Soliciting Inputs
Seven posts in, and I still haven't managed to chase everyone away! One of the most satisfying things about sharing these blogs with you is that I get the chance to talk to people offline about the different models. I mean, I'd probably be making spreadsheets for many of these things anyways, but now instead of relegating them to a random folder on my desktop I get to chat with people who have different (and sometimes better) ways of looking at these things. By all means, let me know if there is something that you think aTo that point, one of the first things my friend Ryan asked me was, "How much should I contribute to my IRA? Can you model that?"
The answer is yes. Yes I can.
First off, I guess I should reiterate that I am not a financial planner, and you should make your own financial decisions, keeping in mind what is best for you. Secondly, you should totally invest in bytecoins. By definition they should be 8 times more valuable than bitcoins.
Thirdly, fill up your IRAs if it makes sense to do so. I could (and will) go through a ton of math and modeling, but all of that pales in comparison to one piece of logic: if something has limits to check its power, it is likely to be very powerful indeed. The limits on IRA contributions tell me that, in the absence of these limits, people would abuse the system for their own gain. This means that there is likely no "sweet spot" where you should only partially fill up your IRA, but instead you should take it to the limit each year if you can.
To Roth or Not to Roth
I'm not going to go into the advantages of Traditional vs Roth IRAs too much, but one way to think of it is this:- If you are going to be taxed more now than you are later, choose a Traditional IRA. They let you evade some tax now in exchange for taxing your distribution later.
- If you are going to be taxed more later than you are now, choose a Roth IRA. The contributions are taxed normally, but the distributions are not taxed.
One funny side benefit of the Roth IRA, and the reason I will use it for today's post, is that it is much easier to model. Unless you were going to spend your money on something tax deductible, investing in a Roth IRA basically allows you to ignore tax all together, which takes out an extremely complicated variable. I'll just assume that if you have $5500 to contribute to an IRA, it has already been taxed, and would otherwise have been spent on something fun like a year's worth of coffee or a 3-D printer (and not, for instance, your pain medication, last month's mortgage payment, or a donation to your church).
Competing Interests, aka Saver's Remorse
Before we get to the modeling, lets first predict what we want the model output to look like. For most people, what they want their IRA investment to pay for is, wait for it... retirement. (I know, it seems silly because it is right in the name "Individual Retirement Account", but you can take out money for your first house or pay penalties to take it out before age 60. I'm saying that that isn't what we're modeling.) Basically, every year you want to add a little money to your investment and let it grow. At or after age 60 you will make withdrawals such that hopefully the rate of money growing matches the rate you are withdrawing and you live out your golden years in financial independence. This is what it looks like if you grew your retirement account at 7% and withdrew at 24x your contribution rate at age 65 ($5.5k contributions and $130k withdrawals):
But one menace is waiting for you... the same one that saved our hypothetical country last week. Inflation. Inflation is basically good if you are in debt and bad you are invested. That same graph with inflation of 2.5% (which is usually considered the achievable target):
So a model of our Roth IRA has to start with a model of inflation. Inflation stacks year over year, so lets make our first variable age. Other important things are the age you would retire at, and the inflation rate.
Follow my work!
Current Age = B1
Age at Retirement = B2
Inflation Rate = B3
I will assume you can figure out your age. (I'm this many!) Age of retirement is a bit tricksy because it may be way in the future and it is hard to plan that far ahead. There are Roth penalties if you withdraw before 60 so lets make that the lower limit and let people choose 60, 62, 65, 67, 75 or... 100? I guess some people never retire, but for modeling purposes we'll say that our age list goes to 100. Lets do that now. Make a column from C11:C93 with the numbers 18:100. The inflation rate is variable, but is targeted at 2.5% and has historically averaged 3.37% in the US (including spikes where it went over 5%). Lets make all those values possible. We can define the inflation factor (typing the [In Brackets] portion) as:
(Cell D11) [=B$3^(C11-B$1)]
Complete the column by dragging the cell down to D93 (or double click the bottom right corner). If you put in an age like 30, that should correspond to an inflation factor of 1. Ages older than it should have values greater than 1, and ages less than it should have values less than 1. As you can see graphically, a higher inflation rate can get exponentially out of control pretty fast.
Fertilizing Our Nest Egg
The next thing we need is some way to personalize the model. You may be 20 years old and just starting out or 50 years old and several thousand dollars invested. Lets define some more terms:
Starting Nest Egg = B4
"Real" Contributions (in 2013 dollars) = B5
"Real" Withdrawals (in 2013 dollars) = B6
Interest Rate = B7
Contributions for Roth IRAs are limited at $5500 per year per person right now, but they started out in 1998 with a limit of $2000. That works out to an increase of ~7% for the limit raising. Lets be cautious and say that in the future they will only raise the limit at the rate of inflation. That means that even 30 years from now your "real" contribution would still be limited at $5500 factored at today's dollar value. Also, you could choose $11000 for a couple, although thats really just two individuals.
The same considerations go into determining withdrawals. Once you turn 60 you could take out as much as you like! But really you just want to take out some to let the rest keep growing. This variable should be how much you would take out in today's dollars. Keep in mind that you are only replacing expenses and not adding more to your savings at this point (although technically with a Roth you could). You might not have a mortgage any more either. Make your own assumptions as to social security and medicare offsetting your needs, but a conservative estimate for withdrawals would be your all your current income minus investments and housing costs.
The long term interest rate for the stock market has been 7%, but is quite volatile and not guaranteed to be 7% in the future. You could also have a Roth IRA that holds other assets like Bonds, Cash, or CDs. (At this point would investing in Nickleback albums count as "buying low"?)
Oh, and if you haven't contributed yet, enter "0" for your starting nest egg. Otherwise set it accordingly.
Cool! Now, in the interest of making things more clear, I'll separate the function temporally. There are four periods in your investing life.
- Time before now, which we don't care about.
- Right now, where you have the nest egg you have right now.
- Between now and retirement, where your nest egg grows.
- After retirement, where your nest egg may grow or shrink, depending on the size of the distribution and rate of growth.
Complete the column. Now Make those nominal values real by dividing by the inflation factor:
(Cell F11) [=E11/D11]
Complete the column. I also want to know if the money has run out yet. I use nested if statements to check if the real value of the IRA is above 0. If it is, we should check last year. I want it to report the earliest year that the money runs out, thus:
(Cell G11) [="not yet"]
(Cell G12) [=if(F12>0,"not yet",if(F11>0,C12,G11))]
Complete the column and we are good to go! Lets test it out!
Running with the Devil
I guess the simplest way to run the model is to check and see what an 18 year old could do if they routinely filled up their IRA until age 60, got the market rate of 7% during a period of low inflation, and took distributions at, lets say, twice the US minimum wage (~$30k/yr):
Thats how it is supposed to work. A Roth IRA should allow someone of modest means to save for a modest retirement. I'm guessing that is how they determined the contribution limits too, as the money starts to decay precipitously right at the end of life. Some would say that if you haven't used up the last dollar then you didn't really optimize things perfectly.
But what if two 18 year old newlyweds routinely filled up their IRAs until age 60, got the market rate of 7% during a period of low inflation, and took distributions at the average income level of $51k.
Now the IRA has taken on a life of its own. It isn't decaying, but instead it is still growing. The government allows this and even after you die your Roth IRA can be passed down to your children who must take distributions (tax free) according to their age.
In Case of Emergency, Break IRA Glass
But what if that couple waits until they are 30 to start up their IRA.
Technically they have only lost 12 years, but that is more than the doubling period of 7% interest. They have less time to save, and the years they put in compile to give a nest egg only half the size (even though they invest for 71% of the time). They run out at age 77, which isn't horrible (as the US life expectancy is about 80), but they would worry about finances. Perhaps they keep working until 65. Perhaps they take out only $35k a year. (Both of these let the money last until age 95.) Either way, what I learned from this is that time is very important.
What else is important?
Fees. That 1% mutual fund fee seems small, but it effectively takes you from 7% returns to 6% returns. Big deal? Our happy newlyweds in example two with the self-sustaining portfolio? With 6% returns they suddenly run out of money at age 90. The closest thing to investment advice I'll give is that you should be extra-aware of fees. There are funds available that have tons of diversity and only charge 0.06 to 0.1%. If you are being charged more than that they had better make up the difference with performance.Inflation. Just going from the optimal inflation (2.5%) to historically average inflation (3.37%) makes our happy newlywed self-sustaining portfolio run out at age 93.
Contribution. To answer the initial question, what if we only half-fill our IRA? The happy newlywed self-sustaining portfolio runs out at age 77. If you have them work until age 63 and only take out $30k/yr, you can get it self-sustaining again, but that is a huge decrease in standard of living. Even filling it up only 90% takes it from being self-sustaining to a slow draw-down. Again this comes back to time. A dollar you didn't invest at age 18 is worth about two dollars at age 28, four at age 38, and sixteen at age 58. The money you put in the last couple years of saving is barely going to grow at all. And this doesn't even count the volatility of the markets!
I encourage you to definitely take the model for a test run!
Take Home Message
You basically want to invest early and often. Don't take out your investment to buy something shiny, because replacing your time is only possible through pushing off retirement. Also, hope that the Fed knows what it's doing with monetary policy.I made this model much simpler than it could be. Perhaps you stop contributing at age 60 but leave the money in for another few years. Perhaps you shift the interest rate from risky to conservative as you age. Feel free to suggest improvements.
I didn't mean for this post to be a downer (although you wouldn't know it from all the "things I learned"), so lets look at one rosy scenerio. One thing to consider (and possibly post on later) is that if you look at all of human history, life-spans are increasing at a crazy rate. What does that mean for investing? If instead of "retire at 60, enjoy 20 years of retirement", the average human condition was "retire at 75, enjoy 50 years of retirement", we would get that precious commodity (time) that is the key to all investing. At that point, our happy (not-so) newlyweds will have an IRA that is nearly indistinguishable from exponential growth.
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