Thank you so much for this brilliant and simple explanation! I've watch several videos on this topic, which all explain one and the other return reasonably well but I kept feeling a little lost regarding the connection between the two and the reason why I would want to "bother" with the ln() return in general. Your video very well explains the connection (by "unlog"-ing at the end) and also the last example shows very well what can happen when using the "wrong" return in that scenario. This certainly teaches people to look more closely at their investment return statement.
How does this affect your variance, Covariance and SD calculations? Do they essentially remain the same, but use e^(average(log returns)) as the average that deviations are calculated from?
I have created an investment strategy and I have first calculated simple returns for the portfolio and after that the log-returns. Now I want to run a linear regression model with FamaFrench factors. Should the Fama French data also be converted to log-returns if the dependent variable (portfolio return) is in log-form? I suppose that I cannot have the portfolio return in log-form and Fama French factors as they are(?)
I have seen people using Natural Log "log (p2/p1)", while calculating daily returns of stock/Index for long period data (15-20 years), instead of using '(p2 - p1)/p1'. Could not know very good reason. Is it more accurate to use Natural Log ? Can you make a Video on this in detail for benefit of all of us. Rgds.
It's not more accurate, it's just more practical to manipulate. It's like shifting to a parallel universe with LN, where multiplication turns into addition (easier to use), then coming back to the "normal" world with EXP for the final result.
But how do you find the excess real log return? Do you first find the real log return by subtracting off log inflation from nominal log return… then subtract off log inflation from nominal risk free return… then take the difference between the real log return and the real log risk free return to arrive at excess real log return? Or… do you find excess nominal log return by taking the difference between nominal log return and nominal log risk free return, and then subtracting off log inflation? It’s all very confusing to me.
Assume share return = 9.0% and expected return = 6.0%, then the excess return = (1+9.0%)/(1+6.0%)-1 = 2.83%. Since we are using Ln returns, we must divide (not subtract).
@@MichaelWardFinance so assuming 6% is risk free rate and 9% is share return (both on returns), then the excess on return is 2.83%? Then how do you get to ln real excess return?
The gist of it is that the more periods you have in a year the more you'd benefit from continuous compounding. In the example given with 12% annualised, if you compound the interest 12 times in a year (approximately each month for example) the actual interest rate is (1 + 0.12/12)^12-1 = 0.12682503013196977 (or 12.6825%). If you compound it 24 times (every 365/24 day) you'd get an annualised rate of (1+0.12/24)**24-1 = 0.12715977620538887 (12.7160% slightly higher). So, in order to maximise the interest rate you'd need to have as many periods as possible during a year (i.e. continuous). It turns out that (1+0.12/inf)^inf-1 is e^0.12-1 or more generally: (1+r/inf)^inf-1 = e^r-1 for a given year. Evidently, e^0.12-1 = 0.12749685157937574 or 12.7496%. This would be the maximum return you would possibly get with continuous compounding for r=0.12 Here is also the proof for the more general case when you want to calculate the resulting rate for more than one year: www.onemathematicalcat.org/Math/Precalculus_obj/continuousCompounding.htm
@@thomas9982 Thanks Thomas. I'll study in detail you guided and reference given. I'll come back if any further doubt. Hope you'll clarify if any. Thanks again for your so much concern. 👍🙏
@eggtimer2 I agree with you, but can you give me why we use log normal. Because for the explanation given here could be resolved using geometric linking or geometric mean.
best explenation I have seen so far, thanks a lot!
Thank you so much for this brilliant and simple explanation! I've watch several videos on this topic, which all explain one and the other return reasonably well but I kept feeling a little lost regarding the connection between the two and the reason why I would want to "bother" with the ln() return in general. Your video very well explains the connection (by "unlog"-ing at the end) and also the last example shows very well what can happen when using the "wrong" return in that scenario. This certainly teaches people to look more closely at their investment return statement.
Unlike many others, this is a great explanation. Thanks for the video!
Glad it was helpful!
Excellent explanation! Thank you so much. I look forward to more finance based mathematic breakdowns. You're relieving a lot of stress for students.
Great to hear!
This is the best explanation of log return and returns I've ever saw. Thank you
best expiation available on yt!
you nailed it sir.. i have tried to read it from different sources but never understood. thank you sir...
The video content is so excellent, congratulations
Such a clear example.Thanks
"... because it has!..." this attitude - he feels it in his bones :)
helped a lot, appreciate it. Thanks Michael!
This is an amazing explanation..it would be great if you could provide the spreadsheet too sir!
great content
brilliant, thanks
Awesome! Thank you!
Helpful
may be start out with equations before going to excel. might be easier to see where the excel part is heading to. of course, just my opinion.
How does this affect your variance, Covariance and SD calculations? Do they essentially remain the same, but use e^(average(log returns)) as the average that deviations are calculated from?
Is it more accurate to calculate the deviations using the series of daily log returns and the average of the daily log returns?
I have created an investment strategy and I have first calculated simple returns for the portfolio and after that the log-returns. Now I want to run a linear regression model with FamaFrench factors. Should the Fama French data also be converted to log-returns if the dependent variable (portfolio return) is in log-form? I suppose that I cannot have the portfolio return in log-form and Fama French factors as they are(?)
Hi Sara, yes both should be the same. I doubt it will make any difference if you are using the FF daily data.
I have seen people using Natural Log "log (p2/p1)", while calculating daily returns of stock/Index for long period data (15-20 years), instead of using '(p2 - p1)/p1'. Could not know very good reason.
Is it more accurate to use Natural Log ?
Can you make a Video on this in detail for benefit of all of us.
Rgds.
It's not more accurate, it's just more practical to manipulate. It's like shifting to a parallel universe with LN, where multiplication turns into addition (easier to use), then coming back to the "normal" world with EXP for the final result.
But how do you find the excess real log return? Do you first find the real log return by subtracting off log inflation from nominal log return… then subtract off log inflation from nominal risk free return… then take the difference between the real log return and the real log risk free return to arrive at excess real log return? Or… do you find excess nominal log return by taking the difference between nominal log return and nominal log risk free return, and then subtracting off log inflation? It’s all very confusing to me.
Assume share return = 9.0% and expected return = 6.0%, then the excess return = (1+9.0%)/(1+6.0%)-1 = 2.83%. Since we are using Ln returns, we must divide (not subtract).
@@MichaelWardFinance so assuming 6% is risk free rate and 9% is share return (both on returns), then the excess on return is 2.83%? Then how do you get to ln real excess return?
KINDLY EXPLAIN THE EXPRESSION PLEASE
" (1+12%/infinity)^infinity-1 = 12.7496%"
Can you suggest any book on it ?
The gist of it is that the more periods you have in a year the more you'd benefit from continuous compounding. In the example given with 12% annualised, if you compound the interest 12 times in a year (approximately each month for example) the actual interest rate is (1 + 0.12/12)^12-1 = 0.12682503013196977 (or 12.6825%). If you compound it 24 times (every 365/24 day) you'd get an annualised rate of (1+0.12/24)**24-1 = 0.12715977620538887 (12.7160% slightly higher). So, in order to maximise the interest rate you'd need to have as many periods as possible during a year (i.e. continuous). It turns out that (1+0.12/inf)^inf-1 is e^0.12-1 or more generally: (1+r/inf)^inf-1 = e^r-1 for a given year. Evidently, e^0.12-1 = 0.12749685157937574 or 12.7496%. This would be the maximum return you would possibly get with continuous compounding for r=0.12
Here is also the proof for the more general case when you want to calculate the resulting rate for more than one year:
www.onemathematicalcat.org/Math/Precalculus_obj/continuousCompounding.htm
@@thomas9982 Thanks Thomas.
I'll study in detail you guided and reference given.
I'll come back if any further doubt. Hope you'll clarify if any.
Thanks again for your so much concern.
👍🙏
Why aren't you mentioning interest during this time? 1:30 What an ineffective and incompetent way to go about thing
This is off course not the reason for the log ormal assumption.
@eggtimer2 I agree with you, but can you give me why we use log normal. Because for the explanation given here could be resolved using geometric linking or geometric mean.
@@SD-ze7vu I could.