Post inflation returns are not 9% - 2.5% = 6.5%

[ac]

Hi all

It seems to me that the explanation that the market returns 9% on average, and inflation is 2.5% on average, so therefore returns after inflation = 9% -2.5% = 6.5% is all wrong.  For the same reason that a 50% up year followed by a 50% down year does not equal a 0% net.  You can't just add or subtract percentages.

Example
I retire with $1,000,000 invested.  I spend $40,000/yr.

9% * $1,000,000 = $90,000 return
2.5% * $40,000   = $1,000 inflation

$90,000 - $1,000 = $89,000 = 8.9% return after inflation (this number changes for any invested/spending ratio)

So am I missing something?  Because I see this explanation all over the web including from MMM himself. 

Thanks

[Dodge]

Hi all

It seems to me that the explanation that the market returns 9% on average, and inflation is 2.5% on average, so therefore returns after inflation = 9% -2.5% = 6.5% is all wrong.  For the same reason that a 50% up year followed by a 50% down year does not equal a 0% net.  You can't just add or subtract percentages.

Example
I retire with $1,000,000 invested.  I spend $40,000/yr.

9% * $1,000,000 = $90,000 return
2.5% * $40,000   = $1,000 inflation

$90,000 - $1,000 = $89,000 = 8.9% return after inflation (this number changes for any invested/spending ratio)

So am I missing something?  Because I see this explanation all over the web including from MMM himself. 

Thanks

Inflation is applied to both your spending, and your savings.  It's easier to see this when using big numbers.  Let's imagine 50% inflation.  If you have $1,000,000 in the bank, and you experience 50% inflation one year, your inflation adjusted balance is now $500,000.  While the bank balance will still show $1,000,000, its purchasing power has been halved.

When applying inflation to your expenses, it shows up as increased expenses.  When applying inflation to your savings, it shows up as decreased purchasing power.

[ioseftavi]

Returns are multiplied, not added, if you want to be precise.  In financial textbook jargon, so you can play along at home:

An investor earns a 9% nominal return.  She knows that inflation was 2.5%.  What was her real return?

1+Rn = (1+Ri) x (1+Rr)

Rn = Nominal return
Ri = Return due to inflation
Rr = Real return

1+0.09 = 1.025 x (1+Rr)
1.09 = 1.025 x (1+Rr)
1.09 / 1.025 = 1+Rr
1.0634 = 1 + Rr
0.0634 = Rr

Her real return was 0.0634, or 6.34%.  Notice that this is close, but not equal to, her nominal return minus inflation: 9% minus 2.5% = 6.5%.

Most people use real return + inflation = nominal return.  It's "close enough" for most applications, including MMM and others.

If you want to be precise, use the steps above.

EDIT:  I misread your initial post.  I agree with Dodge - you are comparing apples and oranges.

Both your spending and your savings are affected by the 2.5% inflation.  Your yearly spending amount will go UP by 2.5%.  Your overall 'staches purchasing power will go DOWN by 2.5% worth of purchasing power. 

The latter effect (your stache now buys 2.5% less) is not something you can see - all you see is the 9% nominal return, or the fact that your million bucks now shows an account balance of $1,090,000.  But the fact is, your stache actually only buys 6.34% worth of stuff than it did a year ago.  That is, your nominal $1,090,000 buys as much as $1,063,400 did one year ago.  You'll notice that this is the real return I was showing you how to calculate above: this is that 6.34% real rate of return.

Does that make more sense?

[brooklynguy]

You shouldn't be factoring in your spending/withdrawal when calculating your return.  If the market went up 9% over a period, then your nominal return during that period was 9%.  Assuming inflation during that period was 2.5%, your post-inflation return was 7.5% (meaning that at the end of the period your total portfolio has purchasing power 7.5% higher than it did at the beginning of the period).

[dandarc]

Primarily, you're comparing apples and oranges - spending is not the same thing as investment returns.

Secondarily, you're failing to account for the additional capital required to support that inflation increase.  You don't need 1K next and that's it - it is 1K more per year forever.

Year 1 - spending = 40K
Year 2 - spending = 40K + 1,000
Year 3 - spending = 40K + 1,000 + 1,025

and so on.

So in year 2, your portfolio needs to be 1,025,000 to support the 41K spending forever.  Luckily it made 90K in year 1, so you've got 40K to spend, 25K to support the inflation increase in year 2, and another 25K of extra growth.

[Chuck]

I'd just like to say how happy I am that inflation is super low right now.

[ac]

Thanks all

I appreciate understanding why people cite the 6.5% number.  Reminding me that inflation affects the purchasing power of my investments was especially helpful. 

I still do have a fundamentally different perspective than the one you are describing.  For example, the effects of inflation on my investments' purchasing power assumes I'm looking to purchase something in the short term with a significant amount of my investments. 

For my own forecasting, I will continue to decouple the investment return percentage and the inflation percentage.  But I see why you might couple them. 

[hamildub]

You make a great point, the fact that we calculate "returns" on our holdings is actually a fallacy. Until a gain is realized it's only theoretical, the same with inflation - it has no impact unless you're actually buying something. Inflation, as it is calculated is not really a good measure of anything except a general trend on a very select basket of goods.

I personally do not factor inflation into any investment return calculations for the reasons above. if you really wanted to get serious about tracking inflation to make sure your not drawing down too much capital you'd need to track the pricing of the stuff you actually buy.

[netskyblue]

Where exactly does the 2.5% inflation number come from?  My expenses haven't increased 2.5%/year.

My 2 biggest expenses, rent & taxes haven't increased in YEARS (nor has my income).  I mean, rent's gone up $25 in 7 years (used to be $725, now $750).  The price of groceries has gone up, sure.  Not gonna argue that a gallon of milk costs more now than it did a year or 2 ago.  But commodities like that are a small part of my budget. 

Rent & taxes are over 63% of my spending, though.  And my budgeted amounts on non-necessaries don't go up, even if prices do.  So my $40 budget for eating out per month - even if costs go up, it just means I eat out less, not that I spend more.

It's really only the necessities that inflation counts against - housing, food, utilities, insurance, transportation. 

I feel like I can pretty much guarantee that my spending in 2016 will not be 2015's spending * 1.025. 

But embracing mustachianism alone had me slash my spending 17% from 2012 to 2013 and another 17% from 2013 to 2014.  I'm coming close to "the bottom" without cutting out all fun, just waste.  Within a couple years I expect to bottom out, and I'll watch my spending after that, but I'd be very surprised if it went up 2.5% every year.

[skyrefuge]

I feel like I can pretty much guarantee that my spending in 2016 will not be 2015's spending * 1.025. 

That's only because you're suffering from recency bias. The "2.5%" number given in this thread is some sort of long-term average. There is considerable underlying variability that the average doesn't show. Over the last 6 years, prices have increased only 9% in total, averaging to 1.4% per year. That's a historically low inflation rate. In the 1970s, seeing that 9% price increase in a single year was "normal".

So yes, you're currently seeing very little inflation, but that doesn't mean the current trend will continue indefinitely. If you had been around in the 1970s, you would have instead been shocked to see that your expenses "only" went up by 2.5% in a year (seriously, the numbers from 1979, 1980, and 1981 were 11.2%, 13.8%, and 10.4%.) The flexibility inherent in Mustachianism means that you might be able to mitigate some effects of inflation in the short term, but eventually it will catch up with you, and woe will rain down upon the early retiree who ignores it.

I personally do not factor inflation into any investment return calculations for the reasons above. if you really wanted to get serious about tracking inflation to make sure your not drawing down too much capital you'd need to track the pricing of the stuff you actually buy.

"I personally do not factor weather reports into my decision about what to wear. The weather reporting station is not right at my front door, so it doesn't apply to me. Instead, I step outside naked every morning and then start putting on clothes until I feel warm enough." Yes, of course a statistically-compiled CPI is never going to reflect your exact personal experience, but until you develop your own personal CPI (you won't) and somehow figure out how to project it into the future, you'll be way better off simply using it than ignoring it.

[Sid Hoffman]

The inflation adjusted total return of the S&P 500 alone (not counting diversification into bonds, which have a strong correlation with inflation) is upwards of 6% after inflation for virtually any 30-year time period in the history of the market.  I say that after spending a while looking at what time periods are the worst in the cFIREsim tool and then running simulations in the CAGR tool with inflation and reinvestment of dividends checked.

Seriously, the worst I could possibly make it look was by cherry picking years and using the CAGR tool to run a 35-year period from Jan 1 1973 to Dec 31 2008.  That still gets you a 4.51% annualized return after inflation with dividends included.  Those first two years are killers, yes, but if you have a smart strategy where you pull from cash & bonds to get you through those first two years, before dipping into the stock portion of your portfolio, you make a killing every year after that as you take some of those returns to rebalance and build up the cash/bond portion of your portfolio.

I'm not saying anyone should ignore inflation, but it's a bit of a bogeyman in the developed world.  The true working poor simply don't have savings and their wages tend to keep pace with what's needed for their basic living expenses.  The middle class also doesn't have much to worry about as their wages also generally move related to inflation and the commonality of 401k accounts invested in stock as well as home ownership over 60% (homes with fixed rate mortgages are a hedge against inflation) and extremely low amounts of actual savings account savings mean the middle class doesn't have much to lost to inflation either.  The rich are already smart enough to put their money in investments that provide inflated adjusted yields, regardless if that's stock, direct ownership of businesses, or commercial properties where rents move in line with inflation.

The only people who are at risk to inflation are people who have large sums of cash and then dump all that money in CDs, treasuries, savings accounts, or other such things without a properly diversified portfolio.  Given all the stats showing how little the average American has saved up in the first place, these are genuinely rare cases.

[skyrefuge]

The only people who are at risk to inflation are people who have large sums of cash and then dump all that money in CDs, treasuries, savings accounts, or other such things without a properly diversified portfolio.  Given all the stats showing how little the average American has saved up in the first place, these are genuinely rare cases.

What? Because non-Mustachians aren't terribly affected by inflation, that means Mustachians shouldn't care about inflation? Who cares about "normal" people at this forum?

You seem to overestimate the correlation between inflation and stock market returns. Using cFIREsim with a 100% stock portfolio, a 40-year period, and a 95% success-threshold, it gives a 5.34% SWR if I ignore inflation, vs. a 3.61% SWR if I use historical inflation. That's a 48% difference in required stash size! If I do a 4% WR on a starting balance of $1M, the median final balance is $16M in the inflation-ignoring case vs. $2.5M in the real-world case!

Sure, for retirement planning, the average person doesn't need to concern themselves too much about inflation. But that's only because those who actually do the thinking about this (developers of the 4% rule, Social Security, etc.) have already done with work while understanding how critical it is to include inflation. If they ignored inflation when creating their advice/products, everyone would be fucked.

[Sid Hoffman]

You seem to overestimate the correlation between inflation and stock market returns. Using cFIREsim with a 100% stock portfolio, a 40-year period, and a 95% success-threshold, it gives a 5.34% SWR if I ignore inflation, vs. a 3.61% SWR if I use historical inflation. That's a 48% difference in required stash size! If I do a 4% WR on a starting balance of $1M, the median final balance is $16M in the inflation-ignoring case vs. $2.5M in the real-world case!

Nobody with a brain should uncheck the inflation button.  Ugh, stop being a drama queen.

[hamildub]

I feel like I can pretty much guarantee that my spending in 2016 will not be 2015's spending * 1.025. 

That's only because you're suffering from recency bias. The "2.5%" number given in this thread is some sort of long-term average. There is considerable underlying variability that the average doesn't show. Over the last 6 years, prices have increased only 9% in total, averaging to 1.4% per year. That's a historically low inflation rate. In the 1970s, seeing that 9% price increase in a single year was "normal".

So yes, you're currently seeing very little inflation, but that doesn't mean the current trend will continue indefinitely. If you had been around in the 1970s, you would have instead been shocked to see that your expenses "only" went up by 2.5% in a year (seriously, the numbers from 1979, 1980, and 1981 were 11.2%, 13.8%, and 10.4%.) The flexibility inherent in Mustachianism means that you might be able to mitigate some effects of inflation in the short term, but eventually it will catch up with you, and woe will rain down upon the early retiree who ignores it.

I personally do not factor inflation into any investment return calculations for the reasons above. if you really wanted to get serious about tracking inflation to make sure your not drawing down too much capital you'd need to track the pricing of the stuff you actually buy.

"I personally do not factor weather reports into my decision about what to wear. The weather reporting station is not right at my front door, so it doesn't apply to me. Instead, I step outside naked every morning and then start putting on clothes until I feel warm enough." Yes, of course a statistically-compiled CPI is never going to reflect your exact personal experience, but until you develop your own personal CPI (you won't) and somehow figure out how to project it into the future, you'll be way better off simply using it than ignoring it.

Actually I do have a thermometer outside that I reference, rather than the weather from the airport that's 40km from my place and then dress accordingly. ;)

The thing is, what value is there in calculating my investment returns "post-inflation"? The more uncertain variables we add to investment calculation, the greater the margin of error we create. Thus when I want to know what my investment performance is, I do not include inflation. If, on the other hand I wanted to compare my overall purchasing power on Day 1 to day N I would use whatever the CPI was for that for period. That being said, another poster mentioned their expenses didn't follow CPI, neither did mine and there's no good way to predict how that may play out. Of course calculating inflation adjusted returns is well within the norms of portfolio management theory, and I'm taking a bit of a contrarian stance on it.

[dragoncar]

Hi all

It seems to me that the explanation that the market returns 9% on average, and inflation is 2.5% on average, so therefore returns after inflation = 9% -2.5% = 6.5% is all wrong.  For the same reason that a 50% up year followed by a 50% down year does not equal a 0% net.  You can't just add or subtract percentages.

Example
I retire with $1,000,000 invested.  I spend $40,000/yr.

9% * $1,000,000 = $90,000 return
2.5% * $40,000   = $1,000 inflation

$90,000 - $1,000 = $89,000 = 8.9% return after inflation (this number changes for any invested/spending ratio)

So am I missing something?  Because I see this explanation all over the web including from MMM himself. 

Thanks

I know people are saying you don't apply inflation to spending, but I think it can be done that way too.  Using your numbers:

2.5% inflation on $40k annual budget - next year you spend $41k.
9% returns on $1 million - next year you have $1090k

But how much do you need?  $41k * 25 = $1025k

So you how much better off are you?  You have $1090k and need $1025k.  1090/1025=1.0634, i.e., 6.34% real return

This exactly matches what ioseftavi said, only approaching the math from an expenses point of view.