0
$\begingroup$

I've taken three months of price return data for two instruments and calculated a $\beta$ between the two using the formula $\beta = \frac{Cov(x,y}{Var(y)}$ with the goal of estimating what the percentage change in instrument $y$ should be based on what the percentage change in instrument $x$ is.

I have been applying this by multiplying $\beta$ by the percentage change of $x$ to determine a beta-adjusted percentage change for $y$, but I am wondering if I should actually multiply the derived $\beta$ by the current percentage change of $y$ instead. Could anyone shed some light on whether or not I am properly applying this $\beta$ to arrive at an expected percentage change for $y$?

|improve this question
$\endgroup$
  • $\begingroup$ It appears that you're looking at the Capital Asset Pricing Model (CAPM), It is important to note that the CAPM can be used for prediction, however, I feel that you're slighlt confused. Risk premium is the price of risk, $[E(R_m)-r_f]$ multiplied by a measure of risk, often called $\beta$. The definition of $\beta$ that you have is correct, but are you trying to find out how your two securities impact each other, if so I would suggested a granger causaility model. $\endgroup$ – user22485 Oct 18 '18 at 12:43
  • $\begingroup$ Sort of, I am attempting to derive an estimate for the change in a back month commodity future against how much the front month has changed. So in this case I am treating my front month as a 'spot' and looking at expected changes in the back. I know the instruments are related, and cointegrated over the time interval I am looking at so I'm not sure if granger causality is going to tell me anything new. I am just looking to estimate a coefficient that shows me expected change in the back when applied to what has happened in the front. $\endgroup$ – jod51 Oct 18 '18 at 13:17
  • $\begingroup$ So are you using lagged co-integrated techniques? $\endgroup$ – user22485 Oct 19 '18 at 6:58
  • $\begingroup$ I still think a regression model would help you, but your variables are I(1), (if they are cointegrated), this makes GC using OLS pretty useless. There is a great paper by Campbell and Yogo (2006) and they look at these predictive regression with persistent explanatory variables, its a little bit complicated but worth a read. $\endgroup$ – user22485 Oct 19 '18 at 7:01
0
$\begingroup$

First of all if your model is $r_Y\sim~\beta r_X$ (with $r_X$ and $r_Y$ the returns of assets X and Y) then $\beta = Cov(r_X,r_Y)/Var(r_X)$ not $Cov(r_X,r_Y)/Var(r_Y)$ as stated by OP

Then assuming this model, if you observe $r_X$ the model would associate $\hat{r}_Y = \beta r_X$ to explain the actual return $r_Y$. The unexplained return would be $\epsilon_Y = r_Y - \hat{r}_Y$

|improve this answer
$\endgroup$
  • $\begingroup$ Yep, thx. That's not the issue here. $\endgroup$ – jod51 Oct 24 '18 at 13:04
  • $\begingroup$ i think that's exactly the issue at hand, i responded to your question and corrected your typo on the definition of $beta$ $\endgroup$ – Ezy Oct 25 '18 at 12:20

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.