Lumifer comments on "Risk" means surprise - LessWrong

6 Post author: PhilGoetz 22 May 2015 04:47AM

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Comment author: Lumifer 22 May 2015 03:05:36PM *  1 point [-]

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.

Comment author: Douglas_Knight 24 May 2015 09:59:56PM 0 points [-]

So, it randomly samples from the empirical distribution?

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

Comment author: PhilGoetz 25 May 2015 09:29:22PM *  0 points [-]

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?

See Vaniver's answer below.

Comment author: Vaniver 26 May 2015 01:18:34PM 0 points [-]

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

Comment author: Vaniver 22 May 2015 03:54:17PM 0 points [-]

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.

Comment author: Lumifer 22 May 2015 04:03:29PM 2 points [-]

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).

Comment author: Vaniver 22 May 2015 04:08:21PM 3 points [-]

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.

Comment author: Lumifer 22 May 2015 04:20:34PM 1 point [-]

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.

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