Comments on: Compounding–not as simple as it might seem. http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/ Mon, 15 Mar 2010 15:15:51 +0000 http://wordpress.org/?v=2.9.1 hourly 1 By: Moolanomy weekly roundup #12: “Hello Readers” edition | Moolanomy http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-264 Moolanomy weekly roundup #12: “Hello Readers” edition | Moolanomy Sun, 14 Oct 2007 14:01:32 +0000 http://financefreelancelife.com/?p=100#comment-264 [...] Compounding–not as simple as it might seem @ Mrs. Micah — It really isn’t. In finance, average normally refers to CAGR (geometric mean) and not the arithmetic mean. This is a perfect example. [...] [...] Compounding–not as simple as it might seem @ Mrs. Micah — It really isn’t. In finance, average normally refers to CAGR (geometric mean) and not the arithmetic mean. This is a perfect example. [...]

]]> By: Andrew Stevens http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-263 Andrew Stevens Fri, 12 Oct 2007 19:32:39 +0000 http://financefreelancelife.com/?p=100#comment-263 Take heart. As John Von Neumann famously said, "In mathematics, you don't understand things. You just get used to them." Though if you understand exponents, you already understand logarithms and just don't know it yet. Take heart. As John Von Neumann famously said, “In mathematics, you don’t understand things. You just get used to them.” Though if you understand exponents, you already understand logarithms and just don’t know it yet.

]]> By: Mrs. Micah http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-262 Mrs. Micah Fri, 12 Oct 2007 18:45:33 +0000 http://financefreelancelife.com/?p=100#comment-262 Very nice, Andrew. Though I must say it's intimidating even for me. I suppose if I sat down with a book and a spreadsheet...but once logarithms come into play I start to look worried. Thanks, though, I think I see what you're driving at, I just wouldn't know how to do it. Very nice, Andrew. Though I must say it’s intimidating even for me. I suppose if I sat down with a book and a spreadsheet…but once logarithms come into play I start to look worried. Thanks, though, I think I see what you’re driving at, I just wouldn’t know how to do it.

]]> By: Andrew Stevens http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-261 Andrew Stevens Fri, 12 Oct 2007 18:40:36 +0000 http://financefreelancelife.com/?p=100#comment-261 Since you're a spreadsheet geek, you might appreciate that APY is calculated as a mean, but as a geometric mean rather than an arithmetic mean. The geometric mean is defined as the n-th root of the product of n numbers. To use my prior example, the cube root of .8 * 1.288 * 1.288 (losing 20%, and then two years of gaining 28.8%) is 1.099 or 9.9%. To calculate the APY then, we take the final value ($1327.37), divide it by the original investment ($1000) and then take the n-th root (n being number of years of investment, in this case the cube root). This gives us 1.099 or 9.9%. For the truly geeky, geometric means can also be calculated as arithmetic means, but they're the arithmetic mean of the natural logs (and then you exponentiate the final result to translate it back). I.e. exp((ln(.8)+ln(1.288)+ln(1.288))/3) = 1.099. The reason this method is used to calculate APY is because what we really care about is the final yield, not the individual pieces that went into it. The good news is that APY does mean what you want it to mean. (The bad news is that past performance is no guarantee of future results.) Since you’re a spreadsheet geek, you might appreciate that APY is calculated as a mean, but as a geometric mean rather than an arithmetic mean.

The geometric mean is defined as the n-th root of the product of n numbers. To use my prior example, the cube root of .8 * 1.288 * 1.288 (losing 20%, and then two years of gaining 28.8%) is 1.099 or 9.9%. To calculate the APY then, we take the final value ($1327.37), divide it by the original investment ($1000) and then take the n-th root (n being number of years of investment, in this case the cube root). This gives us 1.099 or 9.9%.

For the truly geeky, geometric means can also be calculated as arithmetic means, but they’re the arithmetic mean of the natural logs (and then you exponentiate the final result to translate it back). I.e. exp((ln(.8)+ln(1.288)+ln(1.288))/3) = 1.099.

The reason this method is used to calculate APY is because what we really care about is the final yield, not the individual pieces that went into it. The good news is that APY does mean what you want it to mean. (The bad news is that past performance is no guarantee of future results.)

]]> By: Andrew Stevens http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-260 Andrew Stevens Fri, 12 Oct 2007 08:53:43 +0000 http://financefreelancelife.com/?p=100#comment-260 When people talk about APY, they're talking about CAGR (compound annual growth rate). I.e., if I invested $1000 and received a 9.9% APY over three years, that means I have $1327.37 in my investment after three years. How I got there isn't relevant. I could have made 9.9% every year, or I could have lost 20% in year 1 and then made 28.8% each year over the next two years (which has an arithmetic mean of 12.5%, but the same APY of 9.9%), or any of an infinite number of other combinations. When people talk about APY, they’re talking about CAGR (compound annual growth rate). I.e., if I invested $1000 and received a 9.9% APY over three years, that means I have $1327.37 in my investment after three years. How I got there isn’t relevant. I could have made 9.9% every year, or I could have lost 20% in year 1 and then made 28.8% each year over the next two years (which has an arithmetic mean of 12.5%, but the same APY of 9.9%), or any of an infinite number of other combinations.

]]> By: Mrs. Micah http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-259 Mrs. Micah Thu, 11 Oct 2007 11:09:10 +0000 http://financefreelancelife.com/?p=100#comment-259 @ Pinyo, you're right, I did the arithmetic mean. Good point, that we can mean different things by "average." If we looked at the end gain and said it came out to an average of x, that would be different. @ Swamproot, I poked around a bit, but there wasn't anything (and I can't do intense internet research at work) which had a nice chart of the percentage returns by year for an index fund. 4-17 is indeed optimistic. It's also a result of me saying "Hmm...(supposedly) random number generator...hmmm" ;) @ Pinyo, you’re right, I did the arithmetic mean. Good point, that we can mean different things by “average.” If we looked at the end gain and said it came out to an average of x, that would be different.

@ Swamproot, I poked around a bit, but there wasn’t anything (and I can’t do intense internet research at work) which had a nice chart of the percentage returns by year for an index fund. 4-17 is indeed optimistic. It’s also a result of me saying “Hmm…(supposedly) random number generator…hmmm” ;)

]]> By: Swamproot http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-258 Swamproot Thu, 11 Oct 2007 06:39:33 +0000 http://financefreelancelife.com/?p=100#comment-258 I'm sorry I didn't actually look at the spreadsheet, but I wanted to take issue with "wild jumps from 4% APY to 17% APY". 4% might be a very optimistic bottom end for the sort of 'non-bank' investments one should probably lean to if one were in their twenties, IMHO. This is just a fellow PF student's half-ass opinion but knowing what I do now, I would say be prepared for more dramatic losses than "only" a 4% gain. I lost a little money in the late 90's tech boom, proof that advice like "invest in what you know" is not always foolproof. But it was a wonderful lesson in not taking such "exuberance" for granted and that it actually should be your second job to manage your money right, including learning all the boring details about investing. But now for better or worse I'm a little obsessed about it. :-) As risk averse as this experience made me, I'm sure you know already that there would be expectable down years in a properly aggressive retirement or long term investment portfolio for a person starting in their 20's or 30's. But it might be appropriate to mention in the context of this article. That seems to be a big problem with beginning investors, being scared to lose money. That might be something to address, if you ever expect gains in an investment over 10%, be prepared for losses some years. [I just made that up, so don't quote me. Unless its totally correct. :-) ] I’m sorry I didn’t actually look at the spreadsheet, but I wanted to take issue with “wild jumps from 4% APY to 17% APY”. 4% might be a very optimistic bottom end for the sort of ‘non-bank’ investments one should probably lean to if one were in their twenties, IMHO. This is just a fellow PF student’s half-ass opinion but knowing what I do now, I would say be prepared for more dramatic losses than “only” a 4% gain.

I lost a little money in the late 90’s tech boom, proof that advice like “invest in what you know” is not always foolproof. But it was a wonderful lesson in not taking such “exuberance” for granted and that it actually should be your second job to manage your money right, including learning all the boring details about investing. But now for better or worse I’m a little obsessed about it. :-)

As risk averse as this experience made me, I’m sure you know already that there would be expectable down years in a properly aggressive retirement or long term investment portfolio for a person starting in their 20’s or 30’s. But it might be appropriate to mention in the context of this article.

That seems to be a big problem with beginning investors, being scared to lose money. That might be something to address, if you ever expect gains in an investment over 10%, be prepared for losses some years. [I just made that up, so don't quote me. Unless its totally correct. :-) ]

]]> By: Pinyo http://financefreelancelife.com/2007/10/10/compounding-not-as-simple-as-it-might-seem/#comment-257 Pinyo Thu, 11 Oct 2007 03:18:49 +0000 http://financefreelancelife.com/?p=100#comment-257 How are you doing the average? Because if they are the same CAGR, the end result should be the same. Sounds like you did arithmetic mean. How are you doing the average? Because if they are the same CAGR, the end result should be the same. Sounds like you did arithmetic mean.

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