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* $\beta$?

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

This is (one way) how to hedge two securities against each other. I am synthesizing the material from here and here.

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.

Note: Obviously, if you want to long one security then you will short the other security.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.