Using Regression Analysis to Calculate a Portfolio Hedge

When managing investments we sometimes wish to profit from superior stock picks while reducing exposure to market wide risks. To do so we use a hedge position that is designed to move the opposite direction of the market. The percentage by which a stock moves when the overall market moves 1% is called the Beta of the stock. It is also the coefficient you would find if you ran a regression of the stock's returns on the market's returns. Our objective in this case is to eliminate market risk, also known as "Beta" risk, by using regression to find a hedging amount for a particular portfolio.

We will consider two potential hedging securities:

First calculate daily returns as: Return(1) = Price(1)/Price(0) -1

Next you must regress daily portfolio returns on each of the hedging securities and determine the optimal amount needed of each security to minimize the volatility of the hedged portfolio.

1 Questions we are interested in answering:

1. If we hedge with SH alone, how many shares of SH should we buy to achieve a net Beta of 0 for the hedged portfolio?

2. If we hedge with RWM alone, how many shares of SH should we buy to achieve a net Beta of 0 for the hedged portfolio?

3. Is it possible to calculate an optimal hedge by regressing on both SH and RWM?

4. If so, what are the optimal positions for the two security hedge.

Minimum Data Analysis Requirements:

1. Show your calculation of portfolio returns and hedging instrument returns over the prior 12 months using daily data.

2. Provide regression statistics for each regression you perform.

3. Using regression results, and a weekly hedge adjustment policy to back- test the performance of the hedged portfolio using SH and using RWM. Calculate hedged returns and volatility of hedged returns. We discussed how the measures of variation are considered a measure of volatility in the beginning of this course.

4. Use data visualization techniques (graphical plotting) to see what the data will tell you - be creative.

5. Calculate correlations among the portfolio, SH, and RWM.

In addition to your analytical results, respond to the following discussion questions.

1. Do you believe the relationships identified are stable and can thus be used going forward?

2. If we are re-adjusting our hedges weekly do we need to use weekly return data instead of daily return data?

3. Which security is better for hedging? Why?