Rabbits, Roths and Returns: A Retirement Primer

Everyone today is worried about their retirement, but most of us do not know just how worried we should be or what exactly we should worry about (other than the general thought of our 401k shrinking), much less what to do about it.  Say what you will about the value of choices, we are so overwhelmed with them today that we don’t have the resources to weigh them.  Just in relation to retirement, there are a number of variables to consider:

• Company funded plan or individual?
• Traditional or Roth?
• How much can I afford?
• How much do I need?
• How much time do I have until retirement?
• Stocks?
• Bonds?
• REITs???
• Money Market?
• Full service broker or discount?
• Domestic or international?
  This list does not even come close to be inclusive.  Under the stocks heading, there are individual stocks and mutual funds; under mutual funds, there are managed funds and index funds, closed and open, tax managed, the list goes on.  So, for the most part, we either do nothing, put away a token amount in a random vehicle, or take the advice of someone who is probably just as lost as we are.
  If this seems a foolish way to handle something so important…. it is!
  Though few of us have the time to fully educate ourselves on every aspect of financial planning, there are a few concepts that are worth being informed on.
  Age Adjusted Allocation and Dollar Cost Averaging
  First is the volatility of the market.  The market decline that followed the housing bust and bank bailouts may not have been the worst ever, but for those watching their retirement dollars shrink, it seemed like it.  Many delayed retirement, while others contemplated pulling their savings out of the market in favor of something more stable.  Neither should have happened if a little more information had come along with the initial decision to invest.
  A quick look at a chart of Dow-Jones monthly opening prices shows that the market has consistently grown in the long term over the last 80 plus years.  The black lines indicate mathematical ‘fit’ lines that attempt to (and do a fair job of) approximate the average growth of the market over time.
  
  It is even possible to use these mathematical models to give an average monthly return on investment (slightly over one percent).
  But look at the yellow line (actual values) and it is obvious that this upward trend is not a smooth climb.  The trend involves numerous small up and down movements, along with a few more major bounces.  It is because of these ‘runs’ and ‘corrections’ that stock market investment should be done with the long term in mind.  Someone early in their career with several decades to weather the ups and downs of the market can afford to have a very large share of their retirement funds in the market.  But as retirement age approaches, the percentage subject to these unpredictable fluctuations should necessarily decrease, so that a large dip does not wipe out the majority of a retirement account just as it was supposed to start paying out.
  Beyond adjusting for risk based on age, the potential still exists for irrecoverable loss, even for the youngest workers.  The worst drop on this chart, in 1929, which appears proportionately smaller than it was due to the scale of the chart, did not recover to its peak levels for over 25 years.  That means that at any time before 1954, some portion of the money invested at the peak in 1929 was gone (a very large chunk for the decade after the crash).  Even after the market returned to pre-crash levels, a dollar in 1954 was worth less than it was in 1929, so there were still losses in real dollars; a certain amount of return on investment is necessary just to break even.
  
  Of course, few of us invest for retirement in one lump sum and this is fortunate.  A look at the value of 1000 dollars invested in a lump sum versus the same amount invested in smaller sums over time, starting just before the crash, demonstrates the advantage to investing over time (called dollar cost averaging).  The third column shows 1000 invested over time starting a year before the crash; more dollars invested at the peak carry a penalty, but this is still overcome by the number of years investing at lower market prices:
  Note that the 1000 invested in a lump sum does not recover its value, even after 25 years, where the 1000 invested over time recovers its value before 10 years is out and shows total returns in the 80-140 percent over 25 years.  Also remember that as the 1000 dollars is spread over time, the amount per month goes down and the percentage of earnings put into retirement shrink as the 3 dollars per month invested in 1954 makes up a smaller part of the average paycheck than the 3 dollars invested in 1929.
  Why is this?
  A quick manipulation of a few Dow averages shows how dollar cost averaging means more stock shares are purchased at market bottoms than at the peaks, so the average cost paid per share is much lower.  This chart compares a few historical values for the Dow with the number of ‘shares’ 1000 dollars would have purchased at that level.
  
  At the pre-crash level, 1000 dollars bought about two and two-thirds times the shares that made up the Dow.  Three years later, the same amount bought over 23 times the shares (or nearly 10 times as much stock as it did pre-crash).  By 1988, that 1000 only got about half the shares (or about 1/5 of what it did in 1929).  So, by investing over time, not only is the risk reduced, there is actually a benefit from market fluctuations, to the point that profit can be made even over time frames where the market’s overall trend is negative or flat.  The magnitude of these fluctuations, by themselves, are unimportant to this principle, as demonstrated by the fact that increasing the size of monthly variation by 10 percent only made a 10 dollar difference over 25 years; what is important is the amount of time the market stays below the level at which withdrawals are made and the average difference between the market level at withdrawal and the level while contributions were being made.  So, a 30 year old who sees their 401k drop by 20 percent should not be considering a change in investment allocation; if anything, they should be thinking about increasing the level of contributions.
  Thinking About Taxes
  Roth IRAs are all the rage right now because of the difference between how they and traditional IRAs are taxed.  Where traditional IRAs, like 401k or 403b plans, are funded with pre-tax dollars, reducing their impact on take home pay, a Roth is funded with after-tax (take home) dollars.  On the other end, a traditional IRA is taxed when withdrawals are made, while withdrawals from a Roth are tax exempt.  So, the argument goes, in an IRA, the contributions and earnings on investment are delayed until the money is accessed, but with a Roth the contributions are taxed upfront, but the earnings on investment are NEVER taxed.  Sounds like a big advantage, right?
  Maybe.
  All things being equal, it really doesn’t matter.  If a certain amount of net or gross income is set aside for retirement, the total contribution that comes out of that is higher for the traditional IRA than for the Roth, which means there is more money in place to grow over time.  For instance, if someone can afford 100 dollars per month out of their household budget for retirement, that hundred can go into a Roth directly as 100 dollars; if they decide to do a traditional IRA instead, assuming a 20 percent tax bracket, they can put 125 dollars in.  This is because the 100 dollar Roth contribution actually came from 125 dollars in gross pay that had 25 dollars (20 percent) taken out for taxes; the IRA, being pre-tax, allows 125 dollars to come out of gross pay, reducing take home by 100.
  Some Roth proponents will now argue that because earnings make up such a large part of long term investment, the tax exempt nature of earnings in a Roth make it preferable, while IRA proponents will say that the tax advantages of their plan allow more money to get in, which means there is more to earn returns on.  Rather than bog down in a mathematical argument on this one, a visual will more easily convey the truth:
  Imagine you have 5 rabbits and ask a friend to help build a cage.  In return, the friend will accept either 20 percent of the rabbits you now have or 20 percent of the rabbits you will have in a year.  For the sake of argument, assume that you have an abundance of rabbit food and that there is no extra cost or effort to take care of the fifth rabbit, so all that matters is how many rabbits you end up with in the end.  Finally, assume that all rabbits are pregnant females and will have two babies by the end of the year.
  To start, you have 5 rabbits (green background represents your rabbits):
  
  Now, if you keep all five and give 20 percent to your friend at the end of the year, the result is 15 rabbits – 3 for your friend (20 percent of 15) = 12 rabbits for you:
  
  Now, consider the other alternative:
  
  Here we have 4 rabbits for you and 1 for your friend.  It should be easy enough to see that the one in the red background will have 2 baby rabbits, while the four in the green background will have eight more, bringing the total to 12 and 3 again:
  
  The allegory is not hard to apply to money: Investing pretax dollars in a traditional IRA, the money grows (tripling like the rabbits, quintupling or just growing by 10 percent does not matter) and taxes are paid on the whole thing.  Investing after tax in a Roth, imagine the dollars invested in the green background, while the dollars paid in taxes sit in the red background, along with the earnings not accrued on them.
  So, all things being equal, how do you decide?  There are a few considerations that vary by circumstances.  An above average earning individual late in their career who has saved nothing to this point will likely be in a higher tax bracket now than in retirement, so getting the break from the IRA now makes more sense (those in the top brackets do not have the Roth option).  A lower earning individual early in their career, especially if they are a disciplined saver, will benefit from the tax exemption later in life, as their bracket will be higher then.  Beyond that, there are personal views on what tax rates may do over time, fear of changing tax laws regarding the status of Roth’s might also play into it.  But there is one case in which the choice is clear.
  If you are eligible for a Roth and will be making the maximum contribution, the Roth has the advantage of allowing a greater amount of gross income into retirement.  This is because 5000 dollars pre-tax into a traditional account is 5000 gross invested.  But 5000 invested after tax represents a greater amount, depending on the marginal bracket of the investor; using 20 percent, 5000 into a Roth is 6250 from gross earnings.  As it has been shown that the outcome for similar contributions from gross is the same for either, the ability to make a greater contribution from gross allows the Roth to yield a greater total value.
  Another feature of a Roth is that contributions (not earnings) may be withdrawn at any time without penalty.  For some, this may be a safety net, but others might find it a temptation- the judgment is up to the individual in this case.
  Finally, for those with 401k or 403b plans that offer an employer match, this is just free money.  Imagine with the rabbits that the store where they were purchased called to say they were retroactively offering a buy one-get one free deal and were bringing 5 more (pregnant) rabbits over.  In the end, you will be losing three more to your taxing friend, but will have 12 more, too.  Other than that and the possibly more limited investment choices (and management costs), these plans offer the same kind of tax treatment as a traditional IRA.
  Investing Early and Often
  There are a number of allegories about compounding returns, one famous one has someone placing a piece of rice in the corner of a checkerboard, two on the next space, four on the next, then eight, etc, covering every space.  Another has someone saving a penny one day, two the next, four, eight, sixteen, and so on for a month.  The questions, respectively, are how many pieces of rice are on the last space of the checkerboard and how much money is saved at the end of the month.
  Taking the second question first, start by summing up the days:

• Day 1- 1c
• Day 2- 1c + 2c = 3c
• Day 3- 3c + 4c = 7c
• Day 4- 7c + 8c = 15c
  The pattern here for the total is that each day’s total is one cent less than the next day’s contribution.  The pattern for the contribution is 2^(x-1), with x being the number of the day (the ‘^’ sign means to the power).  This problem is not too difficult to take to completion with a calculator, but plugging in the formula, the last day’s total is one cent less than the next day’s contribution.  Assuming a 30 day month, the 31^st day would have 2^30 c, so the total for the 30^th day is one cent less than that. This equals 10, 737, 418. 24 – over 10 million dollars!
  The checkerboard problem is simpler, as it only asks for the last entry, which is 2^63, which is over 9 quintillion (a quintillion is a 1 with 18 zeroes after it).
  This relates to investing in that when you double something twice, you actually multiply by four.  So if your investment doubles every 10 years, after 20 you have four times as much and after 30, eight times as much.  By the same principle, it does not take 10 years at 10 percent to double, since each year earnings accrue on the original amount AND the previous year(s)’ earnings.
  For example, 1000 dollars at 10 percent annual yields 1100 dollars after one year.  But the second year, that 10 percent is applied to the 1100 (which is 1000 investment and 100 return), yielding 1210.  The third year yields 1331; the fourth, 1464.10 and the investment doubles after seven and a half years.
  Taking all this together, an investment at 10 percent (which is slightly less than the market average historically) over 30 years is not 10 times 30 =300 percent (quadrupling the original investment by returning triple in returns), but involves doubling 4 times (30/7.5=4), which means 2^4, or 16, times the original investment.  A person putting 1000 in at age 25 will have 16000 at age 55.  Cut that time in half and an investment of 1000 at age 40 will only yield 4000; or, conversely someone who wanted 16000 at age 55 could invest 1000 at age 25 or 4000 at age 40.  Time is a friend to the investor and the more there is, the better.
  Summary
  Investing for retirement can be as complex as desired, but it can only be simplified to a limited extent without losing valuable information.  The basic concepts of compound returns, dollar cost averaging and pre-tax versus after-tax investing are three that every one should understand if they want to get the most out of their retirement contributions.  Beyond that, there is a wealth of information on types of investments, strategies and personal finance, much of it free online, in podcasts or at the library; retirement years are becoming longer each generation- it is worth spending a little bit of time now preparing for what will hopefully be a lot of time in financial security then.