## Thursday, July 9, 2015

### 4% Rule Experiments Using Longevity Statistics

The well-known 4% rule for retirement spending comes from a 1994 paper by financial planner William Bengen called Determining Withdrawal Rates Using Historical Data. Some time ago I repeated his experiments adding in the effect of portfolio fees. This time I include mortality tables so we can see the effect of retiring at different ages instead of using Bengen’s target of a 30-year retirement.

Bengen’s model was to choose a fixed withdrawal rate at the start of retirement and increase the dollar amount by inflation each year regardless of how your portfolio performs. There’s a lot to be said for adjusting your spending based on portfolio returns, but Bengen’s goal was to find a safe withdrawal rate where you wouldn’t have to cut spending. He found that for stock allocations from 50% to 75%, a starting withdrawal rate of 4% (assuming no portfolio costs) was safe for a 30-year retirement.

Here I use mortality statistics from the Society of Actuaries to better model longevity and varying starting retirement ages. Bengen’s 30-year retirement is too short for most 50-year olds and too long for most 80-year olds.

I based the experiments on a century of U.S. stock and bond returns from 1914 to the end of 2013 (using Robert Shiller’s online data). I averaged the results of 100 retirees starting each year during the century. For retirements extending beyond 2013, I wrapped back around to 1914.

There were a number of inputs that went into each simulation:

1. Retirees are single males, single females, or a male-female couple of the same age where I used “joint” statistics.

2. Acceptable probability of running out of money.

3. Age at the start of retirement.

4. Portfolio costs each year.

5. Stock-bond allocation in the retirement portfolio.

The output from each simulation is the starting withdrawal rate that gives the desired probability of running out of money while still alive. In the case of a couple, the withdrawal rate is considered a failure if either person outlives the money. Unless otherwise stated, the default inputs are a 5% chance of running out of money, 60 years old, 0.2% portfolio costs, and a portfolio holding 75% stocks and 25% bonds. I used 0.2% portfolio costs because that is the total of my own portfolio’s expenses (MERs, trading expenses within funds, commissions, spreads, and foreign withholding taxes). Most portfolios have much higher costs than this.

In the first experiment, I examined how the safe withdrawal rate varies with age. As we see from the following chart, when stock allocation is 75% and total portfolio costs are only 0.2% per year, the simple 4% rule is appropriate for 56-year old males, 59-year old females or 63-year old couples.

However, when portfolio costs rise to the more typical 2.5% per year, the following chart show that the ages for a 4% rule rise to 72 for males, 75 for females, and 77 for couples. Keep in mind that these results are based on historical U.S. data and that most experts expect future real returns to be somewhat lower than they were in the U.S for the past century.

Early retirement enthusiasts should make note that the safe withdrawal rate for 50-year olds is about 2.7% for males, 2.6% for females and 2.5% for couples. These rates go up to about 3.7% to 3.8% for rock-bottom portfolio costs of 0.2%. So, for those retiring at 50 or earlier, the 4% rule just doesn’t apply unless you’re prepared to make deep spending cuts as necessary.

In the next experiment, I examined how the withdrawal rate changed with the portfolio’s allocation to stocks. Recall that the default inputs were a 5% chance of running out of money, 60 years old, and 0.2% portfolio costs. As we can see from the following chart, the highest withdrawal rate comes with a portfolio of about 75% stocks and 25% bonds.

It’s just common sense that withdrawal rates must be lower if portfolio costs are higher, but for some reason almost everyone ignores portfolio costs when talking about the 4% rule. It’s possible to be too pessimistic here, though. At first it may seem that 1% portfolio costs would take us from 4% withdrawals to 3% withdrawals, but this isn’t correct. When we’re at risk of running out of money, portfolio costs apply to an ever-shrinking portfolio. This reduces the dollar amount of these costs. As the following chart shows, each 1% of portfolio costs reduces the safe withdrawal rate by about 0.44%.

Some retirees may not be happy with a 5% chance of running out of money. The following chart shows how the withdrawal rate varies as we change the chances of outliving your money. For 60-year old retirees who want a portfolio that would have lasted until age 120 for any starting year in the past century, the safe withdrawal rate is 3.1%. At the other extreme, 60-year old males who can tolerate a 20% chance of running out of money can have a starting withdrawal rate of 5.2%, as long as their portfolio costs are only 0.2% per year. This makes a mockery of common advice from financial advisors to withdraw 5% from portfolios whose total costs are typically above 1.5% per year.

These results can be depressing for the many retirees who don’t have large enough portfolios to generate the income they want. Many otherwise excellent financial advisors seem prone to telling these retirees what they want to hear – that they can withdraw 5% or 6% from their portfolios each year. This is a formula for a few good years of retirement followed by relentless spending cuts for decades.

It’s possible to start retirement by spending a little more than the withdrawal rates calculated here if you’re prepared to cut spending as necessary. However, it’s important to be realistic about how deeply you can cut. I’ve watched people fail to cut enough early on and end up with no savings. My own attempt to design a spending strategy in retirement is called Cushioned Retirement Investing. The main idea is to use fixed-income cushioning to reduce how much you have to cut spending if portfolio returns disappoint.

There are many ways for new retirees to justify spending more right away. Who needs to spend a lot when they’re 90? Unfortunately, a 60-year old retiree who spends too much could be cutting back sharply as early as age 65. It’s much better to make a realistic plan and in the happy event that stock markets soar, you can always find ways to spend more.

1. Interesting results. One thing that doesn't seem to be talked about much is the possibility of earning a bit in retirement.

This could increase the allowable risk and withdrawal rate if someone has reasonable opportunities to earn a bit more when they decide they need it to make up a gap in their income.

Those who have already overspent in the early years could be a good place to look to see how realistic and how common this is.

1. @Richard: For me personally, if I left the work force for a decade and tried to come back, I suspect I'd have difficulty earning even one-quarter as much money as I make now. So I'd rather earn what I need before retiring. Your mileage may vary.

2. I also read-read the cushioned spending post. From what I remember of the relevant research, the performance of a portfolio in the early years after retirement determines a lot of how successful any spending strategy will be. One of the biggest threats to retirees is a large drop soon after they retire combined with inflexible withdrawals.

As hard as it is to come up with reliable rules that don't rely on individual judgement, that seems like one area that could have a large impact.

Personally if I entered retirement with a 5-year cushion and saw a large decline soon after, I would probably avoid replenishing the cushion until it fully ran out or the main portfolio had recovered to its earlier level.

1. @Richard: I suspect I might do the same thing as you describe. But, I haven't attempted to simulate any such strategy to see how it would have worked out in the past.

3. When I run my scenarios, I never take care about the pensions plans from government (fed. + prov.) that kicks in after 65-67 but the reallity is that there is some money there. If a couple needs 40k\$/year and they get 15k\$ from gov's, they only have to pull 25k\$ from their portfolio instead of 40k\$.

I also see a lot of retiree around me working for fun (wood working project, mechanics, landscaping, accounting, paint jobs, artistic project. Some of these jobs pay only few bucks but other pays a lot. Anyway, in the end they can earn few thousands/year. Not every people are dreaming about golf, cruises and expensives retirement.

My plan is to work for the highest salary I can get until I will be FI. My definition of FI is no more debt and enough investments to meet my needs @ 5% return. Then I can work for fun, just enough to earn for my living expenses (50% my actual salary) so I will not touch my portfolio. I will then have more free time to travel and stay in shape.

I'm about 75% from my goal now!

1. @Le Barbu: Government benefits definitely need to be factored into retirement plans. A few thousand per year is probably typical for those who take on infrequent small side projects. I'm not sure what you mean by 5% return. If that's 5% nominal and you're taking into account inflation, then that's fine. If you expect a 5% real return, you could be disappointed. Good luck reaching FI!

2. @Michael, my 5% is just a % I decided to throw in because neither me or anyone else know the future. So, I just figure I reached FI when my spending = 5% of invested assets (100% stock actualy). It could be a strech if I relly on this to live but for me, it's just for psychological purpose.

4. A thoughtful, clever post. Just judging from the first graph based on 0.2% portfolio costs, it seems a very lengthy retirement can be sustainably funded through a withdrawal rate of perhaps 3.4%.

I think this analysis could be useful for someone deciding whether to buy an annuity. The beauty of an annuity is it removes the uncertainty of running out of money. The downside is you forfeit your estate for certain. A friend of mine has purchased an annuity with a life-insurance add on to cover the cost of the annuity. I suspect the life insurance policy will be heavily eroded by inflation, but a stock portfolio suffers the ravages of inflation as well.

Anyway, impressive analysis. I guess one further caveat is that we may be facing poor stock markets going forward due to low interest rates that can only rise or stay the same. I agree with leaving that out of your analysis though, for simplicity, and to allow the long-term data to smooth out possible outcomes.

Prudent retirees should endeavour to over-estimate expenses and under-estimate returns, but this post sure gives a good starting point for assumptions.

1. @Gene: Thanks. I agree that annuities may have a useful place in all this. Their main benefit is that they take care of longevity risk. Their disadvantages are that they are based on today's very low fixed income rates and most annuities are not indexed to inflation. I've been trying to figure out a good way to analyze what benefit you might get from annuitizing part of a portfolio.

I agree that it makes sense to be conservative with expense and income estimates, but I fear that more retirees are aggressive than conservative, even if they're not aware of it.