Quick comment in case this helps someone else: the arithmetic mean is treating each year as independent from the others and the starting value at each year as the new baseline. The geometric mean instead takes into account the returns from previous years and sets the modified values after each year as the new baseline. So instead of 0.2, -0.03, and 0.08, the corrected proportions would be 0.2, -0.03(1.2), and 0.08(1.2)(0.97).
thank you, a further explanation for better understanding is the -100% return (so losing the full investment): In the arithmetic mean it is still just one of several independent numbers -> means, a positive outcome is still possible; within the geometric mean, if you lose everything in let's say the second year, it does not matter (because you multiply with 0) if you make a positive return in third year, your investment is gone, which is the reality.
Hi Matt, great explanation and thank you for it I've been struggling with a question for so long now about parametric VaR. As you may know, 1 part of this method is calculating the average return for the mean of the distribution, but I'm not quite sure if I should use the average on log returns or the average of discrete returns, I tend to associate Geometric mean with log returns and use it for Parametric VaR, but given that you said that for expected values you should use Arithmetic mean I'm so confused on which mean should I use as they may lead to different results: Imagine you have an asset that can only have the following daily returns with 50/50 chance, +50% and -40% discrete returns (the price series would be 100, 60, 90), the log returns would be 40.5% and -51.1%. When you take the average they would be +5% for discrete and -5.27% for log returns. Also, the Geometric mean for the discrete returns would be the same as the Arithmetic mean of the discrete returns. This really confuses me on what mean method should I choose for parametric VaR expected mean. I'll be very thankful for your help with this subject.
I understand both methods. But what I remain confused about is using the Arithmetic method to add percentages to find the mean. I always thought we weren't allowed to add them up and then divide by the total number like we would with regular numbers? I see so many people doing it just like you are, but I don't understand why its allowed because doesn't each percentage represents a different number? in other words were trying to average unlike numbers?
The percentages do represent different "events" but in the arithmetic mean, all events are considered to be equally likely parts of the total sample space (think of a venn diagram with three circles that arent overlapping inside a box. Each circle is an event, and the box is the sample space. You can have a percentage of each circle, but if you add them together and divide by the number you added, you end up with the percentage out of the sample space rather than just one circle
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Quick comment in case this helps someone else: the arithmetic mean is treating each year as independent from the others and the starting value at each year as the new baseline. The geometric mean instead takes into account the returns from previous years and sets the modified values after each year as the new baseline. So instead of 0.2, -0.03, and 0.08, the corrected proportions would be 0.2, -0.03(1.2), and 0.08(1.2)(0.97).
thank you, a further explanation for better understanding is the -100% return (so losing the full investment): In the arithmetic mean it is still just one of several independent numbers -> means, a positive outcome is still possible; within the geometric mean, if you lose everything in let's say the second year, it does not matter (because you multiply with 0) if you make a positive return in third year, your investment is gone, which is the reality.
so say if guy is not reinvesting his dividend from the stock will arithmetic mean work there ?
The simplest explanation about arithmetric v geometric I found on TH-cam. Thanks!
Hi Matt, great explanation and thank you for it
I've been struggling with a question for so long now about parametric VaR. As you may know, 1 part of this method is calculating the average return for the mean of the distribution, but I'm not quite sure if I should use the average on log returns or the average of discrete returns, I tend to associate Geometric mean with log returns and use it for Parametric VaR, but given that you said that for expected values you should use Arithmetic mean I'm so confused on which mean should I use as they may lead to different results:
Imagine you have an asset that can only have the following daily returns with 50/50 chance, +50% and -40% discrete returns (the price series would be 100, 60, 90), the log returns would be 40.5% and -51.1%. When you take the average they would be +5% for discrete and -5.27% for log returns. Also, the Geometric mean for the discrete returns would be the same as the Arithmetic mean of the discrete returns. This really confuses me on what mean method should I choose for parametric VaR expected mean.
I'll be very thankful for your help with this subject.
clean and simple no bs thank you Matt
Hey Matt, I am from Brazil and I don't miss a single video explanation. Thank you!
You're welcome, and happy new year!
Hey Matt I went to Pope, I was a big fan when you played football
@@erinkravchenko1498 It is great to hear from you! I hope all is well.
Great explanation sir...Thank u😊
Excellent video!!
Super well explained, thanks
Brilliant explanation
I understand both methods. But what I remain confused about is using the Arithmetic method to add percentages to find the mean. I always thought we weren't allowed to add them up and then divide by the total number like we would with regular numbers? I see so many people doing it just like you are, but I don't understand why its allowed because doesn't each percentage represents a different number? in other words were trying to average unlike numbers?
I agree that geometric mean can be used to predict, but Arithmetic mean with standard deviation is better
The percentages do represent different "events" but in the arithmetic mean, all events are considered to be equally likely parts of the total sample space (think of a venn diagram with three circles that arent overlapping inside a box. Each circle is an event, and the box is the sample space. You can have a percentage of each circle, but if you add them together and divide by the number you added, you end up with the percentage out of the sample space rather than just one circle
thanks sir
None the wiser
still am confused in geometric part
Arithmetic is to predict future returns
Geometric is to calculate past returns because compounding is built in.