You have a position in $200$ shares of a technology stock with an annualized standard deviation of changes in the price of the stock of $30.$ Say that you want to hedge this position over a one$-$year horizon with a technology stock index. Suppose that the index value has an annual standard deviation of $20.$ The correlation between the two annual changes is $0\mathrm{.}80.$ How many units of the index should you hold to have the best hedge?

Use the same data as presented above to compute the hedge ratio using regression analysis, again using Excel. Explain why the values are different from what you obtained above.