"Risk" means surprise

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...

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.

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.

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.

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.

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?