Periodically we have always believed here that is worth stepping out of the here-and-now-- the noisy world of fluctuating markets and tweeting politicians – and consider some of the big questions from a fresh lens.

None of them is bigger than this: what is investing for and why do we do it?

Investing is, by its very definition, an act of taking a financial surplus (more income than expenses) that exists in one time period and trying to increase its value so it will be worth more during a time period of financial dis-surplus (more expenses than income). If you could anticipate with 100% certainty that your income from labor would always exceed your expenses, then there would be no point to save, and thus no point to invest your savings.

But most people will go through either involuntary or voluntary periods in there life where their income from labor falls short of their expenses, so it makes sense to prepare for these periods by 1) Saving money, 2) Getting as high of a real return on those savings in the intervening years as possible so that you can use them to fund as many expenses as possible in the future (or at least so they will be there if you NEED to fund a large unforeseen expense).

That part is clear – but it begs another question – what should you do when you enter the period where your expenses do exceed your income but you still have accumulated investments to manage? Obviously a portion of this time will consist of “deaccumulating” your investments – of selling some of them to fund your expenses. But how should you manage the rest? And since generating income in these periods is actually the rational goal of investing, should we spend more time thinking about how to manage them most optimally?

For most people of course, the longest period of time in which they will be “de-accumulating” savings is called “retirement.” And there is a prescribed course of action for what you should do in this period, which usually involves transitioning to more conservative forms of investment that are less likely to lose value. Below, we will explain how a data-driven analysis shows that to be largely unfounded advice. But first, some basic principles.

At IvyVest, we get a fair share of questions about investing in retirement. Questions generally fall into two categories – “how” and “how much”:

- How much do I have to save before I can retire? Relatedly -- how much can I safely withdraw when I’m in retirement?
- Should
*how*I invest change (asset allocation) as I enter retirement?

We’ll answer each of these below. But before addressing each issue, we should state up front some principles. We assume that retirees are interested in:

- Taking stable withdrawals that increase at the rate of inflation
- Cutting withdrawals up to 25% in event of a market disaster (this would cause an accompanying change to standard of living in that year of course)
- Maximize to near 100% the chance of not outliving your portfolio. Subject to previous constraints, we think most will want to maximize the residual value of the portfolio as it will be passed on to heirs and/or charity

To be brief: investors want to take as much income as they can while they are alive without worrying (too much) about running out of money before they die.

With this in mind, let’s take discuss the first issue first: How much can you safely withdraw from an investment portfolio in retirement to meet the above objectives?

Having a ballpark idea of this figure is important not just in retirement, but also to know how much money you should accumulate before retiring. For instance if you want to generate $50,000 in income from your investments in retirement and you can bank on a 5% withdrawal rate, than you need to save about $50,000 / .05 = $1,000,000 to retire (this may seem like a lot, but keep in mind that living expenses can be lower in retirement and you may have additional sources of income like social security or a pension).

There was a time when some people looked at the average return on stocks in the 20th century (about 7% after inflation) and said you could withdraw that much, with the logic being that over time as long as you were able to return this amount, your principal would stay intact. This is obviously wrong because stocks are volatile and have significant periods of negative returns. If you happened to retire just before a downturn, a 7% withdrawal rate might quickly deplete your funds to 0.

Perhaps the first serious effort to look at safe withdrawal rates was a study by Bengen (reference 1) in 1994. His study gave rise to the “4% rule”: you can safely withdraw 4% the first year and then adjust this withdrawal up or down based on inflation so as to maintain constant purchasing power. Note that after the first year you may be withdrawing more or less than 4% of your portfolio depending on market performance and inflation rates. Bengen came to this conclusion by considering a 50/50 portfolio of stocks (the S&P composite index) and bonds (10 year treasuries) and tracking how the portfolio would have performed for various retirement dates and withdrawal rates. Based on historical data, a 4% initial withdrawal rate was always safe for at least 30 years. Higher withdrawal rates resulted in considerable probabilities of failure (total depletion of retirement assets). His retirement dates were for the period from 1926 to 1976 (for the later years, Bengen had to extrapolate the historical data).

Table 1: Portfolio Survival Probabilities (%). The data is taken from reference 2 (Pfau).

Other people have done similar studies. In 2014, Wade D. Pfau did a study that included portfolios with different mixes of stocks and bonds and more recent market data. His results are abbreviated and summarized in Table 1. They show that a portfolio with 50% or 75% stocks lasted for at least 30 years (in most cases, the residual left after 30 years was considerable, but this isn’t shown in Table 1). An all-stock portfolio did almost as well, but going below 50% stocks produced significantly lower portfolio survival rates (which already calls into question rules like “own your age in bonds” which would imply a 70% bond portfolio for a 70-year-old).

We have done a similar study looking at a 30 year duration and retirement dates from 1926 to 1986 (allowing for a full 30 years of historical data for each start date). We used the stock market data from Robert Shiller’s website (econ.yale.edu). We added the possibility that a retiree could reduce his withdrawal in a year when the portfolio was relatively depleted due to poor market performance. If the portfolio had declined more than 16% in real (inflation adjusted) value, we reduced the real value of the withdrawal by the same amount, but not by more than 25%.

Table 2 shows our results. The table shows the portfolio survival probabilities, the average real final value of the portfolio after 30 years, and for the cases where withdrawal reductions were taken, it shows the percent of withdrawals that were reduced. The average portfolio value includes all cases, even those that failed (the end value was zero), but the percent of withdrawals that were reduced includes only those portfolios that survived for the full 30 years. As in the Bengen and Pfau studies, the data shows that the 4% rule is valid and there is no advantage to reducing stock exposure to less than 50%. The data also indicate that the initial withdrawal rate can be increased a little, perhaps even to 5%, if you are willing to accept reductions in the withdrawal rate when the market is down. There is no surprise here, and it’s what most people would probably do anyway. The average real final portfolio values show a clear advantage for sticking with stocks as long as the failure rate is acceptable. When the portfolio had 60% or more in stocks, and the initial withdrawal rate was 5% or less, the average final value was almost always greater than the initial value despite the fact that some portfolios might fail and end up with zero balances.

Table 2: 30 Year Portfolio Survival Probabilities with and without Withdrawal Reductions. Reductions are described in the text. The average final portfolio value is given as a percent of the beginning value.

So from a historical perspective, the 4% rule looks good, but does it apply to the present time? It is based, for the most part, on historical data from the middle and end of the 20th century. This was a time when the U.S. population was younger and growing faster than it is now, and it was a time when interest rates were higher than they are now. Pfau (reference 3) is one of several people who have questioned the use of historical data and tried to do something about it. We’ll discuss his approach shortly.

In our newsletters, we have commented that we think future stock market returns are likely to be lower than past returns, so can we really trust the historical data to estimate safe withdrawal rates? Probably not. To overcome this problem, we need a model which predicts future returns based on present conditions. Vanguard has developed the Vanguard Capital Markets Model in an attempt to do this. We have neither the time nor the information to describe this model fully, but we can summarize the information that Vanguard puts on their website. The model is based on historical data and on correlations of past market performance with various economic and market factors. Using these correlations, it assigns probabilities to possible future market developments. Taking account of current conditions, Vanguard computed the probability of portfolio survival for several durations, portfolio assumptions, and initial withdrawal rates.

Table 3 shows results that were taken from information on their website. Note that the 4 % rule gives only an 85% chance of portfolio survival for a 30 year duration. So taking account of current conditions has dropped the portfolio survival rate for a given withdrawal rate. Vanguard doesn’t present, and their methodology probably doesn’t allow, a withdrawal rate for 100% chance of portfolio survival. However, in other respects their results are consistent with the historical studies. Portfolios with 50% to 80% stocks have better survival chances than those with only 20% stocks, and a 4% initial withdrawal rate is a reasonable starting point even if it doesn’t allow for a 100% chance of portfolio survival.

Table 3: Withdrawal rates consistent with an 85% or 75% chance of portfolio survival. Data was taken from the Vanguard website. The shaded values are the withdrawal rates (in percent) that are consistent with the given portfolio survival probability, portfolio composition, and duration.

You may have noticed an apparent (but not real) contradiction in all of the studies just discussed. To get a high probability of long term portfolio survival, you are driven to rather low initial withdrawal rates. But even with these low initial withdrawal rates, the portfolio usually actually grows in value. This apparent contradiction occurs because you can’t predict future economic and market conditions when you retire, and of course you can’t predict how long you will live, so for a high chance of portfolio survivability, you must allow for bad market conditions. Most retirees probably want both portfolio survivability and a significant residual value to leave to heirs (or to take care of unexpected emergencies). Choosing a withdrawal rate requires balancing these two competing objectives. Some people may consider a large residual balance as a wasted spending opportunity. Others may want the satisfaction of leaving something for heirs or a charity. Depending on where you fall on this question as well as how much flexibility you have to adjust your lifestyle in the event of a market meltdown, a withdrawal rate of 4% still seems reasonable, even in today’s low-return environment.

With the “how much” question answered, let us now return to the “how.” So how do we think you should invest in retirement? There is a common opinion in many circles that you should reduce your exposure to stocks as you get closer to retirement and into retirement, and for many people that means increasing the exposure to bonds. Many of the major mutual fund companies follow this advice with their “target date” funds that include stocks and bonds in varying portions.

As the target date approaches, the allocation to stocks goes down and the allocation to bonds goes up. In some cases, this shift in allocations continues even after the target date has passed. So for instance, Vanguard’s Target Retirement 2015 Fund (presumably for people who are two years into retirement) allocates about 56% to bonds and 44% to stocks. Their Target Retirement Income Fund, presumably for people who are well into retirement, allocates about 70% to bonds and 30% to stocks. T. Rowe Price’s Retirement 2010 Fund, presumably for people who are well into retirement, allocates about 40% to stocks and 60% to bonds.

From one point of view, these recommendations seem reasonable, since retired people don’t have as much time to recover from stock market downturns. Bonds provide a more stable source of income. However, in real (inflation adjusted) terms bonds can take big loses in times of inflation, and bond yields are currently very low by historical standards. Leaving annuities aside for the moment, the analyses that we have looked at and discussed here indicate that a retirement portfolio should have 50% to 80% stocks. Going below 50% stocks does not appear to help either portfolio survivability or residual value – it is just suboptimal in both dimensions so investors would have no reason to choose it. Yet these are the portfolios that the mutual-fund conglomerates put their customers in, despite lack of theoretical or empirical evidence that this makes sense.

To derive a more intelligent approach, we need a better framework. Pfau, reference 3, has provided a framework for considering optimal portfolio construction in retirement that fits the boat with a number of smart elements:

- He incorporated current economic conditions into assumed returns. Pfau did not assume that future stock returns would be the same as historical stock returns. Instead, he looked at 110 years of past data and assumed that, on average, the difference between stock returns and treasury bond returns (the equity premium) would be the same in the future as in the past. Since interest rates are currently very low, this yields a low value for stock returns. He derived a mean (geometric) real return on stocks of 3.1%. This is well below the 20th century value, which is more like 7%. His estimate for mean (geometric) bond returns was based on the current (at the time he did the calculations) return for TIPs and was 0.1%.
- He includes volatility (year to year variations) in these values by looking at the historical record and using historically derived standard deviations. This introduces probability into the calculations, so for a given portfolio there will be a wide range of possible outcome. The performance of each portfolio must be simulated many times to determine the range of results.
- Whereas the other studies that we have discussed considered fixed durations (lengths of retirement), Pfau considered the age of the retiree (at retirement) and incorporated the mortality tables into his calculations. It’s easier to discuss this if we consider a cohort of say, 1000 retirees, who all retire at the same age at the same time. So in any given year after retirement, a certain number of them will die based on the probabilities in the mortality tables. If their portfolio still has value, that value will be added to “value at death” sum. For each year that a retiree lives and is able to receive the full income requirement, that sum is added to the “requirement needs met” sum. If the retiree is unable to receive the full income requirement, the shortfall is added to the “un-met retirement needs” sum (note that after the volatile portion of the portfolio is exhausted, the retiree may continue to receive annuity payments).

Pfau ran these calculations for a variety of portfolios that consisted of some combination of stocks, bonds, and several types of annuities. You probably know what an annuity is, but in any case we’ll come back to that shortly. Based on their chosen portfolio composition, the retirees will have a portion of their funds in volatile assets (stocks and bonds) and a portion in non-volatile assets (annuities). In some cases, the annuity benefit is not inflation adjusted, so the real value of the benefit may decline with time. Each year the retirees will use the annuity payments to cover as much of their required income as possible and rely on the volatile assets for the rest. If the annuity income exceeds their requirements early in retirement, the extra income is added to the volatile portion of the portfolio. If the volatile portion of the portfolio is exhausted, and the annuity portion doesn’t cover all of their required withdrawal, they will suffer a retirement shortfall.

Because of the probabilistic nature of the assumed market returns, any given portfolio can give many results for the same cohort of retirees and the same withdrawal rate. However, by running the simulation many times, one can determine an average value of the portfolio at death. For each simulation, the total amount of met and unmet retirement needs will vary, but in the interest of conservativism, Pfau chose to present a “percent of retirement needs met” as the 10 percentile worst case (90% of simulations did better, 10% did worse).

For many portfolios, Pfau then plotted the average value at death versus the percent of retirement needs that were met. Note that in both cases, these quantities apply to the whole cohort of retirees, not to any one individual. Figure 1 is a figure that we replotted from Pfau’s paper. It refers to a cohort of retirees (each a married couple) that retire at age 65 and need to take an initial 4% withdrawal from their portfolio. The simulations are continued until both members of each couple die. As in all other cases discussed here, the withdrawal rises with inflation in the years after retirement. The vertical axis is the average value of the portfolio at death. The horizontal axis is the percent of retirement needs that were met, but in this case Pfau is presenting the 10 percentile worst case. Note that the horizontal axis begins at about 83%, so in all cases most of the retirees needs were met (but if your situation happened to be one of those who fell short, you might be rather unhappy).

The best results are the ones that are as high as possible on the graph and as far right as possible, but it is necessary to make a tradeoff between the two objectives. The results that have the best survivability (horizontal axis), don’t have the best death value (vertical axis). The portfolios that have the best survivability for a given death value and the best death value for a given survivability form what Pfau calls the “income efficient frontier” (the terminology is borrowed from Modern Portfolio Theory, but we won’t go into that).

The thing that is notable and somewhat surprising is that the income efficient frontier is composed of portfolios having only stocks and single premium income annuities (SPIAs). It doesn’t have bonds or any other type of annuity. This frontier is the blue curve to the right in figure 1. If Pfau considers only stocks and bonds, leaving out annuities, the income efficient frontier is the red curve to the left. Note that on the red curve, the best survivability is with a portfolio containing about 50% stocks. This is in line with the other calculations that we have discussed.

However, with a 4% initial withdrawal, this portfolio only meets about 88% of retirement needs (but remember that this is a 10 percentile worst case). Also, the average real value at death for this portfolio is only about 50% of the initial portfolio value. Both of these results are much worse then the results presented earlier. The reason is partly due to the use of the mortality tables, which means that some retirees will have a very long retirement. However, the biggest reason for the difference is that Pfau is assuming that future returns will be much lower than past returns. Predicting the future is hard, but we agree, and have often said, that future returns are likely to be considerably less than historical 20 century returns. Nevertheless, we think Pfau’s 3.1% predicted return (real) for stocks may be too pessimistic.

Figure 1: Pfau’s data showing the retirement income tradeoffs for a 65 year old couple who need to withdraw 4% of their initial portfolio value, inflation adjusted, per year. The numbers on the blue curve are the percent stocks followed by percent SPIAs. The numbers on the red curve are the percent stocks followed by the percent bonds.

So a first glance, Pfau’s figures seem to say that a retirement portfolio should consists of stocks and income annuities. So let’s discuss annuities. You don’t know how long you will live, so it is difficult to know how much of your savings you can spend per year. Annuities are a way around this problem. An insurance company will take your accumulated funds and give you a fixed stream of income that lasts until your death. They will even give you a stream of income that is inflation adjusted. Basically, they are using the funds from those who die early to pay benefits to those who live longer. Annuities have a bad reputation in some circles because they have sometimes been sold by aggressive salespeople who earn high sales commissions (which of course reduces benefits to the annuitant). In some cases, other fees and administrative expenses may be quite high, but there are reasonably priced possibilities.

There are several types of annuities. The single premium income annuity (SPIA) pays a fixed benefit for life. Inflation adjusted SPIAs (sometimes called real SPIAs) will adjust the benefit for inflation, at the expense of a smaller initial benefit. Variable annuities that invest in a portfolio of stocks and bonds also exist. Their benefit rises and falls with the markets, but they can be purchased with a guaranteed life withdrawal benefit. We aren’t going to discuss variable annuities here, but don’t think they are good investments for most people, and in any case, they didn’t fall on Pfau’s efficient frontier. Pfau considered these three types of annuity in his calculations, but on the efficient frontier, the portfolios contained only stocks and SPIAs (not inflation adjusted).

To give you a feel for what you can get with an SPIA, we took an example from the website immediateannuities.com. For a one-time payment of $100,000 a 65 year old single man can buy an annuity that provides $6516/year fixed or $4464/year inflation adjusted for life. A sales fee in the range of 2% to 3% will probably be added to the $100,000, but the inflation adjusted initial benefit is close to 4.4%, so you could do slightly better than the 4% rule. However, SPIAs have no residual value at death, so to the extent that you annuitize, you are giving up the possibility of leaving something to your heirs or having something to use for emergencies. (Actually, annuities with a guaranteed death benefit are available, but they further reduce the payout).

So what about including annuities? With the assumptions that Pfau made, SPIAs look like a good alternative for part of your portfolio. However, it is important to note that he made very low return assumptions for both stocks and bonds. Also, he assumed that inflation would average only 2%. While inflation has been running under 2% for some time, you should remember that the U.S. had a spell of double digit inflation in the late 70s and early 80s, and that could happen again. For that reason, we think non-inflation adjusted SPIAs for retirement are risky. Inflation adjusted SPIAs are a possibility that should be considered. If you are worried about your funds running out, buying an inflation adjusted SPIA to cover your minimum expenses (after Social Security and pensions) might be a good idea to supplement an IvyVest portfolio.

So what’s our bottom line? We think the 4% rule is still a good place to start when thinking about retirement. You might be able to increase it a little if you are willing to take reductions when the market is down, and you might be able to increase it a little by using an inflation adjusted SPIA, but in the latter case you will do so at the cost of giving up part of your legacy to your heirs (and access to emergency money). For investments, we don’t think moving to a high percentage of bonds in retirement is helpful. We think a continued exposure to equities is appropriate, and we recommend staying with the IvyVest portfolio. Investors that place a high premium in insuring they continue to have liftetime income with high certainty may want to supplement the overall IvyVest portfolio with an inflation-controlled deferred annuity (one that starts in the future), thereby splitting their portfolio into a "risky" piece (the IvyVest portfolio) and a risk-free piece (the inflation-protected annuity).

References:

1. William P.Bengen, “Determining Withdrawal Rates Using Historical Data”, Journal of Financial Planning, 1994

2. Wade D. Pfau, "Trinity Study, Retirement Withdrawal Rates and the Chance for Success, Updated Through 2009, retirementresearcher.com

3. Wade D. Pfau, “An Efficient Frontier for Retirement Income”, SSRN [http://ssrn.com/abstract=2151259], 2012

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