If I have log returns for a specific stock, then the weekly log return is the log of Friday's closing price minus the log of Monday's closing price, i.e. $R_{weekly} = log(Price_{Friday}) - log(Price_{Monday})$.

However, can I also calculate the log return as the sum of the daily log returns? $R_{weekly}=[log(Price_{Monday}) - log(Price_{Sunday})] + [log(Price_{Tuesday}) - log(Price_{Monday})] + {...} + [log(Price_{Friday}) - log(Price_{Thursday})]$

  • $\begingroup$ Both the methods should lead to the same answer under the assumption that the price changes are relatively small $\endgroup$ – Tim Mar 8 '16 at 21:07
  • 2
    $\begingroup$ +log() and -log() terms in the second expression should cancel out, leaving exactly the first expression. $\endgroup$ – noob2 Mar 8 '16 at 22:44

Your second formula regarding the sum of day-to-day returns collapses as follows:

$$ \begin{align} R_{weekly,2} &= \text{log}(Price_{Mon}) - \text{log}(Price_{Sun}) \\ &+ \text{log}(Price_{Tue}) - \text{log}(Price_{Mon}) \\ &+ \dotsc \\ &+ \text{log}(Price_{Fri}) - \text{log}(Price_{Thu}) \\ &= \text{log}(Price_{Fri}) - \text{log}(Price_{Sun}) \end{align} $$

Compared to the first formula,

$$ R_{weekly,1} = \text{log}(Price_{Fri}) - \text{log}(Price_{Mon}), $$

the difference is

$$ R_{weekly,2} - R_{weekly,1} = \text{log}(Price_{Mon}) - \text{log}(Price_{Sun}). $$

That is, you include one extra day-to-day return in the definition of $R_{weekly,2}$ as compared to the definition of $R_{weekly,1}$.

In my understanding, the relevant weekly return is the cumulative return over all seven days of the week (if there are no trades on, say, Sunday, then define the corresponding day-to-day return as zero), which collapses to

$$ R_{weekly} = \text{log}(Price_{Fri,\ this \ week}) - \text{log}(Price_{Fri, \ last \ week}) $$

(which is what @SimoneBortolato suggested before). However, depending on what you want to do with those weekly returns, other definitions could make sense as well.


I can't still comment a question, since I've still got low reputation, so I'm going to answer. I think you should calculate weekly returns from friday to friday (close of the week to close of the following week).


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.