Moneycle

Journey to Financial Independence

Wed, 08 Aug 2018 00:00:00 -0600

My own journey to financial independence (FI) wasn’t exactly smooth and well executed. I was always a good saver and investor but I didn’t really consider the endpoint thoroughly until I got there. That’s not to say I didn’t have the end goal in mind, I did. But I didn’t have a clear picture of how my assets should be allocated at the time of FI so I had to scramble a little bit at the finish line to make sure my portfolio was set up to support retirement spending.

Part of the problem is that most of the available investment advice is geared towards the accumulation of assets. The accumulation mindset is great while you’re in the portfolio building years. But I think it’s useful to have a clear idea of where you want your portfolio to end up at the time you’re ready to stop taking a real paycheck from a job and start taking money out of your portfolio. This “decumulation” process is something I have a much better handle on now that I’ve reached the FI milestone and it informs how I now think about the whole financial journey in retrospect.

As such, in this article I propose what I think is a lifelong investment strategy that is better geared towards achieving and maintaining FI. The graph below illustrates this strategy using a hypothetical timeline from an investor’s beginning all the way through FI.

In order to keep the discussion simple, I have identified just 3 types of investment buckets: growth (red), stability (blue), and safety (green).

Generally speaking these buckets are what they sound like:

Growth - assets that aren’t needed for at least 10 years. Growth assets have the advantage of time and this is the part of your portfolio that can take maximum risk. Invest in assets that can be volatile in the short term but give you higher returns in the long term such as stocks, real estate, long-term bonds.
Stability - assets that may be needed in the medium term (5-10 years). Invest in assets which have a relatively low risk but still some possibility for gain to keep up with inflation such as medium-term bonds or long-term CDs.
Safety - assets that might be needed in the near term (less than 5 years). Invest in assets that have very low risk of losing value such as savings, CDs or short-term bonds.

Understand Your Expenses

Before you do anything, you really need to have a handle on your current monthly expenses. Knowing your expenses is a key to implementing this strategy and allows you to easily monitor your progress. Also, being aware of your expenses drives home the fact that lowering your expenses is a key towards reaching your goals sooner.
It’s the one variable you have the most direct control over.

If you’re not sure of your expenses, sign up for one of those services that will help you track them. Understanding where your money goes and how much you spend every year is vital to informing where you are and how to invest your assets.

Milestone #1 (M1) - Emergency Fund Invested in “Safety”

The first milestone in any investor’s life should be to set up an emergency fund using “safety” investments. In my opinion, the primary purpose of the emergency fund is to handle employment gaps. So the size of your emergency fund should reflect how much time it might take you to find a new job if you find yourself temporarily unemployed. For example, if you work in a high demand field then maybe just having 3 months worth of expenses saved in your emergency fund is adequate. But if your skills are very specialized, you might want to consider something like a year’s worth of emergency funds. If you’re not sure, default to 6 months of expenses.

The emergency fund is the ballast of your “safety” bucket and should be invested for safety only. Resist the urge to invest these assets for growth. The purpose of this fund is as a safety net, so you don’t want to risk having it decline in value when you need it most. After you have fully-funded your emergency fund it’s time to switch gears and invest for long-term growth. The simplest “growth” investment is 100% stocks using something like a total market stock index fund. But if a 100% stock allocation seems too risky for you then consider a mix of stocks and bonds such as 90/10 stocks/bonds, or 80/20 stocks/bonds. But I wouldn’t go above 30% bonds in the “growth” bucket because you will be adding more bonds to the overall portfolio later when you start adding to the “stability” bucket.

Milestone #2 (M2) - 20 Years of Expenses Invested in “Growth”

You can certainly celebrate other milestones such as 1, 5 and 10-years of expenses in your “growth” bucket. But the 20-year milestone is a big deal! When you have 20 years of expenses saved in growth, then the light of retirement is visible at the end of your investment tunnel. After you hit this milestone you are beginning a transitional phase that sets you up for FI.

A Better Rule of Thumb for Bonds

Having hit 20x expenses in growth, it’s now time to start investing for “stability”. Ultimately the “stability” bucket is the part of your portfolio that helps to cover expenses that are a few years out, say 5-10 years. So instead of the rules of thumb for investing in bonds that are based on your age, I believe it should instead be based on how much you have invested in the “growth” bucket. I would state this new rule of thumb for bonds as follows:

Start investing in your “stability” bucket (bonds) after you have accumulated 20 times your annual expenses in your “growth” bucket.

There are 2 key points to this seemingly simple rule. First, it’s not based on age but rather on your progress towards your goal of financial independence. Second, this rule puts the focus on your expenses as the key to measuring how close you actually are to that FI goal.

After having hit the 20x milestone (M2), then once every year I suggest you sweep your “growth” gains into your “stability” bucket while keeping the “growth” bucket at 20x expenses. Conversely, if your “growth” bucket had a bad year, then rebalance some “stability” bucket funds back into the “growth” bucket to get it back up to 20x expenses.

This is a little different than traditional rebalancing concepts that are based purely on target percentages. Instead of a using target percentage, you are rebalancing based on a targeted expense multiplier (20x in “growth”). Think of it as filling in your ultimate FI allocation from the riskiest assets down to your least risky assets.

Milestone #3 (M3) - 5 Years of Expenses Invested in “Stability”

Once you have 5 years of expenses in “stability” and 20 years in “growth”, your overall portfolio will be at 80% “growth” and 20% “stability”. So you can see that your portfolio is becoming more conservative as you get closer to FI.

When you hit this milestone (M3), you’re not quite there yet but you can start to think seriously about your impending financial independence and whether you will want to continue working. As such, the next investment is back into “safety”. I’m suggesting that you save 5 years of expenses in “safety” but that number is somewhat arbitrary. The key is to have a comfortable amount of expenses in non-risky buckets so that you will be positioned to pull the trigger on retirement and not have to worry about a market correction in the first few years of retirement.

If you want, you can just add these “safety” funds into your existing emergency fund because the primary need for the emergency fund, to cover employment income gaps, is going away. In effect, your emergency fund is transforming from a safety net into a spending bucket.

Also, as with the previous milestone, you should still rebalance every year to keep your “growth” bucket at 20x expenses and you “stability” bucket at 5x expenses. Based on market conditions you may find you need to backfill either growth or stability. But you can also use gains from those buckets to feed into your “safety” buckets and get you to FI that much faster.

Milestone #4 (FI) - Financial Independence (30 Years of Expenses)

When you have 20x expenses in “growth”, 5x expenses in “stability”, and 5x expenses in “safety”, then congratulations! You have reached financial independence!

If you do choose to continue working after FI, I recommend putting all future extra savings into the long-term “growth” bucket because, by design, you won’t need those funds in the near term. Alternatively, you could also just keep the 20/5/5 growth/stability/safety ratios going and increase your spending accordingly when you do eventually retire.

If you had chosen to keep 100% stocks in your “growth” bucket then, when you hit the FI milestone, you will have 67% stocks in your overall portfolio. If you prefer to target a little smaller stock allocation in your portfolio at retirement, then you can use your target percentage to inform how much to keep in your “growth” bucket. For example, if you’d like to hit a target of 60% overall stocks on your FI date, then multiply the targeted stock allocation by 1.5 (30 years total / 20 years in “growth”) to arrive at a 90% stock percentage in your “growth” buckets. I think any stock allocation between 75-100% is fine for the “growth” bucket but you should give some serious thought to how you would feel if you reached FI right before the market takes a big hit. If you’re not sure, start with 90% stocks in “growth”.

Not Quite a Target-Date Fund

Astute readers may notice that this investment strategy has similarities to target-date funds. Generally those funds invest aggressively early on and become more conservative as you approach the target date. While I think target-date funds are pretty good for many people because of their simplicity, they differ slightly from the strategy in this article in a few distinct ways:

First, target-date funds become too conservative if you hold them to maturity. Most target-date funds end up with a stock mix below 40% and some go as low as 24%. I think this is okay for a fund where you’re targeting a big purchase near that target date, but not necessarily for FI. You want your assets to keep up with inflation so I think your post-FI stock allocation should be somewhere in the 45-65% range.
Second, target-date funds don’t give you a convenient way to access just the “safety” part of the portfolio such as the short-term bonds and money market funds. There is a peace-of-mind in being able to access risk-free funds for day-to-day expenses and ignoring the gyrations of the stock market.
Third, target-date funds don’t adjust the goal date if your financial independence date changes because your portfolio is doing better or worse than expected. The strategy in this article would better be described as a “target expense” fund than a “target date” fund as it is personalized to your level of spending rather than an arbitrary future date.

So, if you use target-date funds during accumulation that’s fine. But consider that you will probably want to switch out of them at or near the time when you start the transition to retirement.

Other Considerations

While understanding your expenses is a key part of this strategy, it’s also important to consider any future pensions or social security payments you may receive. For example, if you expect to be receiving a $1000/month social security check at retirement, then you can effectively subtract that $1000/month from your expenses for the purposes of figuring out how much you need to reach FI. This could dramatically reduce the amount you need to invest/save to reach retirement.

Also, because it targets 30 years of expenses, this strategy effectively presumes a 3.33% withdrawal rate (1/30 = 3.33%). If you feel like your withdrawal rate should be different, you can modify this plan accordingly by changing the sizes of the different buckets slightly. But I think the plan as presented here is a good baseline for most people.

Finally, I didn’t give any details on the types of accounts used to invest these bucket assets. While that’s important I didn’t want to confuse the point of this article too much. Suffice it to say that it’s a good idea to have some tax diversity utilizing a combination of Roth, traditional and taxable accounts for your portfolio.

Key Takeaways

This strategy is geared towards achieving your actual future spending goals instead of aiming for an arbitrary retirement date.
This helps to clarify what you actually need while simultaneously giving you a good measure of your progress towards financial independence.
Put as much into the “growth” bucket as early as possible, then add “stability” and “safety” later as you approach retirement.
This approach maximizes the amount of time your riskier assets have to grow.
Invest in “stability” (bonds) only after you have accumulated 20 years worth of expenses in “growth”.
Multiply your desired stock allocation at retirement by 1.5 to arrive at the percentage of stocks to have in the “growth” bucket during accumulation.
Following this investment strategy will slowly transition your assets into retirement so you don’t have to scramble to reallocate assets to an appropriate post-retirement mix.
This strategy could be implemented with as few as just 2 or 3 funds. For example, you could put all of your “growth” assets into a total stock market fund, all of your “stability” assets into a total bond market fund, and all of your “safety” assets into a savings account or short-term bond fund. Also, after you reach FI you could combine your “growth” and “stability” buckets into a single balanced fund.
Don’t forget to consider other sources of income in retirement such as Social Security or pensions. These other income sources effectively reduce the expenses you need to cover with your investment portfolio and can get you to FI faster.

Comparing Target-Date Fund Glide Paths

To Roth or Not to Roth - Part 3, Retiring at Age 70

Mon, 14 Aug 2017 00:00:00 -0600

Retiring at 70

Age 70 is the focal point of this article because it’s the age (technically 70.5) where you must begin taking distributions from your Traditional accounts in the form of required minimum distributions (RMDs). It’s also the latest age (and possibly the optimal age) to which you can delay taking social security.

In order to figure out the maximum Traditional portfolio value at age 70, we need to figure out what portfolio value will generate the amount of income that fills in the lowest tax brackets during retirement. Combining that future income level with the minimum withdrawal rate will allow us to calculate what the portfolio size needs to be at age 70.

Starting Simple

To keep things simple, let’s start with the idea of just filling in the 0% tax brackets in the future. Just about everybody would benefit from deferring taxes into a future time when the funds are taxed at 0% (untaxed) so this simple case applies to most people.

Technically there isn’t a 0% tax bracket but rather income that is exempted from taxes via the deductions and personal exemptions. This is further complicated by the effects of taxes on social security so, for now, let’s just assume that the first $20k of income for a married couple ($10k for singles) is not taxed. If that’s the case, then the goal would be make sure your Traditional IRA/401k/403b generates no more than $20k of income ($10k single) at age 70 and beyond.

Furthermore, the government requires that you start taking distributions from your tax-deferred accounts in the year you hit age 70.5. In that first year, you are required to distribute at least 3.65% (portfolio_value/27.4) of your tax-deferred portfolio as income.¹ As such, the amount that must be taken in that first year dictates how big your portfolio could be before you must start taking income that creeps into higher tax brackets.

Simple example

Let’s use some real numbers to get an idea of what we’re talking about. If you want to make sure your future portfolio (age 70.5) generates no more than $20k of income, then the upper limit on your portfolio value at that age is determined by

portfolio_income = portfolio_at_70 / 27.4 < $20k

So it’s a simple case to solve for the portfolio value

portfolio_at_70 < $20k * 27.4 = $548k.

So finally we have a number, $548k for a married couple ($274k for a single). It’s a number with lots of assumptions and what-ifs but it’s gives you an idea of about how much to put into your tax-deferred accounts under those simple assumptions.

The more general version of this equation is to use the income level, in the future, that is taxed at or below your current tax rate. Determining that income threshold is more of an art than a science since future tax brackets are somewhat unknowable.

portfolio_at_70 < income_threshold * 27.4

If you were born in the 2nd half of the year, replace 27.4 with 26.5 in the above equation.

Back to the Future

Having a future number or goal is nice, but in order to be useful, you need to take into account your current situation in order to determine how much you should contribute each year going forward in order for your non-Roth accounts to stay at or below that number. For example, if you are now aged 45 and expect to work until age 70, then you have 25 years of appreciation in your portfolio that you want to keep at or below $548k. How does that translate to this-year’s contribution amount?

Let’s break this down. First, while the target amount is in today’s dollars, you should expect some amount of appreciation in your portfolio after inflation. For example, if you expect your portfolio to earn 6% and inflation to be 2% over the next 25 years, we could calculate what portfolio value today would grow to $548k as,

portfolio_target = portfolio_70 / (1 + net_return)^(70-age)

where,

net_return = portfolio_return - inflation

So for that 45-year old in the example,

portfolio_today = $548k / (1.04)^25
                = $205k

What does this mean? If that 45-year old has already managed to save $205k in tax-deferred accounts which return 4% after inflation, then they may want to consider going all Roth contributions from here on out. Remember that this assumes they work until age 70 and only want to generate $20k of income (in today’s dollars) from the 401k/IRA portfolio.

Today’s Contributions

But what if our 45-year-old hasn’t saved anything yet or only saved a smaller amount? Let’s determine the upper limit on their tax-deferred contributions going forward.

Since we are representing the portfolio in today’s dollars, let’s calculate the contributions needed in terms of the portfolio’s actual value in today’s dollars.

portfolio_shortfall = (portfolio_target - portfolio_today)

Simply put, we need an annual contribution going forward that is big enough to fill that shortfall, so using the present-value calculation,

contribution = PV(net_return,
                  70-current_age,
                  portfolio_shortfall)

The present value calculation represents what level of regular contribution that are needed to produce the present value of portfolio_shortfall.

contribution = portfolio_shortfall * net_return ÷
                (1 - (1+net_return)^(age-70))

Using our 45-year-old example, and assuming they have already saved $105k, then the shortfall is $100k. With a 4% return after inflation they could contribute up to,

contribution = $100k * 0.04 / (1 - 1.04^-25)
             = $6401

So a contribution of $6401/year would get this theoretical person’s portfolio to the level that would produce $20k of income (in today’s dollars) at age 70 using RMDs. Any contributions above $6401 could go to a Roth account.

Likewise, if they are starting with zero savings, then the shortfall in today’s dollars is $205k which means they could contribute up to $13,122 to their Traditional account every year to produce that same income in the future.

Another Fun Interactive Plot

We now have a set of equations (highlighted) that help you determine the contributions you should make until age 70. But they are very sensitive to the assumed rate of return. Below is a plot the needed contribution amounts as a function of the assumed rate of return. Move the sliders around for your age, inflation rate and future tax-deferred income target to see how it looks for your situation. For help on setting the future tax-deferred income target take a look at the article about how social security messes with your tax brackets and choose a value that will be taxed below your current marginal tax rate (defaults to $20k as a crude approximation of the 0% tax bracket for a married couple).

If you are seeing a puppy image below, then you are missing out on the amazingly excellent interactive content on the site. Click on the puppy to open the article in a browser and see what you are missing.

Current Age ():

Inflation Rate ():

Future Tax-Deferred Income Target in Today’s Dollars ():

When You Assume

Beware of the assumptions made in this article. First and foremost, figuring out what future tax brackets will look like is anybody’s guess. So determining your how much income to generate in the future is a guessing game. I suggest erring on the conservative side and using the current 0% tax bracket (deductions and exemptions) as a starting point.

The assumed rate of return is also tricky. If you use this article to set your contribution amount, then do so knowing that things will change every year. So make sure you revisit your assumptions every year with updated portfolio values.

There are many ways you could generate income in the future. Taking RMDs as suggested in this article is just one method for taking income from your portfolio. Another possibility is buying a single premium income annuity (SPIA) which guarantees lifetime income. An annuity would likely return a rate much higher than 3.65% (over 5%) so if you convert your Traditional account to an annuity at ge 70, you could have higher income that you would with RMDs. That could suggest lower contributions than calculated by this article.

Finally, this article is meant to provide a framework for calculating the limit on Traditional (tax-deferred) contributions if you work until age 70.
That doesn’t mean you shouldn’t save more. On the contrary, save as much as you can but put extra contributions into a Roth account if possible. And if you don’t want to work until age 70, forthcoming articles in this series will discuss how to calculate your contributions when retiring before age 70.

Technically, if your birthday is between July and December then you can begin RMDs in the year in which you turn 71 which has a divisor of 26.5 instead of 27.4. For simplicity, this article only uses the 27.4 number but you may want to substitute 26.5 for your own calculations if you were born in the 2nd half of the year. ↩

Super-Simple Virtual-Buffer Withdrawal Strategy - Revisited

Sat, 17 Jun 2017 00:00:00 -0600

I was recently re-reading the original article that presented the concept of this simple withdrawal strategy and found the explanation to be overly complex which seems wrong for something that’s supposed to be simple. So I ask you, dear reader, for another chance to describe the strategy in a way that is more approachable (with less math) to the average reader. In fact, the most complex thing about the strategy is the name¹.

The Simplest Version

In it’s simplest form, the strategy boils down to the following 2 equations:

initial_monthly_withdrawal = portfolio_value / 400
next_monthly_withdrawal    =
     ⅔ * current_withdrawal + ⅓ * current_portfolio_value / 400

The first equation tells you how much you can withdrawal monthly from your portfolio in the first year that you start taking withdrawals. Dividing your portfolio value by 400 is equivalent to taking a 3% annual withdrawal and gets the process started. Conversely, if you multiply your monthly expenses by 400, that can give you an approximation of how big your portfolio needs to be in order to retire.

The second equation tells you how much you should adjust your withdrawal amount each year. This particular version of the equation assumes a buffer-size of 3 years and 3% withdrawal rate. In case you haven’t been reading other articles on this site, the buffer is what provides ballast to the withdrawal equation so that your withdrawal amounts aren’t whipped around too much by a volatile investment portfolio.

That’s it! If you’re comfortable with the assumed withdrawal rate of 3% and buffer of 3 years then you can stop reading and just follow the above equations (which I use for my own situation).

Example: $900,000 portfolio

Let’s take a simple example, start with a portfolio worth $900k. Dividing a this by 400 gives the initial monthly withdrawal of,

initial_monthly_withdrawal = $900000 / 400
                           = $2250/month

Piece of cake. It’s up to you if you actually save the full 3-years of that withdrawal amount into a safe place. I recommend you at least save 1 year’s worth, $27k in this example, in a safe account such as an interest-bearing savings. Or maybe you’d feel better putting the entire 3-year buffer, $81k, in savings, that’s fine too. It mostly depends on your risk tolerance.

Next, after one year, you re-evaluate the portfolio to decide whether to increase or decrease your withdrawal amount. Let’s say portfolio has had a good year, and is worth $990k at the end of the year. Your next year’s withdrawal rate is computed as,

next_monthly_withdrawal = ⅔ * 2250 + ⅓ * 990000 / 400
                        = 1500 + 825
                        = $2325/month

So even though the portfolio grew by 10%, you only increase the monthly withdrawal amount by 3.33% (because of the buffering). It works both way, if the market has a particularly bad year, it won’t kill your monthly withdrawal income.

In every year after the first year, you just use the 2nd equation to determine the withdrawal amount for the following year. Over the long haul, with these equations, your withdrawal amount will hover around 3% of your total portfolio value².

The General Version

If you prefer a little more control over the withdrawal rate and buffer size, then here’s the more general equations for this strategy:

initial_monthly_withdrawal =
     portfolio_value * withdrawal_rate / 12
next_monthly_withdrawal    =
     (1-1/buffer_size) * current_withdrawal +
       (1/buffer_size) * portfolio_value * withdrawal_rate / 12

For example, if you prefer a more aggressive 4% withdrawal that is stabilized by a larger 5-year buffer then the withdrawal equations would simplify to,

initial_monthly_withdrawal = portfolio_value / 300
next_monthly_withdrawal    =
     ⅘ * current_withdrawal + ⅕ * current_portfolio_value / 300

Easy Peasy

That’s all there is to implementing the Super-Simple Virtual-Buffer Withdrawal Strategy. If you want to see the math behind the strategy, refer to the overly-complex original article. The main takeaway from this strategy is that you only need to know two data points each year, (1) the current withdrawal amount and (2) the current portfolio value. With those two numbers, you can calculate the next year’s withdrawal amount in a way that is simple to compute but still buffers your retirement income against wild fluctuations in the market.

I’m open to suggestions on better names for the strategy ↩
Technically if the market steadily increases over the long term your withdrawal amount would probably lag slightly below 3% on average, but who’s counting? ↩

To Roth or Not to Roth? - Part 2, Reframing the Question

Thu, 06 Apr 2017 23:54:55 -0600

Many articles are written about the virtues of the Roth account¹ or the Traditional account types, but it’s rare to find an article suggesting why you should probably consider having both types.

In this article I try to show that both types have their place, but the important thing is to understand the main concept that will help you to determine how much of each type you should have. In short, the thesis of this article is that you should first determine the maximum amount to contribute to your Traditional account, then you should allocate the remainder of your qualified savings to your Roth account.

Basics - Tax Efficiency

The core decision of choosing Roth vs Traditional comes down to your tax rate now (when you save the funds) versus your tax rate in the future (when you withdraw the funds). If your tax rates are identical now and in the future you should choose the Roth because it has more flexibility (access to principal, no distribution requirements). But if your tax rates in the future, at the time of withdrawal, are lower than your current marginal tax rate, then you could save money by deferring those taxes into the future.

If you’re a good saver, then there’s a pretty good chance that you should be using both Roth and Traditional. Why? Because there’s a very real possibility that your Traditional savings will outgrow the lower tax brackets, especially when you consider other future income sources.

Filling Future Tax Brackets

Think about your tax brackets over time. For example, in an over-simplified view of the world (ignoring inflation and other adjustments), your tax brackets might look like this.

Granted this is a naive view of tax brackets (they actually do change over time), but I’m just trying to make a point so ignore those details for the moment.

The general idea of saving to a Traditional account is that in the future you will take those withdrawals out in lower tax brackets. I like to visualize this as pouring those Traditional IRA funds into the lower tax brackets over the time that spans all of your retirement years. For example, the following picture shows IRA funds filling up the 0% tax bracket from retirement forward, which would be appropriate for anybody in a tax bracket above 0% (probably everybody reading this).

The idea of the above picture can be extended to higher tax brackets. For example, if you’re in the 33% tax bracket now, any savings you put into a Traditional IRA now could save you money in the future if they were poured into any tax bracket below 33% over the course of your retirement.

You might be thinking that the growth on the assets matter, but for this decision it really doesn’t. That’s because taking a percentage out now and letting your investment grow (Roth) is mathematically equivalent to letting your entire investment grow and taking the same percentage out later (Traditional). So it just comes down to figuring out when the tax rates will be lower.

The trick then is to figure out how big your Traditional account savings bucket can get before it starts to leak into your current tax bracket in the future. Because if you’re going to fill in your future tax brackets at your current (or higher) rates, then you might as well contribute to a Roth.

Upper Bounds for Traditional Accounts

So instead of determining what percentage to put in a Roth, the problem becomes one of figuring out the maximum absolute amount to put into a Traditional account.

We can approach this problem by putting an upper bound on the size of the Traditional IRA bucket (in the picture). Once you know what that upper bound is, you can project the maximum that your Traditional contributions should be in order to fill that bucket by your retirement date. The projection will never be an exact number because returns are unpredictable and retirement dates change. But if you have this framework in place, then you can make minor adjustments every year to account for the shifts in your portfolio balance and retirement date.

Other Income Sources

Probably one of the hardest variables to predict ahead of time is the amount of money you might get from other income sources. Social Security is one source that is fairly predictable, but what about income interest, dividends, side-job income, pensions, inherited IRAs, annuities, et cetera. You may have a good handle on what those sources are now, but it’s not always easy to predict all future income sources.

The effect of future income sources is that they fill in your lower tax brackets before withdrawals from your Traditional accounts. This means that you might have less room to withdraw funds in those lower tax brackets in the future. So the more future income you have from other sources, the less you should contribute to Traditional accounts now.

Realistic Tax Brackets

To determine the maximum Traditional contributions, we also should consider a more realistic view of tax brackets in retirement. If you’ve read previous articles on this blog you may be familiar with the effects of taxes of a couple life situations. There are 3 general bands that can effect tax brackets as show below. The picture below does not represent every situation but is meant to suggest how complicated it can get (your situation will be different).

If you are getting health care from the ACA before age 65 then you would fall into the band I’m calling the “ACA years”. Those people eligible to receive Affordable Care Act premium credits may see their tax brackets jumbled up by those credits before they start taking medicare at age 65. And this situation could very well change by the time you read this given the current political climate.

The second band, which I call the “early medicare years”, is the time before age 70 and after age 65. This band has a fairly “normal” tax bracket signature because it is not affected by ACA or Social Security effects on taxes.

Taking social security can effect the tax brackets at the lower end of the income spectrum. As discussed in a previous article on this blog these effects can have significant impacts to tax brackets at or below 25%. Also, since most people should probably delay taking social security until age 70 (your situation may vary), we will consider the case of retiring at age 70 while taking social security in the next article in this series in this band which I call the “Social Security years”.

Coming Next

The next articles in this series will attempt to address the different bands of time and how they might inform how much to save in Traditional accounts. Ultimately the goal is to give you the tools (and maybe a calculator) to estimate how much to contribute to Traditional accounts every year going forward until you exit the rat race.

I use the generic terms “Roth” and “Traditional” to refer to all qualified accounts such as IRA, 401k and 403b. The basic concepts are the same regardless of the actual account vehicle you use. ↩

How Social Security Messes With Your Tax Brackets

Wed, 18 Jan 2017 00:00:00 -0700

While Social Security provides a nice base-level of income for many retirees, it can have some interesting effects on the tax brackets. The basic philosophy of Social Security taxation is that you won’t be taxed on Social Security benefits if you have no other income sources. But as your other income sources grow, your Social Security benefits may be subject to taxation. This is really just a means test that allows Uncle Sam to increase your taxable income if you are well off.

Getting into the weeds for a minute, the rules for taxation of Social Security are as follows:

First, calculate what’s called the “provisional income” by adding half of your social security income to your “other income”.
“Other income” is my term, but it represents your taxable income (AGI) plus your non-taxable interest income.
If your “provisional income” is above the first threshold ($25,000 single, $32,000 married), then 50% of the amount above that threshold is added to your taxable income.
If your “provisional income” is above the second threshold ($34,000 single, $44,000 married), then an additional 35% of the amount above the second threshold is added to your taxable income, for a total of 85%.
A maximum of 85% of your Social Security benefit may be taxed.

The net effect of these rules is that, as your “other income” rises, then your tax rate can rise proportionally. So while the IRS frames it as a taxation on your Social Security benefits, it’s mathematially equivalent to an increase in your marginal tax rate. For example, if you are married and your provisional income is above $44,000, then your tax rate may be 85% higher than you think it is because 85% more of your total income will be taxed.

For Math Nerds click to show/hide

The graph in the previous section was generated by calculating the taxable income and applying that to the income tax brackets to figure out the actual marginal tax rates. Here is the math that is used to calculate the taxable income.

As mentioned above, provisional income is defined as half of social security income plus “other” income,

income_prov = income_ss/2 + income_other

Half of the provisional income above the first threshold (single = $25k, married = $32k) is taxable,

income_taxable = income_other +
                 max(0, 0.5(income_prov - threshold_1))

The max() constraint makes sure anything below the threshold is not subtracted from income_other. Likewise, adding in the second threshold (single = $34k, married = $44k), 35% of income above that threshold is added to the 50% above the first threshold (for a total of 85% above both thresholds),

income_taxable = income_other +
                 max(0, 0.50(income_prov - threshold_1)) +
                 max(0, 0.35(income_prov - threshold_2))

But we also need to add in the constraint that no more than 85% of social security is taxed. This gives us a unified equation to calculate taxable income,

income_taxable = income_other +
                 min(0.85*income_ss,
                     max(0, 0.50(income_prov - threshold_1)) +
                     max(0, 0.35(income_prov - threshold_2)))

Interactive Plot

This is all pretty abstract so let’s plot what the tax brackets looks like versus income levels for a married couple in 2017 with social security income of $50,000. Move the social income slider below the graph to see how it affects the tax brackets.

If you are seeing a puppy image below, then you are missing out on the amazingly excellent interactive content on the site. Click on the puppy to go to the website post in a browser to see what you are missing.

Social Security Income ():

Observations

As you move the Social Security income slider, you may notice the following:

Social Security = $0 - with no Social Security, your tax brackets are just the normal stair-step brackets that we are all used to hearing about. The larger your income, the more your marginal tax rate is.
SS > $8,000 a “new” tax bracket of 27.75% appears and gets wider as your income increases. This is due to the 15% tax bracket being increased by 85% as your provisional income goes above the 2nd threshold.
SS ≈ $17,000 at approximately $17,000 the 10% tax bracket effectively disappears! That is due to the fact that 10% bracket is increased by 50% to 15% because your provisional income is between the 1st and 2nd thresholds.
SS ≈ $47,000 a crazy new 46.25% tax bracket appears and represents the 25% tax bracket being increased by 85%.
SS ≈ $53,000 the 15% tax bracket becomes extinct if you are lucky enough to get this much Social Security income (for a married couple). In other words, beyond the tax-free zone of deductions and exemptions, the first tax bracket you hit will actually be an 18.5% tax bracket (10% increased by 85%).
Increasing income reduces the size of the tax-free zone. The tax-free zone represents the standard deduction and personal exemptions. This is effectively decreased because it is absorbed in the taxable portion of the social security income. So even though it’s not technically decreased, mathematically the amount of untaxed income above and beyond Social Security decreases.

Implications

The effects of Social Security taxation can significantly impact how you save for retirement and affects the Roth vs Traditional account tradeoff. That’s why I decided to write this article before writing Part 2 of the Roth or Not to Roth series. The basic implication is that your future tax rate not be what you think it will be (even without changes to the current tax code). Given that your tax rate could very well be higher than you think, this could push you to use a Roth account more often than you do currently.

There’s not a single solution for all cases, but let’s break it down a little for different levels of Social Security income.

SS = $17,000, at this level you still have $23,300 of untaxed “other” income beyond SS so you would ideally like to defer income that fills that tax-free zone. But above this, your first tax bracket is effectively 15%. If your current tax bracket is 15%, you might want to consider saving to a Roth account at the point you think your Traditional accounts will generate $23,300 of income.
SS = $47,000, for this higher level you still have $18,367 of untaxed “other” income to play with. Beyond that tax rates increase pretty quickly into the 18.5% and 27.75% brackets. If you’re in the 15% tax bracket now, you should consider using Roth accounts to the extent that your future other income sources are above $20,000. If you’re in the 25% tax bracket you should consider using Roth accounts to the extent that your future other income sources are above $28,000.
SS = $53,000, as your SS benefit increases to this higher level, the amount of “other” income is tax-free down to about $17,000. Above that your lowest tax rate is above 18.5%, so if you are currently in the 15% bracket, the Roth option is best beyond the point where you have $17,000 of other income. If you’re currently in the 25% tax bracket, consider using Roth when your future income from taxable sources goes above $27,000.
If you retire early (before taking any SS), then your tax brackets won’t be affected until you start taking SS. So plan on using the existing unaltered tax brackets for your tax planning in the time before you start taking Social Security.

The general upshot of all of this is that, if you are not using Roth accounts for retirement savings, you might want to take another look at that decision in light of how your Social Security benefits affect your future tax rates.

To Roth or Not to Roth? - Part 1, The Ideal World

To Roth or Not to Roth? - Part 1, The Ideal World

Wed, 19 Oct 2016 00:00:00 -0600

Most often when you see an article discussing whether to choose a Roth over a Traditional option (401k/403b/IRA), the decision is stated as a comparison between current and future tax rates. While that’s mostly correct advice, it fails to recognize that future withdrawals tend to occur across multiple tax brackets while current contributions tend to be in a single tax bracket. I first became aware of the concept of filling in lower tax brackets from an excellent piece written by The Finance Buff.

In this first of two articles, I take a look at an ideal-world example that explores the concept of how much should go towards a Roth versus a Traditional option. In the second article, I will take a look at some more real-world cases that should give more concrete advice on how to determine how much to contribute to each option.

Basics of Roth vs Traditional

First, let’s discuss the basic differences between the Roth and Traditional options. The most important difference between the two options is when you are taxed. Roth options are taxed now in that you fund them with after-tax dollars and you are not taxed again when you withdrawal the funds. Traditional options are taxed later, so you deduct your contributions from your taxes now and pay income taxes later when you make withdrawals.

If you want to maximize how much money you keep, the basic tradeoff becomes one of shifting the taxes to the point in time when you have the lower tax rate.

When the tax rates are equal now and in the future, then mathematically the amount you end up with is identical after the taxes are accounted for. However, in this case I recommend using the Roth option primarily because the Roth has fewer requirements on the distribution of funds.

The Tradeoff

When deciding how much money to allocate to a Roth, the basic goal is to allocate funds to the Roth that will be taxed at the same rate or higher in the future. Conversely, all funds that will fall into lower tax brackets in the future should be allocated to the Traditional option now. This last part is where most people fail to consider the whole picture. Just because you may be in the same or even higher tax brackets in the future does NOT mean that some of the funds won’t be taxed at a lower rate.

Filling Up The Tax Brackets

When you make a contribution to a Traditional IRA/401k/403b today, in most cases all of that contribution will be in your current income tax bracket. Sometimes you might also cross over to the next lower tax-bracket when making a contribution if you are near a tax boundary when you begin your contributions.

But in the future, when you start making withdrawals from your Traditional IRA, your withdrawals start filling in the tax brackets from the bottom up. I like to visualize this as pouring money into the income “funnel” as depicted below:

In 2016, for a married couple filing jointly, the personal exemption plus standard deduction is $20,700 so that amount is taxed at 0% (which I think of as the 0% tax bracket). Then the 10% bracket swallows up the next $18,550 of income, and the 15% bracket gets the next $56,750, and so on. I have made the tax brackets to appear as funnel-shaped because the brackets get bigger as income increases.

Of course, most people will have other sources of income filling in the lower tax brackets, and we will consider that case too. But the key point is that future withdrawals fill in tax brackets from the bottom up before reaching today’s marginal tax bracket.

So the goal of an investor should be to plan for today’s Traditional contributions to fill up tomorrow’s lower tax brackets, then invest the remainder in the Roth option. That sounds easy on the surface, but the hard part is figuring out how to translate that statement into actionable numbers.

Saving within a Single Tax Bracket

Let’s start by looking at a typical example where somebody has all of their savings occur within a single marginal tax bracket. Consider a married couple named Jon & Sally that makes a total income of $120,000 and saves a total of $16,000 to their retirement plans. If that money is saved in a Traditional retirement plan then they would have a gross income (AGI) of $104,000. With the standard deduction, the low-end of the 25% tax bracket occurs at $96,000 of gross income so the $104,000 puts them $8,000 above the lower threshold of the 25% tax bracket.

Let’s further assume that they are saving all they can afford to and that the $104,000 of income represents their current AND future day-to-day expenses. This is a bit of a stretch, but I would argue that most people’s spending habits don’t change all that much when they transition into retirement. You will probably be spending more in some areas in less in others but basically your spending profile won’t change by a drastic amount in retirement. Mostly I’m just trying to get a baseline equation, so stick with me for now. If that $104,000 of income represents what they need in the future (albeit in today’s dollars), that suggests that in the future their “livable income” would be roughly $8000 into the 25% tax bracket. In the extreme case where this couple has no other sources of retirement income, that would mean they would need about 96k/104k (92%) of their withdrawals to occur in tax brackets below 25% and the remaining 8k/104k (8%) would come out in the 25% tax bracket.

If you knew that your future funds would come out in the same tax bracket, then those funds might as well go into a Roth account today. So in this example, the couple could contribute 8% to their Roth. Mathematically,

percent_to_roth = (livable_income - tax_threshold) / livable_income

Assigning variables,

L = livable_income = current_income - max_savings
T = tax_threshold

then,

percent_to_roth = (L - T) / L

Other Income sources

The one assumption that is hard to ignore is that the couple has no other income sources in retirement. But almost everybody has at least one other source of income such as Social Security or pensions, and many people will have multiple sources of income. So let’s adjust the math to account for that.

If Jon & Sally expect to receive other income in the form of social security that will total $36,000/year in today’s dollars, then their savings don’t have to provide the full $104,000 of income. Their savings only have to fill the funnel up between $36,000 and $104,000, which is a difference of $68,000. So when they convert their nest egg to future income, 8k/68k or about 12% of that future income is in the same tax bracket they are saving in today. That suggests that they could save 12% today in a Roth because it would likely be in the same tax bracket if deferred to the future.

Modifying the first equation,

percent_to_roth = (L - T) / (L - B)

where,

B = base income from "other" sources (in today's dollars)

Knowing what your future base income from “other” sources can be a difficult thing to figure out. But if you’re only expecting Social Security, I suggest you start off with about 40% of your current income. This is a very rough estimate based on the idea that, on average, people receive around 40% of their income back in social security. But you really should take a look at your actual social security (or equivalent) statements to get an idea of how much you’ll really get.

At what point does 100% of your total savings go towards a Roth? Mathematically, if (L-T) > (L-B) the equation goes above 100%. This simplifies to the comparison of B > T. So you should contribute everything to Roth when your “base income” sources equal or exceed your current lower tax threshold. That makes sense because it means that if you know that you will be at or above the current tax rate in the future you might as well contribute everything to Roth today.

Let’s just modify the equation slightly to account for this scenario,

percent_to_roth = min((L - T) / (L - B), 100%)

Saving Across Multiple Tax Brackets

Now let’s consider the case where Jon & Sally, are able to save enough to cross over into a lower tax bracket if the entire savings were deductible. So consider with the same $120,000 of income and a savings rate of $30,000 per year. This suggests that they are able to live comfortably off of the remaining $90,000 of income.

With the bottom of the 25% tax bracket is at $96,000, Jon & Sally would then be descending into the 15% marginal tax bracket. Since we’re assuming that the $90,000 of income represents their future income needs and $90,000 of income would be marginally taxed at 15%, everything they save in the 25% tax bracket should simply go to the Traditional savings option. Then they would apply the equation from earlier but only to the portion in the 15% tax bracket.

So the first $24,000 of savings goes into Traditional. The remaining $6000 of savings would follow the previous equation, (90000-39250)/(90000-36000) or 94% of $6000, that goes to Roth. Notice that I’m using $39,250 as the low end of the tax bracket because that’s where the 15% tax bracket bottoms out (for a married couple using standard deductions). Finishing the math for this example, 94% of $6000 is 0.94*6000/30000 or about 19% of the overall savings that goes to Roth.

Mathematically, we can express the overall equation for the dual-tax bracket case like this:

percent_to_roth = everything in lowest tax bracket * previous equation
                = min((T1-L) / S, 100%) * min((L - T0) / (L - B), 100%)

where,

S = total amount saved
L = livable_income
T0 = tax bracket threshold below L
T1 = tax bracket threshold above L
B = future base income

Here’s a plot of what Roth percentage looks like versus income levels for a married couple¹ in 2016 with a savings rate of 12% and a future base income equal to 40% of their current income (move sliders below the graph to change percentages).

Savings Rate as Percentage of Income ():

Base Income as Percentage of Income ():

Insights

Looking at the plot of Roth percent versus income and playing with the sliders gives a few of insights.

The Roth savings rate drops off rapidly right above each tax bracket. This is due to the fact that your savings at those income levels can quickly push you into a lower tax bracket. So if you save enough to cross over into a lower tax bracket, all of the savings in the higher tax brackets would tend to go towards the Traditional option, while most of the savings that cross-over into lower tax brackets would go towards the Roth option.
The Roth savings rates tend to peak just below the tax bracket boundaries. That’s because you are as far away as you can be from the lower edge of the tax bracket which means that a higher percentage of your retirement income is likely to be in the same tax bracket (or higher) as you are in now.
Increases to future income pushes the entire curve up. This means that the more you expect to earn from other sources such as social security and pensions, the closer your retirement tax bracket will be to your current tax bracket so you would tend to want to save more to a Roth.

When You Assume, You Make Me Read Part 2

While this analysis is interesting and moving the sliders around is fun, there are many assumptions that make it not particularly useful. Here are some of the more egregious assumptions:

The model assumes that the investor will retire exactly when they have enough to retire without considering the probability that most people will either have too little or too much at the time of retirement. Assuming you work a little past the point of being financially independent, then you would probably want to allocate a little more to the Roth option because the extra savings in the Traditional option would fill up the lower tax brackets in the future.
Returns on the invested funds and inflation were both ignored. If your investments beat inflation then the amount you have at retirement to fill in lower tax brackets would be larger. This also suggests allocating more funds to Roths.
Employer matches were completely ignored. Since those matching funds would normally be in before-tax dollars, this would tend to suggest higher allocations towards the Roth option than shown in this analysis.

In Part 2 I’m going to change the perspective of the analysis from mostly theoretical to be a bit more practical. Also, instead of focusing how much to put in a Roth, I will change the perspective slightly to examine how much total money you should save in your Traditional savings option.

For the plot, I capped the qualified contribution at $48,000 because each person in a couple over 50 can contribute a max of $24,000 to qualified accounts. ↩

Radioactive Half-Life of Expenses

Thu, 25 Aug 2016 00:00:00 -0600

In the world of science, the term “half-life” is used to describe “the time required for a quantity to reduce to half its initial value”. One common application of this concept is for radioactive decay and the half-life is a useful measure in science to characterize how quickly something will decay over time. Probably the most common application of this concept is used in carbon dating which allows scientists to fairly accurately estimate the age of objects containing radiocarbon.

It occurred to me that portfolio expenses can have a similar effect as radioactive decay. Namely, the higher the expense, the faster your portfolio will reduce to half of the value it would have achieved without the expense. Let’s take a look at the math of compounding returns to see how quickly a portfolio’s value decays with expenses.

Lump-Sum Investment

Consider the case of investing a lump-sum amount. The compounded return of the investment with a rate of return r, after N years is

final_value = initial_value * (1 + r)^N

So, without any expenses eating into the return, the ratio of the final_value to the initial value represents how much your portfolio would grow without expenses

growth_without_expenses = final_value / initial_value
                        = (1 + r)^N

Now consider a expense or expense of e being subtracted off of that return every year.

final_value = initial_value * [(1 + r)(1 - e)]^N

Now the growth is smaller,

growth_with_expenses = final_value / initial_value
                     = [(1 + r)(1 - e)]^N

And to compute the half-life of these expenses, we want to know when the the growth with expenses is half of the growth without those expenses.

growth_with_expenses / growth_without_expenses = 1/2

or,

[(1 + r)(1 - e)]^N / (1 + r)^N = 0.5

Solving for N gives us the half-life as a function of expenses,

N = log(0.5) / log(1-e)

That’s it! We now have an equation that directly computes how many years it takes for a given expense to cut your total portfolio in half. Notice that for a lump-sum investment, it doesn’t matter how big your return is, it only matters what the expense is.

In the following plot I show the half-life as well as the 3/4-life and 7/8-life. Losing half of your portfolio is terrible, but even losing a quarter or eighth can be painful, especially when we’re talking about a portfolio that might need to grow to over $1 million to support a comfortable retirement. Do you want to pay $125,000 (1/8 of $1M) or more in expenses over the course of your investment life?

Let me walk you through some key points from the graph above.

You want your half-life number to be very large which means you want to be as close to zero expenses as possible.
According to Morningstar, in 2013 the “typical” managed fund of stocks has a expense of 1.2%. Such a expense would eat up half of your gains in 57 years which seems like a long time. But you would lose an eighth of your portfolio value in just 11 years.
It gets even worse if you consider the “all-in” costs of actively managed funds. John Bogle suggests that there are many unaccounted costs in an actively managed fund that can increase the actual “all-in” expense to something more like 2.21%. The main unaccounted for costs are “transaction costs, cash drag, and sales loads”. These extra costs are hard to quantify but they effectively can reduce your expected return beyond the published expenses. In any case, if you believe Bogle’s hypothesis, then an actively managed fund with a 2.2% expense has a half-life of only 31 years and a 7/8-life of just 6 years! That means that you could be losing as much as an eighth of your portfolio every 6 years if you invest in actively-managed funds.
Contrast this with a leading low-cost index fund from Vanguard like the Total Stock Market Index fund (VTSAX) which has an expense ratio of 0.05%. This expense would take 1385 years to lose half it’s value or 267 years to lose an eighth. To put it another way, after 40 years an expense of 0.05% would only take 2.0% off of your portfolio value which is less than some funds would cost in a single year.

By now, just about everybody knows that low-cost funds are a great way to invest and maximize returns. Putting these expenses in terms of how they eat away at your portfolio can be eye-opening.

Super-Simple Virtual-Buffer Withdrawal Strategy

Tue, 31 May 2016 00:00:00 -0600

While the 30-30 Withdrawal Strategy is a nice clean method for withdrawing money from your portfolio, it does require you to keep track of a buffer which drives the calculation for your withdrawal amount every year. I felt like there should be a way to calculate the withdrawal in terms of only your current withdrawal amount and your current portfolio value thus alleviating the need to keep track of a separate spending buffer. After playing with the math, it turns out there is a pretty simple formula that achieves this goal.

A Bit of Math

The amount that is initially spent from your portfolio is determined directly by multiplying your withdrawal rate by your portfolio value. Using the same variables as the Safe Withdrawal Rates for Vampires article,

W = Pw

where,

W = annual withdrawal amount
w = annual withdrawal rate
P = portfolio value
k = buffer size in years

And if we have a buffer of k years, then the total buffer size initially is,

initial buffer size = kW

After a year of spending from the buffer, it is reduced by the withdrawal amount, W. So we are left with,

 buffer after 1 year of spending = kW-W = W(k-1)

At this point, we add back an amount equal to the new portfolio value times the withdrawal rate to arrive at the new buffer size,

 updated buffer value after 1 year = W(k-1) + Pw

And to compute the new withdrawal amount, we just divide this amount by the size of the buffer in years (k),

new annual withdrawal amount = W(k-1)/k + Pw/k

Because I prefer to think of my withdrawals as monthly, let’s rewrite this in terms of monthly withdrawals,

new monthly withdrawal amount = (W/12)(k-1)/k + Pw/12k

Given that k and w are constant values, we now have a formula for computing our new withdrawal amount from the current monthly withdrawal (W/12), and the current portfolio value (P).

Example Using 30-30 Numbers

Let’s put some numbers to this to make it less abstract. Start with a portfolio of P = $720,000 and go with the 30-30 Withdrawal Strategy numbers for buffer size (k = 2.5 years), and withdrawal rate (w = 3.33%). For these values, the initial monthly withdrawal is simply,

Pw/12 = $720000*0.0333/12 = $2000/month

If you want, you can set aside your buffer of 2.5 years ($60,000) in a safe place. But the beauty of this strategy is that you don’t have to do so. You can also just assume that your buffer is fully invested within the bond portion of your portfolio; it’s up to you. This is why I call it a “virtual” buffer because you get the advantages the buffer gives you without having to keep track of it.

Now, let’s assume a year has passed and it has been a good year and the portfolio has gone up to $765,000. Now your monthly withdrawal amount is computed as,

(W/12)(k-1)/k + Pw/12k = $2000(1.5/2.5) + $765000*.03333/(12*2.5))
                       = $2000 * 0.6 + $765000/900
                       = $1200 + $850
                       = $2050

So even though the portfolio increased by 6.25% (765000/720000), the monthly spending only went up 2.5% (2050/2000) due to the virtual 2.5-year buffering.

Also, look how simple the calculation is every year. In this example, multiplying your current income by 0.6, divide your portfolio by 900, and add those 2 numbers together. Pretty simple right?

Making it Even Simpler

As easy as this calculation is, I couldn’t help but noticing that dividing by 900 is a little awkward. What if we changed the buffer size so that we ended up dividing by 1000? If we can divide by 1000 then the calculation can almost be done in your head. To state this mathematically, we want,

12k/w = 1000

If the annual withdrawal rate is fixed, then we solve for the buffer size to get,

k = 1000w/12

Substituting this back into our withdrawal equation,

new monthly withdrawal amount = (W/12)(1-0.012/w) + P/1000

Revisiting the first example with a portfolio of $720,000 and a withdrawal rate of 3.333%, the first year withdrawal is still $2000/monthly because the withdrawal rate is the same. After the first year with a new portfolio value of $765,000, the new monthly withdrawal now becomes,

(W/12)(1-0.012/w) + P/1000 = $2000(1-0.012/0.03333) + $765000/1000
                           = $2000 * 0.64 + $765000/1000
                           = $1280 + $765
                           = $2045

So, you can see that the slightly modified equation only decreased the income by $5/month. This decrease is due to a slightly larger buffer (2.778 years vs 2.5 years) which means that the market gyrations are smoothed a little more than before.

The Super-Simple Virtual-Buffer Withdrawal Formula

To summarize all the above math, in the first year of withdrawals, you withdrawal from your portfolio by simply multiplying your portfolio value by your withdrawal rate.

initial monthly withdrawal = Pw/12

Then, after each year you compute your new withdrawal amount with this super-simple formula.

new monthly withdrawal = M * beta + P/1000

where,

M = previous monthly withdrawal
beta = monthly withdrawal multiplier = 1 - 1.2%/w
w = annual withdrawal rate
P = current portfolio value

The graph below shows the monthly withdrawal multiplier as a function of annual withdrawal rate. If you hover over the chart you will see other information including a “Sample Allocation” which shows how you might need to allocate more to stocks as your withdrawal rate goes up.

Sample Portfolios

Here are a few possible portfolio types you could choose from depending on your risk tolerance. The Step-By-Step section that follows walks through a simple example using the “moderate” strategy numbers.

	annual withdrawal rate	monthly withdrawal multiplier	virtual buffer size
conservative	2.40%	0.5	2.00 yrs
moderate	3.00%	0.6	2.50 yrs
moderately aggressive	3.33%	0.64	2.78 yrs
aggressive	4.00%	0.7	3.33 yrs

Step-By-Step

Implementing the Super-Simple Virtual-Buffer Withdrawal strategy is as follows:

Compute your initial monthly withdrawal from the equation Pw/12. For example, with a $400,000 portfolio (P) and a 3% withdrawal rate (w), your monthly withdrawal is,

$400,000*0.03/12 = $1000
Withdrawal from the portfolio for a full year using the last computed value.
At the end of each year, compute your new monthly withdrawal rate using the equation M * beta + P/1000. For example, with a 3% withdrawal rate (w), your beta multiplier is 1 - 1.2%/3% = 0.6. If your portfolio (P) has increased to $420,000 after the first year, then your new withdrawal is,

$1000*0.6 + $420000/1000 = $600 + $420 = $1020
Go back to step 2 and repeat.

Nerd Alert

Some readers may have noticed that the formula for this withdrawal strategy looks an awful lot like an exponential smoothed average. If we rewrite the withdrawal formula like this,

M(t) = (1-alpha) * M(t-1) + alpha * Pw/12

where

alpha = 1.2%/w

then you can see that it is indeed an exponential moving average of the term Pw/12. That term represents the annual withdrawal rate projected down to the monthly level.

For exponential smoothed averages, a smaller alpha represents an average that has a larger smoothing effect. In the case of this withdrawal strategy, the smaller alpha corresponds to larger withdrawal rates which means that larger withdrawal rates will have larger smoothing effects.

Parting Thoughts

Albert Einstein has been attributed with the saying that “everything should be made as simple as possible, but not simpler”. The super-simple virtual-buffer withdrawal strategy is simple and requires no bookkeeping other than checking your portfolio value once a year. Is there a simpler strategy? Yes, you could simply take a constant value out without checking your portfolio balance. But such a strategy could be risky since it ignores the possibility of a declining portfolio balance.

The super-simple strategy also has flexibility which comes from the fact that the buffer is “virtual”. Whether or not you keep an actual buffer is up to you. Generally it’s a good idea to keep a couple years or so of spending outside of your investments so that you know it will be there when you need it. But this strategy doesn’t require you do so, it’s up to you.

Affordable Care Act May Increase Your Marginal Tax Rate

Sat, 07 May 2016 00:00:00 -0600

If you retire before you are eligible for Medicare at age 65, then you may find yourself buying health insurance through one of the Affordable Care Act health exchanges. Furthermore, if your taxable income falls below 4 times the Federal Poverty Level (FPL), then you will qualify for a subsidy which could pay for a nice chunk of your health insurance premium. For 2016 the FPL is set at $11,770 for singles and $15,930 for couples, so you could be eligible for a tax credit for incomes below $47,080 (single) or $63,720 (couples).

What does this have to do with marginal tax rates? It turns out that the subsidy is a tax credit which gradually decreases as your taxable income increases. For example, if your modified adjusted gross income (MAGI) is between 3 and 4 times the FPL ($47,790 to $63,720 for couples), then your tax credit decreases by 9.56% for every extra dollar earned. And even though it’s a credit and not a tax, the effect of a decreasing credit is mathematically equivalent to a tax because the end result is that you will have 9.56% less money in your pocket for every dollar of increased income. Adding that to the marginal tax rate means that your effective marginal tax rate is higher if you’re in the income range where you receive a health care premium subsidy.

It’s certainly not bad to receive the tax credit because that’s free money. But it’s good to understand how this affects your tax rate so that you can plan on how and when to take income from your portfolio.

Marginal Tax Rates

If you pay your taxes, then you’re probably already well aware of the tax brackets, from 10% all the way up to 39.6% for the highest earners. This article is focused on the 10% and 15% brackets because that’s where the ACA credits occur.

To keep things simple, I’m just going to consider the simple case of a married couple using the standard deduction ($12,600 in 2016) and the the personal exemptions ($4,050 in 2016) which means that the first $20,700 of adjusted gross income is tax free. The same issue applies to single filers, just at a lower income level. Here’s a graph of the marginal tax rates versus income for joint filers in 2016.

If you itemize deductions, this graph will shift to the right by the amount that your deductions exceed the standard deduction ($12,600).

Marginal Effects of Tax Credit Decreases

The IRS publishes a table that is used to calculate how much to reduce your ACA subsidy by comparing your income to the Federal Povery Level (FPL). This table can be found in Table 2 of the instructions for Form 8962 which lists incomes levels from 100% through 400%. For a married couple, the FPL is $15,930, so 100% to 400% of FPL corresponds to incomes between $15,930 and $63,720.

Since the IRS table publishes different values for each FPL percentage point, I have computed the marginal tax effect for every 1% of FPL ($159) between 100% and 400% FPL to come up with the following graph.

Let’s break down this chart by income ranges:

$15,930 - 21,187 (100-133% FPL) - in the lower range the premium subsidy is reduced by the smallest amount, 2.01%. But many people in this range would be eligible for Medicaid and may choose to not buy insurance and thus may not be affected at all.
$21,187 (133% FPL) - there is a spike at this income level because there’s a jump in the subsidy reduction from 2.01% to 3.02%. So as your income increases from 132% to 133% of FPL, your subsidy goes down by 133*.0302-132*.0201 = 136% ($217 more taxes for $159 increase in income).
$21,187 - 47,790 (133-300% FPL) - in this range the IRS table publishes an ever increasing subsidy reduction rate which translates to a gradually increasing marginal tax rate. The jaggedness is due the rounding of the values in the IRS table. The average effect on marginal tax rate across this range is (300*.0956-133*.0302)/(300-133) = 14.8%. At it’s peak it approaches 18.5% for incomes right below 300% of FPL.
$47,740 - 63,720 (300-400% FPL) - this is the top range in which a subsidy is available and the reduction is a constant 9.56% across the entire range.
$63,720 (400% FPL) - technically there could be a huge spike (cliff) at this income level because when you make $63,720, you lose all remaining premium credits. There could also be no spike if you choose the cheapest health care plan, in which case your premium subsidy may have already been exhausted at this income level. I chose not to show it on the graph because it’s not a constant percentage for all situations but it’s important to be aware of this premium cliff.

To summarize, you will see an increase anywhere from 9.56% to as much as 18.5% in your effective marginal tax rate due to the reduction of the premium tax credit. The average increase across the whole range (133-400%) is 12.8%. Since this occurs in the 10-15% income tax ranges, this is a big jump in marginal tax rates.

Effective Marginal Tax Rate

The next graph simply combines the marginal tax rates with the effects of the reduction in premium subsidies to come up with the effective marginal tax rate. It’s somewhat startling to see that the effective marginal tax rates can be higher than those for people earning over $96,000 (603% FPL).

What we normally think of as the 10% tax bracket is now approximately a 25% tax bracket. The lower end of the 15% tax bracket (below $48,000) has become a 32% tax bracket. And between $48,000 and $64,000 the marginal tax rate is nearly 25%. We finally return to the 15% tax rate above $64,000 but lose the premium subsidy.

Capital Gains

Long-term capital gains are are similarly affected. Instead of having zero marginal tax rates up to the 25% bracket, there are now significant marginal effects in the 133-400% FPL range. And in the 250-300% FPL range you would be at a higher marginal rate (> 15%) than people with much higher incomes.

Strategies

The discovery of this increase in marginal tax rate has colored my views on how and when to take income from my portfolio. It mostly boils down to the concept of delaying my taxable income until age 65 when Medicare kicks in and I no longer am eligible for ACA credits. Alternatively, either Mrs. Moneycle or I could get a job with health benefits, but that requires working.

Here are some things you can do to push income forward.

Deplete taxable and Roth assets before touching IRA/401k funds
Perform tax-loss harvesting to capture losses now (taking gains after 65)
Defer IRA to Roth conversions which produce taxable income
Move dividend-producing assets like bonds into IRAs
Delay taking pensions and social security until after age 65
When buying annuities, add a cost-of-living adjustment (COLA) which gives you less income in the early years and more income later.
Use delayed income annuities which start at age 65 or beyond

If most of your investable assets are in tax-qualified accounts (IRA/401k), then you may not be able to defer your taxable income as much. In this case I would recommend spreading your Roth and taxable asset withdrawals from now until age 65 so that you can get a little benefit each year. But you might want to consider lumping those same assets over just a few years if it allows you to push your income below 400% FPL and get a tax subsidy for a few years.

Keep in mind, if you are able to push income forward until age 65, you probably want to take as much income as you can between ages 65 and 70 while staying in the 15% tax bracket. This is because at age 70, you will most likely begin taking social security and also be required (at age 70.5) to take required minimum distributions from your IRAs which all adds up to more taxable income.

So the overall strategy is, (1) take as little taxable income as possible while receiving ACA subsidies, (2) take as much taxable income as possible while not receiving ACA subsidies, and (3) make it to age 70 and thank your younger self for planning ahead.

HSA Tax Advantages

Fri, 22 Jan 2016 00:00:00 -0700

This time of year has me thinking more about taxes than normal because I recently took a first stab at income taxes for 2015. While doing my taxes I noticed the subject of Health Savings Accounts (HSAs) coming up in a couple different places so I thought I would share why HSAs can be an awesome place to invest your savings.

The main reason that HSAs are great is the ability to pay for things with pre-tax dollars. Depending on your tax bracket, this can be a huge “investment”. Consider going to the doctor and spending $100 from an HSA with before-tax dollars. If you had to use after-tax dollars for that same $100 expense, and you were in the 25% tax bracket, you would need to earn $133.33 in order to have the $100 left over to pay the doctor. Or to look at it another way, by using an HSA you avoided spending $33.33 before tax, which is $25 after tax.

To put that mathematically, the money saved by using money from an HSA instead of after-tax dollars is,

money_saved = (money_without_hsa - money_with_hsa)*(1-tax_rate)
money_without_hsa = invoice_amount/(1-tax_rate)
money_with_hsa = invoice_amount

which reduces to,

money_saved = invoice_amount*tax_rate

So, if you know you are going to have X dollars in medical expenses, it behooves you to have X dollars sitting in your HSA because you will save X dollars multiplied by your marginal tax rate in after tax dollars.

Common HSA uses

The most common uses for HSAs are basic medial expenses.

Dentist - use your HSA card to pay for that cleaning or root canal.
Doctor - doctor bills could be has high as your deductible, so you probably want to build your HSA up to the amount of your deductible to cover large expenses.
Prescriptions - those Viagra pills are expensive!
Vision - in addition to regular visits to the eye doctor, you can use HSA funds to pay for eyeglasses and eye surgeries including laser surgeries.

Lesser Known HSA uses

Here are some ways to use HSA dollars that you may not have heard about.

Long-Term Care (LTC) premiums - there are limits, but LTC policy premiums can be paid in part using HSA dollars. The older you are, the more of your premiums are allowed to be paid using HSA dollars. For tax-year 2015 the limits are as follows:
- 40 years old and younger – $380
- 41–50 years old – $710
- 51–60 years old – $1,430
- 61–70 years old – $3,800
- 70 years old and older – $4,750
Medicare premiums - you can’t continue contributing to your HSA after you hit medicare age (65). But you can use your HSA funds to pay for supplemental Medicare insurance such as Medicare Part B, D or Medicare Advantage. This is a good reason to contribute above and beyond your deductible level before you hit age 65.
Construction expenses - as you get older, you may find you need to need to make modifications to your house. Construction expenses to accommodate somebody with medical issues may be paid for using HSA funds. Examples include wheelchair ramps, hand rails, widening doorways, etc..
Vasectomy - pair your vasectomy operation with your Viagra prescription and put the whole thing on your HSA debit card!

There are a ton of other things you can use HSA funds for. Check out the IRS publication for details.

In the grand scheme of investing, HSAs are generally considered the 3rd priority behind (1) getting your 401k match if you have it and (2) paying off credit cards. Besides the advantages described above, HSAs also act like an IRA in that the growth of funds inside the HSA are tax deferred. While you can take the funds out after age 65 and be taxed on them just like an IRA, it’s probably best to leave your money in the HSA and continue using it to pay for medical expenses until the HSA is drained.

Moneycle

Journey to Financial Independence

Understand Your Expenses

Milestone #1 (M1) - Emergency Fund Invested in “Safety”

Milestone #2 (M2) - 20 Years of Expenses Invested in “Growth”

A Better Rule of Thumb for Bonds

Milestone #3 (M3) - 5 Years of Expenses Invested in “Stability”

Milestone #4 (FI) - Financial Independence (30 Years of Expenses)

Not Quite a Target-Date Fund

Other Considerations

Key Takeaways

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To Roth or Not to Roth - Part 3, Retiring at Age 70

Retiring at 70

Starting Simple

Simple example

Back to the Future

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Another Fun Interactive Plot

When You Assume

Super-Simple Virtual-Buffer Withdrawal Strategy - Revisited

The Simplest Version

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The General Version

Easy Peasy

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To Roth or Not to Roth? - Part 2, Reframing the Question

Basics - Tax Efficiency

Filling Future Tax Brackets

Upper Bounds for Traditional Accounts

Other Income Sources

Realistic Tax Brackets

Coming Next

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How Social Security Messes With Your Tax Brackets

For Math Nerds click to show/hide

Interactive Plot

Observations

Implications

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To Roth or Not to Roth? - Part 1, The Ideal World

Basics of Roth vs Traditional

The Tradeoff

Filling Up The Tax Brackets

Saving within a Single Tax Bracket

Other Income sources

Saving Across Multiple Tax Brackets

Insights

When You Assume, You Make Me Read Part 2

Radioactive Half-Life of Expenses

Lump-Sum Investment

Super-Simple Virtual-Buffer Withdrawal Strategy

A Bit of Math

Example Using 30-30 Numbers

Making it Even Simpler

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Sample Portfolios

Step-By-Step

Nerd Alert

Parting Thoughts

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Affordable Care Act May Increase Your Marginal Tax Rate

Marginal Tax Rates

Marginal Effects of Tax Credit Decreases

Effective Marginal Tax Rate

Capital Gains

Strategies

HSA Tax Advantages

Common HSA uses

Lesser Known HSA uses