation

Securities alone -0.58% 4.06
Securities and Options -0.14% 4.25
Securities and Futures .04% 3.76

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