# 12

I lost about \$20,000 in 2013 because I didn't notice that a company managing some of my retirement funds had helpfully reallocated them from 100% stocks into bonds and real estate, to "avoid risk". My parents are retired, and everyone advising them tells them to put most of their money in "safe" investments like bonds.

Vanguard has an online retirement advisor that asks you 11 questions, most of which are variations of "Will you panic and sell everything if the market falls?" (I was especially amused by one that added, "Tell us what you did, not what you think you would do.") I filled them out for a hypothetical 65-year-old who is retiring immediately and expects to live another 20 years, (answering the "Are you stupid?" questions with "No, I am not stupid.") It advised this hypothetical person to put his money 50% in bonds and 50% in stocks.

Vanguard also has a neat Monte Carlo retirement simulator that runs 5,000 simulations of an initial investment with a given stocks/bonds allocation using random (non-Markovian) historical data, and tells you in what percentage of these simulations you went broke. I put the same numbers into this retirement simulator and ran it with 100% stocks:

Then I ran the same simulation with the recommended 50% stocks, 50% bonds:

So, 100% stocks is 3 times as likely to last for 20 years as the recommended 50% stocks / 50% bonds. (For the Bayesians out there, it gives an odds ratio multiplier over the recommended allocation of 3.5.) It also has a much, much higher expected value. The only sense in which the 50% stocks / 50% bonds allocation provides less risk is that the worst cases--and we're talking about 5% of results--are a few percentage points less bad.

If you play around enough with the simulator, you can find situations in which the 50% bonds allocation gives a smaller chance of running out of money. They're all situations where you have a lot of money and not much time to spend it. One I found is: \$1,000,000, spend \$48,000 (2015 dollars) per year for 20 years. 50% stocks / 50% bonds allocation leads to 97% survival. For 100% stocks, it's only 90%.

Yet for most people, 100% stocks is far less risky, by which I mean their chances of running out of money are lower, by which I mean they're not 100%. The median retirement savings for Americans age 55 to 64 is \$103,000. The recommended "safe" allocation guarantees quick bankruptcy for them.

(That's not to say the safe allocation at this moment is 100% stocks. I just moved money out of stocks. If you're willing to continually change your allocations, the situation is more complex. But the standard retirement fund allocation recommendations aren't based on that; I've never seen them change.)

So what do people mean by "risk"?

I think they can only mean either "variance" or "badness of worst case", and the differences in the worst cases are negligible. It seems people are giving investment advice not to minimize the chances of running out of money, but to minimize the chances of being surprised, even when the surprises are almost always good. Whether that's what the people receiving the advice want, I don't know.

# 12

New Comment

I'm reminded of a silly question I once asked, that I'd like to ask an investment professional:

I have \$500,000 in cash-equivalent assets. Normally this would be a pretty good thing, but I also have a \$1,000,000 debt to Tony Soprano that comes due in one year, and if I don't pay it, he'll have me whacked. I could take the money to a Las Vegas roulette wheel, bet on red, and have a slightly less than 50/50 chance of not being killed. (I'll worry about the IRS later.) Can you recommend an alternative investment?

You're asking the simulator something similar. If you ever can't take out as much money as you wanted, it counts as a failure, regardless of whether you're \$1 short or \$100,000 short. This isn't necessarily bad, though...

[-]gjm100

One lesson your hypothetical 65-year-old should take away from both graphs is that they can't afford to spend what they're proposing to spend. The question they actually want anwered (or ought to) isn't "what's my probability of lasting 20 years with these numbers and a given investment allocation?", it's more like "given this much to invest and a given investment allocation, how much can I take out every year and still have, say, a 98% chance of not running out in 20 years?".

(Ideally we'd do this with a more brutal simulation that allows for occasional events substantially better or worse than in the historical record. And ideally the simulation would allow you to say not "take \$X out every year" but "take out between \$X and \$Y every year, depending on the outcome of simulations performed at that point".)

Unfortunately the Vanguard simulator doesn't work on the computer I'm currently sat at, so I can't tell how stocks and bonds compare according to a metric of that sort. I firmly expect that stocks will still win, for what it's worth.

[-]gjm60

Nope, actually stocks don't still win when what you want is to maximize widthdrawals subject to keeping Pr(run out of money) very small. The 98% level for bonds only is between \$15k and \$16k; for 50:50 it's a little better, somewhere between \$16000 and \$17000; for stocks only it's about \$12k

(Another thing the simulator notably doesn't let you do: adjust your portfolio allocation over time.)

That's correct.

Had I invested 100% in a NASDAQ ETF 15 years ago, I would have lost >60% 2 years later and only got back up to the book value this year, not even taking inflation into account. This is what they want to protect you from, models or no models.

Exactly. Stocks are almost always better long-term investments than anything else (if mixed properly; single points of failure are stupid). The point of mixing in "slow" options like bonds or real estate is that it gives you something to take money out of when the stocks are low (and replenish it when the stocks are high). That may look suboptimal, but still beats the alternatives of borrowing money to live from or selling off stocks you expect to rise mid-term. The simulation probably does a poor job of reflecting that.

That's no reason to tell someone with hundreds of thousands of dollars to put half of it in bonds. The market isn't going to stay down for 10 years.

That's no reason to tell someone with hundreds of thousands of dollars to put half of it in bonds.

As a matter of empirical observation, rich people with millions of dollars do NOT keep them all in equties and, in fact, tend to allocate a chunk of their wealth to bonds. How large a chunk is debatable.

The market isn't going to stay down for 10 years.

Tell that to the Japanese.

The market isn't going to stay down for 10 years.

...Yet it has, multiple times in the last 100 years, if you invest a lump sum. Regular contributions are a different story.

The US stock market? No, it hasn't. I checked a graph of it before writing that. "Time the market is down" is not the time between peaks on the graph. It's the time between periods when stocks are a better investment than bonds. For the Great Depression, that was 3 years.

The market isn't going to stay down for 10 years.

Both the Nasdaq composite and the SP500 reached peaks in early 2000 which they did not get back to until 2013.

As at least one of the other commenters pointed out, you're proposing to withdraw 10% a year, so of course the higher-average-return works better. The rule of thumb for safet is usually said to be around 4%/yr. Ass you point out, most Americans don't have nearly enough retirement savings.

In the simulator, the crossover where 50/50 becomes safer is around 5%/yr withdrawal rate for a 30 yr retirement, and around 6.5% for 20 yrs.

• I think they can only mean either "variance" or "badness of worst case"

In the context of financial markets, risk = variance from the mean (often measured using the standard deviation). My finance professor emphasized that although in everyday speech "risk" refers only to bad things, in finance we talk of both downside and upside risk.

So "risk" really does mean surprise to them. Do you think this impairs their ability to reason about risk? E.g., would they try to minimize their risk because that's a good thing, for the ordinary definition of risk, but then actually minimize their variance? Do they talk to clients using the word "risk", and being aware on one level that they mean something different, yet not explain the difference?

In the context of financial markets, risk = variance from the mean

That it not true, or, rather, not entirely true. VAR is very widely used in the real world and it's not variance. I also think Taleb would facepalm at this definition X-)

If you plan on investing now and letting the money sit there for the next few decades, stocks are the way to go. The occasional slump won't hurt much in the long run.

If you plan on withdrawing money every year for living expenses, then things get tricky. Taking out a fixed amount each year will amplify the effects of stock market slumps. You might get low enough that you're withdrawing all your returns for the year. That leaves you running in place, falling behind inflation, and one recession away from getting completely wiped out.

The risk here is the risk of ruin. Once your investment hits \$0, you're out of the game.

Vanguard also has a neat Monte Carlo retirement simulator that runs 5,000 simulations of an initial investment with a given stocks/bonds allocation using random (non-Markovian) historical data

So, it randomly samples from the empirical distribution? That's not a good idea, returns (especially of bonds) have time-series structure which should not be ignored. And what about asset class correlations?

All such simulators essentially specify a model of the market(s). Before taking its results seriously you should think about the underlying model and how adequate it is (usually not very).

So what do people mean by "risk"?

This is a very long discussion, several book-lengths long. There are multiple definitions, from precise but not always helpful (e.g. "sample standard deviation") to intuitive but not very useful (e.g. "the chance of bad things happening"). The two main varieties are some more or less symmetric measures of variance (e.g. volatility), and specifically asymmetric measures of the left tail (e.g. VAR, value-at-risk).

"People giving investment advice" are, as usual, acting according to their incentives. I recommend figuring out what their incentives are.

So, it randomly samples from the empirical distribution?

You seem to be reading "non-Markovian" as "Markovian."

No, he's reading it correctly. It randomly samples from the distribution, not from the time-sequence. And that isn't a good idea. But this Monte Carlo simulator is still better than the others I've looked at. I'm surprised, given the amount of money at stake, that I haven't seen a personal finance simulator that doesn't completely suck.

And what about asset class correlations?

I was surprised by your use of "non-Markovian," by the way, because this seems like a Markovian model to me.

So, it randomly samples from the empirical distribution? That's not a good idea, returns (especially of bonds) have time-series structure which should not be ignored. And what about asset class correlations?

I don't know how Vanguard does their simulator, but as a technical point it's easy to encode time-series structure and asset class correlations into Monte Carlo simulations. Correctly estimating that time series structure and the correlations may be another story, especially for financial data.

What's hard is producing a reasonable model. Once you have one, sampling from it is easy.

I expect the Vanguard simulator to be an exercise in marketing and so be trivially simple (pick a random historical return for S&P500, pick another random historical return from, say, some aggregate bond index, combine according to portfolio weights, repeat).

What's hard is producing a reasonable model. Once you have one, sampling from it is easy.

Agreed.

I expect the Vanguard simulator to be an exercise in marketing and so be trivially simple (pick a random historical return for S&P500, pick another random historical return from, say, some aggregate bond index, combine according to portfolio weights, repeat).

Clicking through the link, this is close to what they're doing (they appear to select the same year to preserve the asset class correlations):

For each year of each simulation, we randomly select one year of stock, bond, and stable-value returns from the database. Using those values, we calculate what would happen to your portfolio—subtracting your spending, adjusting for inflation, and adding your investment return. We repeat this process, one year at a time, until the end of your retirement or until your portfolio runs out of money. The next simulation starts the whole process from the beginning. After 5,000 independent simulations, we've tested a broad range of possible scenarios, and clear patterns begin to emerge.

This seems to be a rather inefficient method of calculating an average return :-/ I'm not being quite fair here because doing it this way accounts for things like higher moments and so is better, but still...

The underlying assumption is that both the stock market (represented by different proxies at different points in time!) and the bond market (ditto) are stable unchanging processes since 1926. That, um, does not look likely to me.

Something I just noticed: If you click on the graph, it switches to a graph of the probability of survival over time. But that graph doesn't match up at all with the reported numbers. It shows about 16% survival for 100% stocks, and ~0% survival for 50% stocks, 50% bonds.

That's not to say the safe allocation at this moment is 100% stocks. I just moved money out of stocks.

Why? How do you go about judging the safe allocation?

I'm not good at it. The people who are good at it seem to be arguing about it more this year. Surely there'll be some bump when the Fed raises interest rates. I know that's supposed to be priced into the market, but it doesn't appear to be, based on the lack of any permanent market change after each of the Fed's prior surprising statements. Possibly the market is playing a game of chicken.

The people who are good at it

It is likely that there are no people who are good at timing the market. I am not aware of anybody that is good at timing the market. The best investor in the world, Warren Buffett, does not time the market at all. His high investing returns over more than half a century do suggest he has some credibility when he suggests that no one can time the market successfully.

I am not aware of anybody that is good at timing the market.

Why would you expect to be?