Log Returns in Finance: Continuous Compounding and Euler's Number (e) Explained

[@RyanOConnellCFA]

🎓 Tutor With Me: 1-On-1 Video Call Sessions Available ► Join me for personalized finance tutoring tailored to your goals: ryanoconnellfinance.com/finance-tutoring/ 💾 Download Free Excel File: ► Grab the file from this video here: ryanoconnellfinance.com/product/log-returns-introductory-excel-toolkit/

[@saheedsimisaye8978]

The only video that has been able to make the relationship between Euler's number and continuously compounding returns meaningful to me. Thanks a lot for this video.

[@RyanOConnellCFA]

My pleasure, I appreciate you taking the time to leave me this feedback!

[@hungphutr]

appreciate this video Ryan. It used to take a while for me to really grasp the need for the existence of logarithm.

[@RyanOConnellCFA]

It is my pleasure and I'm really glad it helped you!

[@Abdullah19Fin]

Great Ryan, I appreciate your efforts of making great videos. But I have a question in min 9:57 if you try to solve the equations they not going to be equal.

[@darshanrajanderan4084]

Thank you for the content!

[@RyanOConnellCFA]

My pleasure!

[@victoricus1]

thank you, Ryan, now it makes perfect sense!

[@RyanOConnellCFA]

Glad to hear it! Its my pleasure

[@balkrishnaparab3353]

When we take log returns of stock prices, how do we average log returns? Please make a video on operations on log returns, such as sum, average, etc.

[@RyanOConnellCFA]

You can see in this video I annualize the the standard deviation using an average of log returns and I annualize annual return using a sum and an average: kzbin.info/www/bejne/joK2YmqPp7-pe9U

[@DrMohammedFHasan]

Great explanation. Please, would you make a similar video on calculating treasury bills rates compound as proxy for (Rf)?

[@RyanOConnellCFA]

Thank you! Just to make sure I understand your request, you'd like to see a video on how to calculate the rate of return of a treasury bill? If so, I should be able to do that!

[@DrMohammedFHasan]

@@RyanOConnellCFA till now, I had never seen such video. I meant the video about investing in treasury bills as continuous investment or a safe alternative to a risky asset ( as Tobin mentioned in separation theory ). I’ll be thankful for your support.

[@rickguerrero2282]

A really nice explanation of the math behind ln returns. Question: if you redid the formulas in the "simple return" section of the spreadsheet, and used n=12 (monthly compounded), or n = 365 (daily compounded), what would the 1st year, 2nd year, and cumulative return % be? And how would it compare to the natural log calculation?

[@RyanOConnellCFA]

Thank you! I just tried this summing experiment with a list of 20 different stocks in my own portfolio for daily compounding for a 1 year time frame. When using daily returns, every single one had a larger value when summing the simple returns than summing the lognormal returns. The values were extremely off when trying to sum daily simple returns to come up with an annual return. I assume we should see similar results for monthly compounding. Making the time frame 2 years rather than one should only exacerbate the discrepancy