5 ms·

> That comes from the fact that they don't understand the data they are dealing with (as you said with dimensions). You cannot use the arithmetic mean on intere

by darawk 6y ago

> That comes from the fact that they don't understand the data they are dealing with (as you said with dimensions). You cannot use the arithmetic mean on interest rates because it does not make sense to add them up. If you just go for the geometric mean "because it's a rate and I have read online I should use geometric mean" then you won't learn why you need to use the geometric mean. This isn't quite correct. You can take the arithmetic mean of interest rates, and it is meaningful. The ensemble average of interest rates might tell you the expectation of interest rates over a class of instruments at a point in time. However, if you want to know the compound growth rate of a single instrument or portfolio, then you're going to need to use the geometric mean.

ttoinou 6y ago
You can average mathematically anything you want but it won't have the unit you want it attached, and the meaning you would like. Averages of interest rates, are not interest rates
- darawk 6y ago
  Yes they are. They are expectations of interest rates, as I said. Ensemble averages of interest rates are plenty meaningful.
  - ttoinou 6y ago
    Meaningful how ? If product A grows by 20% and product B grows by 50%, what are you going to do with 1.2 and 1.5 exactly ? (1.2+1.5)/2 has what meaning ?
    - darawk 6y ago
      In your specific example, the company is very interested in the ensemble average of their products growth rates, because that represents their rolled up revenue growth rate at a point in time (weighted by sales of each, of course). An alternate example is the ensemble average of all corporate bonds in a particular ETF. People who hold that ETF are very interested in this number, because it represents the interest rate that they're earning when they hold that basket of bonds. In both examples they are also interested in the geometric (time averaged) growth rate as well, because that represents their steady state earnings over time. What they really care about, in both examples, is the time-averaged rate of the ensemble rates.
      - ttoinou 6y ago
        > weighted by sales of each, of course So you are averaging amounts of money, so you are averaging things that can be added and you are not averaging interest rates. So you're not doing what you think you were doing and everything is good. (1.2+1.5)/2 doesn't have a meaning but (1.2moneyA+1.5moneyB)/2=moneyAB and growth rate has nothing to do here > because it represents the interest rate that they're earning when they hold that basket of bonds No it doesn't. Look at my example, you would think that the arithmetic average growth rate is 1.35. But now if I told you product A is in fact made up of two subproducts, one is not growing (1) and the others is growing a lot (2), you would compute a new average of (1+2+1.5)/3=1.5
        darawk 6y ago
        > So you are averaging amounts of money, so you are averaging things that can be added and you are not averaging interest rates. So you're not doing what you think you were doing and everything is good. (1.2+1.5)/2 doesn't have a meaning but (1.2moneyA+1.5moneyB)/2=moneyAB and growth rate has nothing to do here You're taking a weighted average of interest rates. You can call it an amount of money if you like, but you can also call it a weighted average of interest rates. This is no different from a weighted average of time-varying interest rates over irregular intervals of time.

by darawk 6y ago

ttoinou 6y ago

You can average mathematically anything you want but it won't have the unit you want it attached, and the meaning you would like. Averages of interest rates, are not interest rates

darawk 6y ago
Yes they are. They are expectations of interest rates, as I said. Ensemble averages of interest rates are plenty meaningful.
- ttoinou 6y ago
  Meaningful how ? If product A grows by 20% and product B grows by 50%, what are you going to do with 1.2 and 1.5 exactly ? (1.2+1.5)/2 has what meaning ?
  - darawk 6y ago
    In your specific example, the company is very interested in the ensemble average of their products growth rates, because that represents their rolled up revenue growth rate at a point in time (weighted by sales of each, of course). An alternate example is the ensemble average of all corporate bonds in a particular ETF. People who hold that ETF are very interested in this number, because it represents the interest rate that they're earning when they hold that basket of bonds. In both examples they are also interested in the geometric (time averaged) growth rate as well, because that represents their steady state earnings over time. What they really care about, in both examples, is the time-averaged rate of the ensemble rates.
    - ttoinou 6y ago
      > weighted by sales of each, of course So you are averaging amounts of money, so you are averaging things that can be added and you are not averaging interest rates. So you're not doing what you think you were doing and everything is good. (1.2+1.5)/2 doesn't have a meaning but (1.2moneyA+1.5moneyB)/2=moneyAB and growth rate has nothing to do here > because it represents the interest rate that they're earning when they hold that basket of bonds No it doesn't. Look at my example, you would think that the arithmetic average growth rate is 1.35. But now if I told you product A is in fact made up of two subproducts, one is not growing (1) and the others is growing a lot (2), you would compute a new average of (1+2+1.5)/3=1.5
      - darawk 6y ago
        > So you are averaging amounts of money, so you are averaging things that can be added and you are not averaging interest rates. So you're not doing what you think you were doing and everything is good. (1.2+1.5)/2 doesn't have a meaning but (1.2moneyA+1.5moneyB)/2=moneyAB and growth rate has nothing to do here You're taking a weighted average of interest rates. You can call it an amount of money if you like, but you can also call it a weighted average of interest rates. This is no different from a weighted average of time-varying interest rates over irregular intervals of time.