4 ms·

How Much Is Enough? A Formula for FU Money

20 points by skbohra123 14y ago

compsciphd 14y ago
your FU money formula doesn't work. don't have time to figure out where you might have made a transcription error.
- nileshtrivedi 14y ago
  I have verified the formula by simulations in excel. Perhaps you're doing something wrong.
  - gibybo 14y ago
    He's right. I'm not sure what your 'simulation' involves, but it's possible you just happened to pick numbers where the ratio produces similar results to the difference. Try inflation = 0.0001% and interest = 10%, for example.
    - nileshtrivedi 14y ago
      r stands for F/I which is (1+f)/(1+i). This terminology seems to be creating a lot of confusion. I will add a clarification. :)
      - deleted 14y ago
        [deleted]
gibybo 14y ago
It's not the ratio of interest to inflation that matters, it's the difference. The easiest way to conceptualize it is to consider an inflation rate of near-0, or even negative. The ratio would imply a months salary would be sufficient FU money if you could invest it at even 1%. A slightly more mathematical example: Consider $100 in today's money. Invested at 10% annually, it will become 100 * 1.1^25 = $1,083 in 25 years. If inflation is 1%, it will require $100 * 1.01^25 = $128 for every $100 in today's money, thus the $1,083 is worth $846 in today's money. If inflation is 2%, it will require $164, or $660. Despite the F/I ratio doubling, the difference is only ~22% after 25 years. If you use ((1+I) - F), you can achieve the same $846 and $660 numbers with a very straightforward calculation: S_0 * ((1+I)-F)^N e.g. $100 * (1.10 - 0.01) = $846, $100 * (1.10 - 0.02) = $660 EDIT: Also, you mention the it is very hard to get r below 0.9, but it's not really. Or at least, it hasn't been for the last 100 years (I am not able to predict the next 100 years as accurately as the past). The average inflation rate of the US Dollar for the past 100 years is roughly 3% and the average annual return of the S&P 500 is 10%. That would produce an r = 0.3, well below 0.9.
- nileshtrivedi 14y ago
  r = F/I = (1+f)/(1+i) according to what I have defined. So inflation of 3% and return of 10% means r = 1.03 / 1.1 = 0.9363, not 0.3.
  - gibybo 14y ago
    Sorry, I missed the F = (1+f)/R = (1+r) line. Pretty sure the rest of my argument holds though. Your formula merely approximates the correct answer for low values of i and f.
- nileshtrivedi 14y ago
  I also left out explanation for the edge cases. For low enough values of r, savings will never decrease and never reach zero. For practical values of r, the equation is correct.
  - gibybo 14y ago
    Ok I think I've got a counter example. First of all, I'm only going to consider values where N approaches infinity && r < 1 && r > 0 to make the math easier. lim [n-> inf, r < 1, r > 0 ] of S_0 = E_0 (1-r^n)/(1-r) -> S_0 = E_0 * 1 / (1-r) I propose that the actual relationship is: S_0 = E_0 / (i-f) E_0=1,f=.07,i=.10 - Original: S_0 = 36.666..., My proposal: S_0 = 33.333... E_0=1,f=.80,i=1.00 - Original: S_0 = 10, My proposal: S_0 = 5 So it seems your formula approximates mine at low values of i and f, but diverges strongly at higher values. I believe I can show mine is the correct one with a small amount of intuition when we let f=0: If I make 10% annually in interest, then $1mil will provide $100k/year forever. The same thing more concisely: i * S_0 = E_0 r = F/I = (1+0/1+i) After substitution and division, your formula is E_0 = S_0 / ((i+1)/i) In words: If I make 10% annually in interest, then $1mil will provide $90.9k/year forever, which is intuitively false.
    - nileshtrivedi 14y ago
      It is not. As I mentioned in the post, you need to set aside the money for the year's expenses at the beginning of the year. $1mil provides $90.9k/year because (1m - 90.9k)*0.1 = 90.9k. Interest is received at the end of the period but we need cash in hand throughout the year to pay for the expenses.
HockeyPlayer 14y ago
Conservatively, a portfolio can produce 3% over inflation forever. So you need to start with 33x your desired annual spending. Aggressively is 5%, which means you need 20x your spending.
- nileshtrivedi 14y ago
  This is an overestimate because you don't need perpetual income. You only need income till your death. So for the case when portfolio return is 3% higher than inflation, 21x of your spending is fine (assuming 30 years of life after retirement).
sopooneo 14y ago
"Research has found that there is a connection between wealth and happiness, but only upto a limit. The beneficial effects of wealth taper off almost entirely once a comfortable living standard is reached". But which study? I've heard that thrown around a lot, and probably with citation a few times. But I don't see a linked study here, and I recently read (or heard, maybe on Radiolab?) that further studies have contradicted that. And in fact various happiness metrics increase pretty much linearly with wealth. And they came at it from another angle, saying that the biggest jump after basic security comes when you have somewhat more than others around you. That is, are you richer than your neighbor? Does he covet your ox?
- nileshtrivedi 14y ago
  Absolutely. I think there's a lot more we're yet to understand about the connection between wealth and happiness. Here is one research which was cited in the NYTimes article: http://www.people.hbs.edu/mnorton/aknin%20norton%20dunn%202009.pdf http://www.people.hbs.edu/mnorton/aknin%20norton%20dunn%2020... However, this point is not central to my post. My analysis is only concerned with how much savings we need to live a particular lifestyle for a given number of years - including the effect of inflation. I had seen many people using heuristics like this: If you can beat inflation by 3%, 100/3 = 33x times your annual expenditure is your FU money. That turned out to be incorrect because of not considering the life expectancy, and cash flow. Also the critical variable turned out to be (1 + interest rate) / (1 + inflation rate) instead of (interest rate - inflation rate) which can be significant. As I commented elsewhere, 21x may be sufficient instead of 33x. That's what the post is about.
pmiller2 14y ago
I'd just like to point out that the word "tax" does not appear in the article. You need to be sure to include taxes inside the E_n term. This is a bit problematic, since tax rates can and do change, but you can estimate using historical values if you like. Other than that, it looks good to me. :)

20 points by skbohra123 14y ago

compsciphd 14y ago

your FU money formula doesn't work. don't have time to figure out where you might have made a transcription error.

nileshtrivedi 14y ago
I have verified the formula by simulations in excel. Perhaps you're doing something wrong.
- gibybo 14y ago
  He's right. I'm not sure what your 'simulation' involves, but it's possible you just happened to pick numbers where the ratio produces similar results to the difference. Try inflation = 0.0001% and interest = 10%, for example.
  - nileshtrivedi 14y ago
    r stands for F/I which is (1+f)/(1+i). This terminology seems to be creating a lot of confusion. I will add a clarification. :)
    - deleted 14y ago
      [deleted]

gibybo 14y ago

It's not the ratio of interest to inflation that matters, it's the difference. The easiest way to conceptualize it is to consider an inflation rate of near-0, or even negative. The ratio would imply a months salary would be sufficient FU money if you could invest it at even 1%. A slightly more mathematical example: Consider $100 in today's money. Invested at 10% annually, it will become 100 * 1.1^25 = $1,083 in 25 years. If inflation is 1%, it will require $100 * 1.01^25 = $128 for every $100 in today's money, thus the $1,083 is worth $846 in today's money. If inflation is 2%, it will require $164, or $660. Despite the F/I ratio doubling, the difference is only ~22% after 25 years. If you use ((1+I) - F), you can achieve the same $846 and $660 numbers with a very straightforward calculation: S_0 * ((1+I)-F)^N e.g. $100 * (1.10 - 0.01) = $846, $100 * (1.10 - 0.02) = $660 EDIT: Also, you mention the it is very hard to get r below 0.9, but it's not really. Or at least, it hasn't been for the last 100 years (I am not able to predict the next 100 years as accurately as the past). The average inflation rate of the US Dollar for the past 100 years is roughly 3% and the average annual return of the S&P 500 is 10%. That would produce an r = 0.3, well below 0.9.

nileshtrivedi 14y ago
r = F/I = (1+f)/(1+i) according to what I have defined. So inflation of 3% and return of 10% means r = 1.03 / 1.1 = 0.9363, not 0.3.
- gibybo 14y ago
  Sorry, I missed the F = (1+f)/R = (1+r) line. Pretty sure the rest of my argument holds though. Your formula merely approximates the correct answer for low values of i and f.
nileshtrivedi 14y ago
I also left out explanation for the edge cases. For low enough values of r, savings will never decrease and never reach zero. For practical values of r, the equation is correct.
- gibybo 14y ago
  Ok I think I've got a counter example. First of all, I'm only going to consider values where N approaches infinity && r < 1 && r > 0 to make the math easier. lim [n-> inf, r < 1, r > 0 ] of S_0 = E_0 (1-r^n)/(1-r) -> S_0 = E_0 * 1 / (1-r) I propose that the actual relationship is: S_0 = E_0 / (i-f) E_0=1,f=.07,i=.10 - Original: S_0 = 36.666..., My proposal: S_0 = 33.333... E_0=1,f=.80,i=1.00 - Original: S_0 = 10, My proposal: S_0 = 5 So it seems your formula approximates mine at low values of i and f, but diverges strongly at higher values. I believe I can show mine is the correct one with a small amount of intuition when we let f=0: If I make 10% annually in interest, then $1mil will provide $100k/year forever. The same thing more concisely: i * S_0 = E_0 r = F/I = (1+0/1+i) After substitution and division, your formula is E_0 = S_0 / ((i+1)/i) In words: If I make 10% annually in interest, then $1mil will provide $90.9k/year forever, which is intuitively false.
  - nileshtrivedi 14y ago
    It is not. As I mentioned in the post, you need to set aside the money for the year's expenses at the beginning of the year. $1mil provides $90.9k/year because (1m - 90.9k)*0.1 = 90.9k. Interest is received at the end of the period but we need cash in hand throughout the year to pay for the expenses.

HockeyPlayer 14y ago

Conservatively, a portfolio can produce 3% over inflation forever. So you need to start with 33x your desired annual spending. Aggressively is 5%, which means you need 20x your spending.

nileshtrivedi 14y ago
This is an overestimate because you don't need perpetual income. You only need income till your death. So for the case when portfolio return is 3% higher than inflation, 21x of your spending is fine (assuming 30 years of life after retirement).

sopooneo 14y ago

"Research has found that there is a connection between wealth and happiness, but only upto a limit. The beneficial effects of wealth taper off almost entirely once a comfortable living standard is reached". But which study? I've heard that thrown around a lot, and probably with citation a few times. But I don't see a linked study here, and I recently read (or heard, maybe on Radiolab?) that further studies have contradicted that. And in fact various happiness metrics increase pretty much linearly with wealth. And they came at it from another angle, saying that the biggest jump after basic security comes when you have somewhat more than others around you. That is, are you richer than your neighbor? Does he covet your ox?

nileshtrivedi 14y ago
Absolutely. I think there's a lot more we're yet to understand about the connection between wealth and happiness. Here is one research which was cited in the NYTimes article: http://www.people.hbs.edu/mnorton/aknin%20norton%20dunn%202009.pdf http://www.people.hbs.edu/mnorton/aknin%20norton%20dunn%2020... However, this point is not central to my post. My analysis is only concerned with how much savings we need to live a particular lifestyle for a given number of years - including the effect of inflation. I had seen many people using heuristics like this: If you can beat inflation by 3%, 100/3 = 33x times your annual expenditure is your FU money. That turned out to be incorrect because of not considering the life expectancy, and cash flow. Also the critical variable turned out to be (1 + interest rate) / (1 + inflation rate) instead of (interest rate - inflation rate) which can be significant. As I commented elsewhere, 21x may be sufficient instead of 33x. That's what the post is about.

pmiller2 14y ago

I'd just like to point out that the word "tax" does not appear in the article. You need to be sure to include taxes inside the E_n term. This is a bit problematic, since tax rates can and do change, but you can estimate using historical values if you like. Other than that, it looks good to me. :)