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Safe Retirement Spending Using TensorFlow (streeteye.com)
180 points by RockyMcNuts on Aug 31, 2016 | hide | past | web | favorite | 76 comments



I was actually paid to build something like this once.

A financial products company wanted a visualization tool that would let a customer enter their wealth, pick a variety of investment strategies, spending strategies, and retirement durations, and then see how it all played out over historical data.

You could scrub a timeline back and forth to change the starting year, and see your weath and spending charted out over the course of that retirement.

It was best retirement savings education I've ever seen. Almost every retirement planner just shows you averages, and life looks simple and predictable. Reality is very, very different.

Things I learned:

1. The stock market will probably crash at some point during your retirement, and you will loose half of any wealth you have in it.

2. In spite of the big drops, the higher compounding rates of stocks mean that a bond heavy retirement gives you way less money, even in the worst market retirement years. 30 years lets money grow for a long time.

3. Attempting to spend as much money as possible drastically increases your odds of running out of money, or suddenly having a lot less to spend. (Seriously, what is up with people attempting to run out of money exactly on their 95th birthday?)

4. Any retirement planning should take into account that you could end up with way more, or way less money that you thought.

(Sadly, the web app was never released by the company.)


Planning financial investments for a 50 year time horizon when mass-market finance has really only been around since ~the 1970s is crazy. An entire retirement system predicated on long term financial returns > GDP growth, likewise insane.

There is insufficient data regardless of modeling technique to derive decent simulation-based conclusions about asset classes that literally didn't exist 50 years ago. There are decent datasets for precious metals, real estate, and government bonds, but the results aren't super encouraging for average investors.


You're making a weird distinction by saying "mass-market finance" as if the fundamentals of asset classes change radically depending on how they are marketed.

Stocks, as an asset class, have been around a lot longer than the 1970s, and they have on average grown a lot faster than GDP over that time.

That makes sense since stock prices measure a form of wealth, and GDP measures income. Big difference.


"as if the fundamentals of asset classes change radically depending on how they are marketed"

More like the fundamentals of asset classes change radically depending on how they're regulated & taxed, who is willing / able to buy them, what the composition of that asset class is, and how much money there is flowing in and out of that asset class.

And we're not even really talking about "fundamentals", since there is so much path dependency, especially in the context of drawing-down of those assets to finance retirement. A rise in variance would be bad enough.

Stock prices in the long run represent a time-discounted income stream (as do all securities) (plus a bundle of legal rights, which is mostly irrelevant for individuals). It is not mathematically possible to have the stock market growing by 4% and GDP growing by 2% ad infinitum; you would have the value of the stock market exceed the discounted value of all future economic activity.

There is a cogent argument that the inflation in stocks has been due to 1) more economic activity falling under the umbrella of publicly traded corporations (private blacksmith displaced by Ford), 2) capital inflows driven by privatized retirement savings, interest rate manipulation, etc. 3) a legal & economic regime that encourages "paper assets" in general.

None of those are perpetual forces.


> It is not mathematically possible to have the stock market growing by 4% and GDP growing by 2% ad infinitum

Yes, it is.

First, because there is no necessary mathematical relationship between the aggregate market cap of firms and economic output (future or otherwise). There are rational expectations that can be stated, but those aren't actual constraints, since irrationality is a real thing.

Second, the economic universe from which the stock market draws value is not limited to the domestic economy, so even if there was a constraint based on economic output, it wouldn't be GDP.


"Maybe the future will be perpetually irrational about asset prices" is not really a compelling economic story. There is indeed a mathematical relation between long run asset prices and the income generated by those assets. In the short run you can do whatever you want, but the long run constraint is predictably enforced by arbitrage.

(it is left as an exercise to construct the most entertaining arbitrage play in a world where stock prices diverge indefinitely from the value produced by the underlying assets via some magic.)


> "Maybe the future will be perpetually irrational about asset prices" is not really a compelling economic story.

Perhaps, but then we are getting into rational expectations and not mathematical constraints. (Though, really, given that rationality requires perfect knowledge of future utilities, "the future will be perpetually irrational about asset prices" is pretty much guaranteed to be true except for intermittent times when it isn't momentarily largely by chance; even a consistent divergence in a particular direction from rationality isn't surprising, given what we the particular ways in which people tend to be deviate from economic rationality in practice.)

> There is indeed a mathematical relation between long run asset prices and the income generated by those assets.

No, there is a mathematical relation between reasonable asset prices and expected income streams that the assets will generate.

> In the short run you can do whatever you want, but the long run constraint is predictably enforced by arbitrage.

"In the long run, we're all dead" -- Keynes

Even granting your point for the sake of argument, what must ultimately be true in the long run assuming an infinite time horizon need never actually be true in the physical universe we inhabit. Irrationality in prices can be maintained indefinitely, even though not infinitely -- but then, the market can't actually exist infinitely, anyway.


I am talking about a long run relation between two long run quantities, which either fluctuates in a certain band around equilibrium, or allows the economic equivalent of perpetual motion.

You seem to be predicting a diverging trend in that relation towards infinity, which is insane, as infinities tend to be.

I conclude from this you're misunderstanding the notion of "long term equilibrium" as stronger than it is in reality. Construct a model that simultaneously allows infinite divergence between securitized asset prices and their associated incomes, and disallows easy arbitrage, or we have nothing to talk about.

Every fool digs up that Keynes quote when his model is wrong.


Betting that the market reverts to 'rational' pricing in any short time frame is a risky bet, but I'll claim it's much, much more reasonable than assuming that irrationality persists indefinitely.

OTOH, there's another story to why equity returns are higher than GDP returns: equity investors are being compensated for the higher risk.


> OTOH, there's another story to why equity returns are higher than GDP returns: equity investors are being compensated for the higher risk.

This gets mentioned very often in such debates, but the implied causal connection is wrong: There is no guarantee that higher risk leads to higher returns. It's not like the stock market says "We should keep up increasing stock prices so that equity investors are being compensated for their risk."

Over long timespans, stock prices are coupled to the performance of the underlying companies (mostly their income streams), not to risk. So far, there has been a correlation, but there has never been a guaranteed causal relation between risk and stock returns.


> There is no guarantee that higher risk leads to higher returns. It's not like the stock market says "We should keep up increasing stock prices so that equity investors are being compensated for their risk."

The mechanism is much simpler: asset prices of risky assets today will fall because willing buyers demand a higher return for the risk.

E.g. you have a stock and a bond both at $100 with the same expected return. Investors aren't happy with that, so they refuse to buy the stock until its price falls and its implied return rises.


Okay, so let's assume that the stocks are traded with a 10% risk discount ($90). Ten years later, the bonds are about to mature and are valued at $150 (50% profit). The company belonging to the stocks has also become 50% more valuable (because its fundamentals improved, e.g. 50% higher revenue and profit), but its stocks are still just as risky and still trade at a 10% discount, for a price of $150 * 90% = $135 (also 50% profit).

So despite the higher risk, and despite the fact that the stock's price is discounted, the investor did not make more profit from the stocks than from the bonds.

In practice, companies should grow faster than bonds (because they can reinvest their profits to increase their profit – although many companies fail at that), yielding higher returns. My point is, that those higher returns result from the different mechanisms underlying different security types, not from differences in risk.


You arbitrarily fixed the bond return to match that of stocks, but that's not how bonds get their prices set.

Bonds are fundamentally less risky than stocks because in the event of bankruptcy bondholders are paid first. Real recovery rates are around 40% usually.

> Ten years later, the bonds are about to mature and are valued at $150 (50% profit)

No, the value of of the bond is mostly independent of how much the company's future revenues are (as long as they don't go bankrupt). There are few future paths where someone will pay you $150 in the future for a bond that you bought for $100 today.

Bonds mostly have downside risk (you can lose everything), but limited upside participation. OTOH, equity has worse downside risk (if a company has $700m in debt and $300m in equity, it only needs to lose $300m in assets to go bankrupt--but in that case, bondholders would still get paid), but full upside participation.

Another way of looking at this is that if a company triples in size, your equity stake also triples because you now own the same percentage of a much larger company, but the bond cashflows did not change because bonds do not have that upside.


Why are you fixated on bonds? My argument is mostly independent of bonds, I only included them because you mentioned them originally.

Your reasoning was:

> The mechanism is much simpler: asset prices of risky assets today will fall because willing buyers demand a higher return for the risk. [...] Investors aren't happy with that, so they refuse to buy the stock until its price falls and its implied return rises.

I showed that this is not a valid argument, because if the market discounts the price of a stock by x% due to higher perceived risk, then it will discount its price by x% ten years later as well (unless there was a major change in the company's fundamentals, which is another story and not relevant here), meaning that the discounting of risk did not result in higher profit (compared to the return on stocks of a company which is deemed less risky).


Bonds are the natural comparison because bonds represent relatively riskless cashflows. Bonds tell you how much you get paid in the future, stocks don't.

Otherwise, how can you measure the return to risk?

> then it will discount its price by x% ten years later as well

That doesn't follow because you're missing a free parameter. Let's say a piece of stock ought to be worth $110 in 1 year if people weren't risk averse (based on how we think the company will do, etc.), but it'll only be worth $100 because of the risk. It can still be worth $91 today, implying a 10% return, for example.

For any path of future expected equity values, regardless of what future discount you apply, there is a price today that will imply an equity risk premium.

FYI, people have empirically measured the implied equity risk premium over long periods of time. The general consensus is that equity returns around 5-10% more per annum that a risk-free asset, but it varies greatly from decade to decade:

https://www.newyorkfed.org/medialibrary/media/research/staff...

https://en.wikipedia.org/wiki/Equity_premium_puzzle


Those are some good points, thank you. I'll have to think about this for some time.


> Betting that the market reverts to 'rational' pricing in any short time frame is a risky bet, but I'll claim it's much, much more reasonable than assuming that irrationality persists indefinitely.

Rational pricing requires perfect knowledge of future income streams. Unless you have such knowledge, you can't even know what concrete position reflects a bet that the market "reverts" (a misnomer, because it assumes that rationality is a normal state that is only in exceptional circumstances deviated from) to rational pricing.


It's not even that "irrationality persists indefinitely", it's that it increases towards infinity.

Equity > GDP as a return to risk would require you to be able to "invest in GDP" in a relatively variance-free way. Social Security or seizing control of the government (or at least its taxing power) is about as close as you can get, but neither is really securitizable.


> Equity > GDP as a return to risk would require you to be able to "invest in GDP" in a relatively variance-free way

Technically no, it just requires one to be able to construct a basket that approximately returns GDP growth (along with GDP variance).

Note that total returns to equity include dividends, so you can easily have equity give outsize returns without total market cap approaching 100% of assets.


Stock-market-returns are almost always going to be higher than GDP growth, by a significant margin. A GDP growth of X% implies that companies revenues/profits are going to be ~X% higher next year.

But your return-on-investment isn't driven purely by the X% profit growth. It's also driven by the baseline profits that companies make. If you buy a share for $10, and it has an EPS of $0.50, you're immediately getting an ROI of 5%, even in a flat-GDP world. If GDP grows by 2%, and the company's projected-future-profits grow by 2%, you'll get the benefit of that 2% profit growth, in addition to the baselines ROI of 5%.

The PE ratio gives a pretty good indicator of long-term ROI baseline. Given the current PE ratio of 25, which is certainly worryingly high, it still implies a baseline ROI of 4%. Any GDP growth we happen to get, is simply gravy on top of that baseline.


> It is not mathematically possible to have the stock market growing by 4% and GDP growing by 2% ad infinitum; you would have the value of the stock market exceed the discounted value of all future economic activity.

The value of future economic activity is perpetually hypothetical, so when would the reckoning arrive?


When the size of the discrepancy exceeds the risk-adjusted cost of arbitrage.


It is like with long term weather forecasts, people just want to have it regardless if it makes sense or not.


It's more like long term climate forecasts. We know it's probably going to get hotter.


Also taxes have been all over the place in past 40 years. First there were no IRAs or 401ks that long ago. (But you could defer taxes in an annuity, never-sold stock, or carry-forward housing basis) Long term capital gain taxes were only lower than short term during half that time.

So the wisdom is: tax law will change again. Take advantage of what you can now.


That's why I always put more money in traditional 401k vs Roth. Bird in hand.


How are you saving for retirement then?


1. You should not be 100% invested in stocks during retirement (or ever). Diversified portfolios that contain stocks, bonds, cash, and inflation protected assets (such as gold or real-estate) are highly recommended.

2. See #1. Diversification is the way to reduce the risk of stock market crashes, while still getting high annual returns. Diversied portfolios such as the Permanent Portfolio have averaged 9.3% CAGR over the last 40+ years.

3. Average lifespan in developed countries is still increasing dramatically. It might be ~80 years now, but kids just entering the workforce could easily live 100+ years. You better plan for it, unless you want to work right up until the day you die.

4. Agreed.


> kids just entering the workforce could easily live 100+ years

Actually, the average lifespan at 65, i.e. how long can you expect to live given that you've reached 65, has seen a much less dramatic change than life expectancy at birth (often called just "life expectancy"). In 1845 it was 75 years, today it's 82 (data for the UK [1]). Since people who die before 65 don't get any retirement, this is the key figure.

Looking at the graph in that source, life expectancy at 65 has been increasing roughly linearly since ~1900, with a trend around 0.7 years per decade. This means that kids entering the workforce today who survive to 65 can expect to live about four years longer than people entering retirement today.

Given that retirement age is now steadily increasing, it's not likely that people will have significantly longer retirements even in 2050. Four years of increase in retirement age from now until 2050 is highly likely IMO.

Edit: forgot source link:

[1] https://ourworldindata.org/life-expectancy/


Aren't life expectancy numbers at birth inherently flawed because they assume the status quo for 70+ years? I don't think there are any medical breakthroughs around the corner that will dramatically increase the lifespan of someone who is currently 65, but are you willing to bet that won't happen for someone who is born today?


Yes, these numbers are back-calculated as you say (anything else would be witchcraft). And as you say, there could suddenly be a breakthrough technology in twenty years that massively increases life expectancy.

But IMO this is very unlikely, because people die of such wildly varying causes (including lifestyle-induced diseases, accidents and even suicide) that it's hard to imagine what this sudden change could be.

More likely we will keep seeing incremental change, disease by disease, steadily increasing average lifetimes.

Biology and biochemistry is so bloody hard compared to any human tech, it's amazing we have come as far as we have today. People talk about curing cancer like going to the moon, just throw money at it, but that analogy is only accurate if you assume starting your space program sometime around 1870.


Life expectancy is reported at a 50th percentile, right? Is there any site that shows a 90th percentile?


Saying that an investment strategy has averaged positive returns over 40+ years may be true, but is not necessarily useful information. Over very long periods of time, there are many strategies that will provide an average positive return. In this context (retirement spending), investors have to weigh long-term growth with the need to withdraw money from the portfolio every year to live on. Volatility is thus an important consideration.


> Diversied portfolios such as the Permanent Portfolio have averaged 9.3% CAGR over the last 40+ years.

Past performance is no guarantee of future results.


But they sure are comforting.

Past results guarantee future results in the same circumstances. Over time, circumstances change which invalidates their value. But, in the short term, they imply a probability of future results based off of the volatility of the circumstance state.


Negative interest rates, slowing growth, models based on historical returns we'll never see again.

Not comforting at all.


Got another option?


I don't. That's why I'm worried. One of two things will happen:

1. Technology innovation velocity will increase, with the results distributed through society, driving down the cost of living (this is already happening with almost everything except real estate, healthcare, and education [1]). You won't need to invest, because it'll cost nothing to exist (let's call this "Star Trek Future").

2. Technology innovation velocity will increase, but it'll be locked up with copyright, patents, etc. Rent seeking will drive more of the population into serfdom. You will not have a pleasant life, nor will it be long (we'll call this "Elysium Future").

[1] https://www.washingtonpost.com/news/wonk/wp/2016/08/17/the-s...


I think I can tell you which of those is most likely.


I've got a child, I have to push hard for option #1, by any means necessary.


> Seriously, what is up with people attempting to run out of money exactly on their 95th birthday?

Money does you no good if you are dead. And it does you very little good if you are completely out of it in a nursing home. I don't know of any male relative that has ever lived to 95 years old, and only a small percentage of female relatives.

My parents are in their mid-60s, just started their retirements and they are doing as much traveling as they can while they are still both healthy. I applaud their decision.


> Money ... does you very little good if you are completely out of it in a nursing home

Well, there is the question of paying for the nursing home. The sad reality is that the options offered by our social safety nets at lot less attractive than the options available if you can pay for it.

Unless you are completely out of it to the point of not caring, at which point your loved ones may still care though.


I can't speak to the rest of the country, but that's not the case in NY. It's a complicated story with lots of wrinkles, but the long and short of it is that you can buy a long term care policy of a certain length and then the state (under the medicaid program) will take over payments after that. You don't need to change facilities. In any event, I have yet to visit a nursing home that the word "attractive" would be even in the ballpark of appropriate to use.

Separately, optimizing for being able to pay out of pocket for a top tier nursing home seems like a strange life goal to me. Maybe people really do have that preference, but it looks to me like a lot of people in the greater "personal finance" hobbyist world just like saving for it's own sake. Nothing wrong with that of course, but the sanctimoniousness of this group is a way over the top IMO.


> Separately, optimizing for being able to pay out of pocket for a top tier nursing home seems like a strange life goal to me.

Being able to afford a comfortable life after I am literally too infirm to work is the vast majority of the reason I continue to want to earn money. I'd be really interested if you could persuade me that I am misguided on that!


Consider this hypo:

You are now 60 or 65 or maybe even 70, you're slowing down some, but you aren't too infirm to work. You have a fair bit of savings.

Do you:

1) Keep working until you can't work anymore

2) Retire, but live frugally so that you can be sure if you make it past 95 and need skilled nursing care you'll be able to keep private paying for a top notch nursing home.

3) Build out a retirement budget that assumes you won't make it past 95, make the absolute most of the next decade or so of relatively good health (hopefully!)? Go take that trip you and your wife always dreamed. Lavish your adorable grandchildren with gifts that certainly don't need. Fly business class instead of squeezing your old bones into coach.

Keep in mind that if nothing else you'll still have social security no matter how long you live.

Granted this is somewhat exaggerated for effect, but there's a difference between taking the worst case scenario (a funny way of referring to living a long time) into consideration and letting the tail wag the dog.


All the options sound good except for lavishing gifts and travelling business class. But then maybe I'm just funny like that ...


One set of my grandparents ended up on assistance in a $2500/month home. It was like a state prison. There were actual bars.

The other set is 98 & 95. They pay more than 14,000/month! It's like a cruise ship.

The difference is hard to put into words.


> They pay more than 14,000/month! It's like a cruise ship.

I would certainly hope so, considering for 14,000/month you can live on an actual cruise ship with money left over for entertainment and a few other things.

It also pains me to see such luxury spent on the elderly. While you may have a personal attachment to them, the rest of society would do much better with that money spent to educate and help the new generations.


>It also pains me to see such luxury spent on the elderly. While you may have a personal attachment to them, the rest of society would do much better with that money spent to educate and help the new generations.

I don't think we have any reason to believe that this is an unearned luxury lavished on a lucky elderly couple. It appears more likely that this is their own money, saved and invested over their lifetime, and their's to spend how they wish. Furthermore, advanced age is no reason to cast someone off to a bland waiting room. It's not healthy for a society to consider somebody's value limited to their future contribution potential. I'm happy to contribute economically to present-day's elderly folks, not only for my own attachment to someone, but for the social contract that I, too, will be old, and I doubt I'll suddenly just want to stand in the corner.


What should actually pain you is this comment.

Even if we take your claim about society being better off if the 14k goes to education (which is some major hand waving), how would you suggest transferring this?

Unless it's completely by choice, congratulations. You've now created no incentive for people working towards retirement to save enough to spend 14k per month. Now, instead of getting that productivity earlier in life and the 14k going to support a cruise ship business, you'll have people willing to just rest with what they've got.

I think there are better ways to prop up education (some having nothing to do with $). No need to shame the elderly who have worked a lifetime and now get to kick back and enjoy it for a little while.


The counter argument is that those 14k enters circulation instead of laying idly on some account. Not an economist, so don't ask me what's the better alternative...


In normal circumstances, money is rarely idle in an account. It is invested into loans and such. The past decade has been at times unusual in that regard though.


I enjoy Logan's Run too, but I'm not sure it's a palatable option for our society. If these fine people are paying their own way, that's $14k/month that's probably paying for a large staff of hard working people (and some administrators). If they've spent down all their money, and the state is paying for it, the state has a maximum, and it's not $14k/month.

In the alternative, where they're paying $2.5k/month, the other $9.5k/month is going to stay in their investment accounts, and when they eventually die, if they have a large enough estate, it'll be subject to the estate tax and society could use it for education or whatever, but more likely it'll just pass to their heirs, which helps the heirs, but doesn't help society that much.


Many people are employed by the $14k, some to work their way through school so...


This is partly why the standard advice is to purchase an inflation-adjusted fixed annuity: someone else takes over all those risks, including longevity risk.

You can use an annuity for your non discretionary income - rent, clothing, food, taxes - and keep the rest in traditional investments. And don't forget, Social Security acts like an annuity in this analysis too.


those annuities are, unfortunately, very expensive in terms of fees paid to the person who sells and manages it, and you are also exposed to credit risk if the counterparty goes belly-up during your (long) retirement, which seems crazy now, but it would have seemed crazy to worry about AIG counterparty risk pre-2008.


You may be thinking of variable annuities, which aren't really annuities and are something close to an outright scam.

Immediate annuities are a vanilla product offered by almost every life insurance company. There's a competitive market for them and they don't have particularly high embedded fees. That said, they are priced based on a very conservative model--in part because their regulators require them to invest that way--and so you may well be disappointed with what you can get for your money.

The only wrinkle is the is inflation rider which can vary in the details from company to company, so is not as easy to compare, and therefore tends to be less of an efficient market (i.e. has fairly high costs for the protection you get).

One interesting thing you can do with annuities is buy a deferred annuity, again a fairly vanilla, competitive product. If you set the deferred date to well into your old age (usually 85) and no death benefit you can get a relatively large monthly payout. This then acts as a sort of insurance policy (along with social security) that insures you won't outlive your money and allows you to be more aggressive in spending the rest of it.


I'd be interested to see a good in-depth analysis. If you get a vanilla annuity, you have significant inflation risk over decades. The guys who bought annuities in e.g. late 60s saw them destroyed by inflation. It's not a great fit for a 30-year retirement.

You should be able to get an inflation-adjusted annuity at the TIPS rate plus a credit spread. But right now that TIPS rate is effectively nothing. And I don't know whether the credit spread plus the insurance company tax benefit is a good deal.

Packaging e.g. an S&P index fund in an insurance product, so you don't pay taxes until you get payouts, would be a really good idea, but typically insurance companies tack on sales commissions and fees far in excess of e.g. SPY or VFINX. If Fidelity or Vanguard offered that, it would be a good deal, but I hadn't seen that... looking at that Fidelity product now https://www.fidelity.com/annuities/FPRA-variable-annuity/ove...


Wrong. Fidelity sells a variable annuity with no penalty other than the federal less-than-five-years penalty. And a 1/4% insurance overhead. And it has no RMD.


I made something exactly like what you describe as well.

It sounds like mine probably had more features and was slightly more useful, but still, really nice effort. (it was also never released by the company)

I still use the tool today to plan my finances and it is the most amazing thing I have ever used for planning my money. I absolutely owe my wealth to this piece of software.


Not sure if you are aware, but the tone of your comment makes you sound like a jerk.


I'd also be keen to see one if these unreleased tools. My own experience getting into investing out of uni right at the start of the GFC taught me a hell of a lot about these straight line "predictions".


why don't you release it or open source it?


Anyone who's interested in this kind of thing would do well to visit http://www.cfiresim.com/

I think it's probably one of the best historical modelling simulators out there, allows you to save/share your sims, and models all kinds of neat things like inheritances and expected large expenses.


What are the units of spend_mean, spend_min and spend_max in the table, and what exactly are these referring to?

The post says:

>The mean amount you would have been able to spend by year if you had followed this plan, you retired in years 1928-1985 and you enjoyed a 30-year retirement.

But I don't really follow... in year 1, spend_mean is 4.567. Does that mean on average I spend $4.57 in year 1? Is this in addition to the constant spending?

Is variable spending in addition to constant spending? Or is this the % of the portfolio that I am drawing from by spending my const_spend target?


I'm assuming it's all dollars. There is no $4.57, it's actually $4,567 (but I guess the actual number doesn't matter if you treat them all the same).

spend_mean, spend_min, and spend_max are probably the amounts you'd spend if you were in the mean, min and max respectively. For example, according to this data, the mean amount you have saved up is ~$667,459 (I calculated this backwards) - so for the first year you'd spend 2321 + 0.002102*667459 = $3,724. Likewise if you saved the max in the dataset you'd spend $5,358 instead (total, not in addition to anything).

And yes, the var spending is in addition to const spending, it's explained a bit lower in the article.


author of TFA here, I updated the descriptions a little, basically in year 25 you spend $2.321 in constant dollars (starting portfolio in the example is 100, so 2.321% of starting portfolio adjusted for inflation) plus 8.218% of the value of the portfolio in that year.

Using that strategy, over all 59 cohorts 1928-1986,

- median cash flow in year 25 was 12.16

- worst case 3.756

- best case 27.38

- all as a % of starting portfolio, in constant dollars.


From the y axis in the chart: "Annual spending as % of starting portfolio".


Fun article.

> "That being said, this optimization seems to run 4-5x faster on CPU than GPU."

I'm guessing it is a question of throughput. GPUs are becoming almost like vector processors, and so if you do not 'feed the beast' then throwing hoards of threads at the problem will just increase contention, versus improving scalability.

Sort of embarrassing, as I am a Bayes guy, but I've not seen much MCMC performed on GPUs. Given the parallelism, I would expect it could nicely scream with lots of threads (if you also had lots of chains) but this is a guess.


Interesting example, but the model is unappealing to me. The CRRA assumption is definitely untrue for most people, including me.


I agree. I feel that the only reasons to choose an outcome with a value lower than an expected value are ignorance, or aversion to gambling risk (when taking a one-time risk rather than averaging over time), neither of which should be applying here. I'd love to see some counterpoints.


Author of TFA here ...

- suppose you are risk neutral (γ = 0). You just maximize cash flow. The solution the model will output (modulo numerical noise): invest 100% in equities; spend 0 each period until last period, when you spend 100%.

- maybe you truly just want to maximize expected value, and that's your solution, and you don't need a complex model.

- But maybe you value spending cash smoothly over time. Now you have a tradeoff: you can spend more smoothly, and spend some cash early, but that will reduce your overall cash flow. How do you decide how to trade them off?

- that's the role of γ. I would just view it as a tunable parameter that makes a rational tradeoff between spending as much as possible, and as smoothly as possible.

- as you increase γ, the model gradually increases bonds more and does so earlier during retirement, reduces variable spending, and increases constant spending to smooth cash flow.

- as γ → ∞, you are left with perfectly smooth cash flow, and an allocation that maximizes the amount you could have spent without ever running out of cash during the historical period - something like the Bengen 4% rule.

The genesis was that I looked at the literature, saw there were a lot of relatively ad-hoc studies of arbitrarily rules, and asked 'what would Google do', and the answer is to first decide what is your cost function, what are you trying to maximize or trade off.

This is one answer...there are more complex answers, one could use a life table and maximize over all mortality scenarios, one could penalize any decline in spending per a prospect theory utility function, etc., etc.

Main takeaway is, with tools like TensorFlow, you can optimize even pretty complex path-dependent financial questions, which you really couldn't do even a couple of years ago, at least not without some really fancy parallel hardware and programming.

It's a first real attempt at a real TensorFlow model, might not conform 100% to best practice, any pull requests appreciated.


Counterpoints galore here - http://www.financialwisdomforum.org/gummy-stuff/gummy_stuff....

Warning - it can be tough reading (and not in the usual scholarly sense, either!) as the author definitely had his own "style". Also it's written from a Canadian point of view, though the concepts are universal. (ie - Americans shouldn't automatically dismiss the link.)


Being risk-adverse with retirement spending is perfectly rational. Most people will have to take into minimum expense amounts. Pursuing a strategy which will have the more likely outcome of not being able to pay your minimum expenses would not make sense for many people. Comparing only the expected values without including the volatility is an incomplete comparison.

The critique is aimed at the assumption that your risk aversion is scale invariant. i.e. you behave the same when the values are in the 10s of dollars, or the 10,000s of dollars. I might be perfectly fine with taking the coin flip when the outcomes are either $10 or $15, but if the outcomes are $10,000 or $15,000 I might rather take a lower guaranteed amount of $12,000 because that will meet my expenses but the $10,000 won't.


Fair enough, but for this retirement problem you're comparing outcomes within 1-2 orders of magnitude. If you don't have scale invariance you'll get a different answer if you put in $100K, $1m and $10m starting portfolios, but that difference wouldn't tell you anything useful.

IMO best way to look at γ is an arbitrary tunable smoothing parameter, just tune it until it looks like what you're most comfortable with, trading off smoothness for maximizing cash flow.


Might be addressable by solving two scenarios. The first is a highly-risk-averse approach to meeting your minimum needs, the second would be a risk-indifferent approach to investing anything left over. To put it into the coin analogy if your minimum need was $11 but the guaranteed rate is $12 you could take the $12 but then immediately flip again with the left over dollar and get an average of $1.25 with it, for a total return of $12.25.




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