Surely that’s a typo…ergodicity!? No, it’s right! Ergodicity is a powerful concept in economic theory, investing, and personal finance.
Even if the name seems wild to you, the idea is simple—stick with me while I explain it. And then we’ll apply ergodicity to retirement planning and investing ideas.
By the end of this article, you’re going to be seeing ergodic systems and non-ergodic systems all over your life!
Ergodic, Non-Ergodic, and Russian Roulette
Ergodicity compares the time average of a system against the expected value of that system. Let’s explain those two terms: time average and expected value.
The time average asks, “If we did something a million, billion, trillion times…what would we expect the results to look like?” It needs to be a sufficiently long random sample.
The expected value asks, “By simply averaging probabilities, where would we expect the result to be?”
At first blush, you might think, “Those two are the same thing…right?” Right! Or, at least you’d be right if the system in question is ergodic.
I flip a coin a billion times, and I end up with a time average of 50/50 heads and tails. Alternatively, I could just use their known probabilities and surmise the expected value of 50/50.
In this case, the time average and the expected value are the same. Therefore, the system—coin flipping—is ergodic.
But let’s contrast coin flips against Russian Roulette. The expected value of Russian Roulette is optimistic. ~83% success and ~17% failure. But what happens if one “plays” a million times? Ahh! I think you’d agree that the time average of Russian Roulette is 100% failure.
When one fails in Russian Roulette, it is a devastating failure. To only look at the expected value of the system is too simple. The expected value is far different than the time average. Thus, Russian Roulette is non-ergodic.
Ergodicity –> Over and Over, Big & Small
Ergodicity rears its head in two circumstances. First, ergodicity matters when we do things over and over and over. And second, ergodicity matters when certain outcomes are meaningful while other outcomes are insignificant.
To further explain ergodicity, imagine this bet:
I have a 100-sided die.
I’ll roll the die and you pick a number. If it lands on any other number than your number, then you win $1000.
But if it lands on your number, then Mike Tyson punches you in the face and takes your money.
What a deal! You call 99 of your friends and you all come to take this bet. Sure enough, one of your friends loses. But the rest of you win a combined $99,000 and agree to pay for his medical bills (which may or may not be covered by the $99K…which is another crazy blog post waiting to happen).
The “ensemble average” is that you won! One individual loss doesn’t change that.
But would that result be the same if you had played 100 times by yourself? No! In that scenario, there’s a 63% chance that you’d eventually lose the roll, lose your money, and get punched in the face.
The expected value (you and all your friends) is different than the time average (you doing it 100x). This is not an ergodic process.
Revisiting Ergodicity & Coin Flips
We concluded earlier that coin flips are ergodic. The expected value of a single coin flip equals the time average results of many coin flips.
But let’s change the rules a bit. Imagine I promised you a 40% positive return on heads but a 30% loss on tails. You start with $100,000. Would you take this bet?
Again, letâs call up 100 of your friends. You each take the bet.
We can predict that half of you will end up with $140K (40% return) and half end up with $70K (a 30% loss). On average, you each have $105K. As a group, youâll end up 5% higher than you started.
Sure enough, we can run this simulation a million times and thatâs exactly what we see. Both the mean and median results of these simulation show a 5% profit. Taking the bet was smart.
But what if youtook the bet 100 times? Same result?
Same for You?
To start, letâs look at two common snippets in the sequence of returns: one win followed by one loss, and one loss followed by one win.
Win then loss
Loss then win
(You mathematicians will see the commutative property at play. The order of this multiplication didnât matter.)
This result completely shifts our mindset.
When two people share a win/loss, they end up with $140K+$70K = $210K, or $105K each. They gain $5K. But when one person sequentially suffers a win/loss, she ends up with $98K, or a $2K loss.
What happens if you take this bet 100 times in a row? On average, you are going to lose money. Let’s look at a 50/50 heads/tails split.
That’s a 5% profit.
That’s a 64% loss
But you might âspikeâ a certain run where you get more heads than tails. What happens if the group gets 60 heads and 40 tails? What happens if you get 60 heads and 40 tails?
That’s…a big profit. $37.3 million.
I simulated the “you get 100 flips” case 100,000 times. As expected, the median result is a 64% loss. But the best result of the 100K simulations turns your $100K bet into $950 million dollars (68 heads, 32 tails).
This bet is non-ergodic. The expected value (100 friends scenario) is completely different than the time average (you 100x bets scenario).
But it’s also interesting that the distribution in the expected value case is tight (low risk, low reward) while the distribution in the time average case is extremely wide (high risk, potentially high reward).
EV is a profit, while time average is a loss. EV is low variance, while time average is high variance.
In case you can’t tell, ergodicity economics and subsequent economic theory is a serious field. There are big conversations taking place and serious money to be made (or lost).
But let’s focus a little closer to home: ergodicity and retirement.
Ergodicity and Retirement
In retirement planning, probability of success is often used as a figure of merit. I’ve used it here on the blog.
For example, the famous Trinity Study and 4% Rule cite a “95% chance of success,” where success is equivalent to “not running out of money before you die.”
Die with money? Success! Run out of money? Failure! This is an expected value metric—for 95% of all people, the 4% rule would have worked.
But a few problems in this thinking immediately arise and ergodicity is to blame.
Problem 1: Equal and Opposite?
The 5% of retirement fail cases are painful. Very painful. I would argue that the pain of failure in retirement is greater than the joy of success.
This is reminiscent of loss aversion, or the “tendency to prefer avoiding losses to acquiring equivalent gains.” The keyword in loss aversion is “equivalent.” People would rather avoid a $100 parking ticket than win a $100 lotto ticket. Those are equivalent. And yes, loss aversion is irrational.
But is failing in retirement equivalent-and-opposite to succeeding in retirement? I’d argue no. Failing in retirement is akin to a Russian Roulette loss. Devastating! And succeeding in retirement is a Russian Roulette win. It’s “expected.”
Problem 2: Expected Value & Risk Sharing
Let’s assume we all follow the 4% rule. And true to historical form, let’s assume that 95% of us have successful retirements, but 5% of us “fail” and run out of money.
In the previous examples—100 friends and Mike Tyson, or 100 friends and the 40% win/30% loss coin flip—we assumed that the group would share the risk and share the reward.
This guaranteed that we’d see profits, but eliminated our chance to win $950 million. This guaranteed that even if we did get face-punched by Mike Tyson, our winning friends would still help us out.
But in retirement planning, people do not share risk. The 95% winners have no obligation to bail out the 5% losers. This changes the game. This isn’t traditional ergodicity.
Instead, we’re all in the game by ourselves (like the time average participant), but only have one shot to get it right (lest our retirement plan fail). From the ergodicity point of view, it’s a conundrum. It’s like playing Russian Roulette with a 20-chamber gun (5% failure = 1 chance in 20).
How do potential retirees react to this change in the rules?
For starters, many real retirement plans are couched with so much conservatism that the retiree ends up with more money when they die than when they retired. Put another way—their investment gains outpace their ability to spend.
And we know that money is time. Therefore, we can conclude that many people work for years more than they need to. They’re cursing at spreadsheets when they could be sipping mojitos. Pardon my 2020 vernacular, but this is an abundance of caution.
Is there an ergodic solution to this over-cautious planning?
Does Ergodicity Have a Solution?
What did we learn from Mike Tyson ergodicity example? What did we learn from our coin flipping?
If we share risk, we reduce our potential upside but also eliminate downside.
Imagine that 100 retirees pool a portion of their money together. They all know that 95% of them won’t need to dip into that pool. They also know that their money in the pool is probably going to have worse returns than it would outside of that pool.
However! These 100 retirees also realize that the pool will save 5 of them from failure. And thus, the pool guarantees that their retirement will be successful. Instead of 100% of them worrying about a 5% downside, now none of them need to be concerned.
The purpose of investing is not to simply optimise returns and make yourself rich. The purpose is not to die poor.
Some of you will know that this “pool” concept already exists. It’s called an annuity.
Annuities?! Jesse, You Son of a B…
Wait, wait, don’t shoot me! Besides, you only have one bullet in those 20 chambers (thank ergodicity)
Real quick: an annuity is a financial product where a customer pays a lump sum upfront in return for a series of payments over the rest of their life. Insurance companies often sell annuities.
Annuities—on average—are losing propositions. Just like my pool above, the average annuitant will suffer via opportunity costs. Their money—on average—is better invested elsewhere.
Insurance protects wealth. It doesn’t build wealth.
Never let someone convince you that an insurance product is going to build your wealth. Why? There are only two parties involved—you and the insurance company. If you’re building wealth, then the insurance company is…losing money? No way.
Insurance products are equivalent to average mutual funs with high fees. The high fees drain you like a vampire bat. They make money, and you lose via opportunity costs.
But one thingthat annuities get right is that they hedge against downside risk in your retirement planning. The insurance company—i.e. my pool in the example above—collects a loss from most customers in order to provide a vital win to few customers.
This is just like real insurance. Most people pay more in insurance premiums—for their house, their car, their medical life—then they ever see in payouts. But for a vital few, insurance saves them from complete disaster.
Of course, detractors will rightly point out that annuities aren’t always guaranteed. If the insurance company goes belly-up, your state guarantor might only cover a portion of what you’re owed. Yes—that means your risk mitigation technique has risk itself. Riskception.
Annuities aren’t perfect. I don’t plan on buying one. But if the ergodicity of retirement planning has you fretting small chances of failure, annuities are one way to hedge that downside.
Is Robin Hood Ergodic?
Jesse is a boring index fund investor. It’s true.
But not Robin. She day-trades on Robin Hood, often experimenting with exotic trades with high leverage.
We can examine Jesse and Robin using ergodicity.
Jesse is playing the long game. In this simple hypothetical, his yearly returns are +30%, +10%, then -15%. The same three-year cycle keeps repeating. One might look at those three values and think, “Ah. About 8.3% per year, on average.”
Robin thinks daily. She wants money now. In this hypothetical, her daily returns are +60%, +15%, and -50%. The same three-day cycle keeps repeating. Again, one might look at those three values and think, “Ah. About 8.3% per day, on average.”
You might see a problem. We’ve used the arithmetic mean here. The arithmetic mean is useful in finding the expected value, in ergodicity terms. If Person A gains 60%, Person B gains 15%, and Person C loses 50%, their arithmetic average change is an 8% gain.
But sequencing investment returns—e.g. the ergodicity time average—requires that we use a log-average a.k.a. geometric mean. So let’s do that below:
Thanks @pale_blue_dot for catching my original error
Uh oh. Robin’s log-average return is negative. And sure enough, if Robin executed this particular day-trading strategy, she would turn her $10,000 into $500 in less than four months. Meanwhile, Jesse is fine with his 6.7% annual return (trust me…he is).
In financial circles, the log-average of growth rates is known as the CAGR, or compound annual growth rate.
The simple lesson is one that new investors love to scream from the rooftops (and that’s a good thing). Namely, a given portfolio loss requires a larger equivalent gain to return back to even. The arithmetic mean does not capture this fact, while the log-average does.
The larger the loss, the more significant the returning gain needs to be. That’s another ergodicity concept.
E.g. a 1% loss is offset by a 1.01% gain—they’re essentially the same. But a 50% loss—like the one Robin suffers every third day—requires a 100% gain to offset it
Just like we said earlier in the post—big risks matter most, and those large downsides are when we’re likely to see non-ergodic systems.
I would argue that a smooth, ergodic personal life is also optimal. Imagine ranking your days on a scale of 1-10. Would you rather have half 10’s and half 4s? Or all dependable 7’s? Or two-thirds 10’s and one-third 1’s?
To each their own. I’d prefer the 7’s. I don’t want half my days to be “bad,” even if the flip side of that coin is that half my days are “perfect.”
Don’t make ‘perfect’ the enemy of good enough.
-Someone at Jesse’ work
Maybe it’s boring. Maybe it’s the same muscle that pushes me towards indexing and away from Gamestop. To each their own. But I’ll take the 7’s.
Ergodicity in Grad School
In grad school, I studied fluid dynamics. See—this is me! Specifically, I worked on reaction-diffusion-advection problems in the University of Rochester Mixing Lab.
Fluid mixing is a terrific example of ergodicity. Take a few seconds to watch the video below. It’s an aesthetic way to view equilibrium statistic physics. Ergodicity applies to many different dynamical systems, stochastic processes, thermodynamic equilibrium problems, etc. It’s a mechanical engineer’s dream.
If we mix sufficiently, we see that small sub-sections of the fluid are representative of the fluid as a whole. The time average of many mixes is equal to our expected value of a uniform mix. This is ergodicity. This system is ergodic.
If this was butter and sugar—soon to be cookies—we could take any teaspoon of the mixture and draw reasonable assumptions about the mixture as a whole. Mmmmm!
But imagine if we accidentally introduce a dog hair into the mix (not that that’s ever happened in my kitchen). Suddenly, the mix is no longer ergodic.
Why? The expected value of any given cookie is that it will not contain the dog hair. But of course, eat enough of the cookies and you’ll eventually find the hair.
Or put another way, a single teaspoon of the mixture—which will contain either the entire dog hair or no dog hair at all—is no longer representative of the total mixture.
Good Article. Ergo…
Ergo it’s time for the summary.
Ergodicity is a fun concept. Or at least fun for nerds like me. It’s a terrific way to consider risk. It helps us in behavioral economics, personal finance, and real retirement planning.
What do you think? Any cool ergodic or non-ergodic systems in your life?
If you enjoyed this article and want to read more, Iâd suggest checking out my Archive or Subscribing to get future articles emailed to your inbox.
This articleâjust like every otherâis supported by readers like you.
While Medicare and Medicaid both help aging adults afford some of their medical expenses, they may not cover the cost of an extended illness or disability. Thatâs where long-term care insurance comes into play. Long-term care insurance helps policyholders pay for their long-term care needs such as nursing home care. Weâll explain what long-term care insurance covers and whether or not such coverage is something you or your loved ones should consider.
Long-Term Care Insurance Explained
Long-term care insurance helps individuals pay for a variety of services. Most of these services do not include medical care. Coverage may include the cost of staying in a nursing home or assisted living facility, adult day care or in-home care. This includes nursing care, physical, occupational or speech therapy and help with day to day activities.
A long-term care insurance policy pays for the cost of care due to a chronic illness, a disability, or injury. It also provides an individual with the assistance they may require as a result of the general effects of aging. Primarily, though, long-term care insurance is designed to help pay for the costs of custodial and personal care, versus strictly medical care.
When You Should Consider Long-Term Care Insurance
During the financial planning process, itâs important to consider long-term care costs. This is important if you are close to retirement age. Unfortunately, if you wait too long to purchase coverage, it may be too late. Many applicants may not qualify if they already have a chronic illness or disability.
According to the U.S. Department of Health and Human Services, an adult turning 65 has a 70% chance of needing some form of long-term care. While only one-third of retirees may never need long-term care coverage, 20% may need it for five years or longer. With a private nursing home room averaging about $7,698 per month, long-term care could end up being a huge financial burden for you and your family.
Most health insurance policies wonât cover long-term care costs. Additionally, if youâre counting on Medicare to assist you with these extra expenses, you may be out of luck. Medicare doesnât cover long-term care or custodial care. Most nursing homes classify under the custodial care category. This classification of care includes the supervision of your daily tasks.
So, if you donât have long-term care insurance, youâre on the hook for these expenses. However, itâs possible to get help through Medicaid for low income families. But keep in mind, you may only receive coverage after you deplete your life savings. Just know that Medicare may cover short-term nursing care or hospice care, but little of the long-term care in between.
What Does Long Term Care Insurance Cover
So what does long term care insurance cover, Well, since the majority of long-term care policies are comprehensive policies, they may cover at-home care, adult day care, assisted living facilities (resident care or alternative care), and nursing home care. At home, long-term care may cover the cost of professional nursing care, occupational therapy, or rehabilitation. This may also include assistance with daily tasks, including bathing or brushing teeth.
Additionally, long-term care coverage can cover short-term hospice care for individuals who are terminally ill. The objective of hospice care is to help with pain management and provide emotional and physical support for all parties involved. Most policies allow beneficiaries to obtain care at a hospice facility, nursing home, or in the comfort of their own home. However, most hospice care is not considered long-term care and may receive coverage through Medicare.
Also, long-term care insurance can help cover the costs of respite care or temporary care. These policy extensions provide time off to those who care for an individual on a regular basis. Usually, respite care provides compensation to caregivers for 14 to 21 days a year. This care can take place at a nursing home, adult daytime care facility, or at home
What Long-Term Care Doesnât Cover
If you have a pre-existing medical condition, you may not be eligible for long-term care during the exclusion period. The exclusion period can last for several months after your initial purchase of the policy. Also, if a family member provides in-home care, your policy may not pay them for their services.
Keep in mind, long-term care coverage wonât cover medical care costs. Many of your medical costs will fall under your coverage plan if youâre eligible for Medicare.
Long-Term Care Insurance Costs
Some of the following factors may affect the cost of your long-term care policy:
The age of the policyholder.
The maximum amount the policy will pay per year.
The maximum number of days the policy will pay.
The lifetime maximum amount that the policy will pay
Any additional options or benefits you choose.
If youâre in poor health or youâre currently receiving long-term care, you may not qualify for a plan. However, itâs possible to qualify for a limited amount of coverage with a higher premium rate. Some group policies donât even require underwriting.
According to the American Association for Long-Term Care Insurance (AALTCI), a couple in their mid-50s can purchase a new long-term care policy for around $3,000 a year. The combined benefit of this plan would be roughly $770,000. Keep in mind, some policies limit your payout period. These payout limitations may be two to five years, while other policies may offer a lifetime benefit. This is an important consideration when finding the right policy.
While itâs highly likely that you may need some form of long-term care, itâs wise to consider how you will pay for this additional cost as you age. While a long-term care policy is a viable option, there are alternatives you can consider.
One viable choice would be to boost your retirement savings to help compensate for long-term care costs. Ultimately, it comes down to what level of risk youâre comfortable with and how well a long-term care policy fits into your bigger financial picture.
If youâre unsure what long-term care might mean to your retirement plans, consider consulting a financial advisor. Finding the right financial advisor that fits your needs doesnât have to be hard. SmartAssetâs free tool matches you with financial advisors in your area in 5 minutes. If youâre ready to be matched with local advisors that will help you achieve your financial goals, get started now.
The looming costs of long-term care may have you thinking about how much money youâll need for retirement. If you arenât sure how much your 401(k) or Social Security will factor into the equation, SmartAssetâs retirement guide can help you sort out the details.
If you’re thinking about how much is enough for retirement, you’re probably contemplating a retirement and need to know how to pay for it. If you are, that’s good because one of the challenges we face is how we’re going to fund our retirement.
Determining then how much retirement savings is enough depends on a number of factors, including your lifestyle and your current income. Either way, you want to make sure that you have plenty of money in your retirement savings so you don’t work too hard, or work at all, during your golden years.
If you’re already thinking about retirement and you’re not sure whether your savings is in good shape, it may make sense to speak with a financial advisor to help you set up a savings plan.
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How Much Is Enough For Retirement?
Your needs and expectations might be different in retirement than others. Because of that, there’s no magic number out there. In other words, how much is enough for retirement depends on a myriad of personal factors.
However, the conventional wisdom out there is that you should have $1 million to $1.5 million, or that your retirement savings should be 10 to 12 times your current income.
Even $1 million may not be enough to retire comfortably. According to a report from a major personal finance website, GoBankingRates, you could easily blow $1 million in as little as 12 years.
GoBankingRates concludes that a better way to figure out how long $1 million will last you largely depends on your state. For example, if you live in California, the report found, “$1 Million will last you 14 years, 3 months, 7 days.” Whereas if you live in Mississippi, “$1 Million will last you 23 years, 2 months, 2 days.” In other words, how much is enough for retirement largely depends on the state you reside.
For some, coming up with that much money to retire comfortably can be scary, especially if you haven’t saved any money for retirement, or, if your savings is not where it’s supposed to be.
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Your current lifestyle and expected lifestyle?
What is your current lifestyle? To determine how much you need to save for retirement, you should determine how much your expenses are currently now and whether you intend to keep the current lifestyle during retirement.
So, if you’re making $110,000 and live off of $90,000, then multiply $90,000 by 20 ($1,800,000). With that number in mind, start working toward a retirement saving goals. However, if you intend to eat and spend lavishly during retirement, then you’ll obviously have to save more. And the same is true if you intend to reduce your expenses during retirement: you can save less money now.
The best way to start saving for retirement is to contribute to a tax-advantaged retirement account. It can be a Roth IRA, a traditional IRA or a 401(k) account. A 401k account should be your best choice, because the amount you can contribute every year is much more than a Roth IRA and traditional IRA.
1. See if you can max out your 401k. If you’re lucky enough to have a 401k plan at your job, you should contribute to it or max it out if you’re able to. The contribution limit for a 401k plan if you’re under 50 years old is $19,000 in 2019. If you’re funding a Roth IRA or a traditional IRA, the limit is $6,000. For more information, see How to Become a 401(k) Millionaire.
2. Automate your retirement savings. If you’re contributing to an employer 401k plan, that money automatically gets deducted from your paycheck. But if you’re funding a Roth IRA or a traditional IRA, you have to do it yourself. So set up an automatic deposit for your retirement account from a savings account. If your employer offers direct deposit, you can have a portion of your paycheck deposited directly into that savings account.
Related: The Best 5 Places For Your Savings Account.
How long do you expect to live? Have your parents or grandparents lived through 80’s or 90’s or 100’s? If so, there is a chance you might live longer in retirement if you’re in good health. Therefore, you need to adjust your savings goal higher.
Consider seeking financial advice.
Saving money for retirement may not be your strong suit. Therefore, you may need to work with a financial advisor to boost your retirement income. For example, if you have a lot of money sitting in your retirement savings account, a financial advisor can help with investment options.
Figuring out how much is enough for retirement depends on how much retirement will cost you and what lifestyle you intend to have. Once you know the answer to these two questions, you can start working towards your savings goal.
How much money you will need in retirement? Use this retirement calculator below to determine whether you are on tract and determine how much you’ll need to save a month.
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Working With The Right Financial Advisor
You can talk to a financial advisor who can review your finances and help you reach your goals (whether it is paying off debt, investing, buying a house, planning for retirement, saving, etc). Find one who meets your needs with SmartAssetâs free financial advisor matching service. You answer a few questions and they match you with up to three financial advisors in your area. So, if you want help developing a plan to reach your financial goals, get started now.
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