# Is this the correct way to hedge two securities against each other?

Let's say I believe that $ts_1$ and $ts_2$ move together and I would like to pairs trade them. Am I correct in understanding that to hedge them against each other I would get their $Var_1$, $Var_2$, and $Cov_1,_2$ all in USD, then I would buy 1000 USD worth of $ts_1$ and then find how much money to put into shorting $ts_2$ by doing $\beta = Cov_1,_2$/$Var_1$, and then doing $\$\_position\_ts_2 = $\$1000* $\beta$?

• What you are looking for is called the hedge ratio. For your formula to make sense, you need to be dividing by $\beta$. – msitt Apr 3 '17 at 4:28
• Just to make sure I follow, you mean $USD\_position\_ts_2 = 1000 USD/ \beta$ where $\beta = Cov_1,_2$/$Var_1$? – user1367204 Apr 3 '17 at 4:30

Let's call one security the $security_{market}$, and another $security_{unique}$. I'm taking for granted that you have done your research and believe that you found a good pair of securities for hedging.
1. Convert each security time-series from a price to a daily percent change. Call this $pct\_change_{market}$ and $pct\_change_{unique}$.
2. Get $Var(pct\_change_{market}$), $Var(pct\_change_{unique})$ and $Cov(pct\_change_{market}, pct\_change_{unique}$).
3. $\beta$ = $Cov(pct\_change_{market}, pct\_change_{unique}$)/$Var(pct\_change_{market}$).
4. Buy \$100,000 (or whatever amount) of$security_{unique}$. Now you need to know how many dollars to sink into$security_{market}$. 5. Multiply \$100,000 by the $\beta$, this will be the amount of dollars to spend on your hedge.
6. Divide the number of dollars you came up with in step 5 by the price of $security_{market}$. Just to be clear, numerator is number of dollars, denominator is price of $security_{market}$. This will be your position for the hedge.