Are log normal distributions the right distributions to use for a Monte Carlo Simulation of Stocks?

This is such an important topic! Jim Otar's just released book (he too is a Nassim Taleb fan) has an amazing chapter on Monte Carlo ("MC") models as used in retirement planning. His bottom line is that typical MC simulations tend to result in overly optimistic retirement planning results. Otar goes into great detail about why this is so (and it's not solely due to the distribution shapes being used). His conclusion is that until better models are developed, the best approach is to use actual history ("aftcasting"). For example, if you are projecting 30 years out and you have nominal market returns and inflation data since the year 1900, you would construct a scenario using the actual data from 1900 through 1929. That would give you one line (trajectory), say of your total portfolio amount. Then you would construct a scenario using the 1901 through 1930 data. That would give you a second line, etc. If you have data through 2008, you would be able to construct 80 of these 30 year trajectories. When you plot these lines using actual histories and compare the result with standard MC generated trajectories, the aftcast tends to show a significantly greater probability of portfolio depletion.

I would love to see what my ESPlanner MC trajectories (inflation adjusted) would look like using those 80 actual history scenarios...I should post that on the feature wish list thread. It's probably not computationally feasible with ESP's underlying design. But even though I'd perfer an aftcasting approach over ESPlanner's current MC module, I'll take ESPlanner's comprehensive consumption smoothing approach over any tool anyday, including Otar's.

I do wish someone could address this question...can it really be shown that MC trajectory probabilities are not affected by using real returns and constant inflation (as ESPlanner and most MC programs seem to do) vs using nominal returns with varying inflation, with inflation adjusted results calculated at the end? I guess I'm thinking that inflation's effect is more important in distribution portfolios than in accumulation portfolios (i.e. in the accumulation phase, inflation affects income and expenses pretty equally so it's OK to ignore inflation uncertainty, but in the distribution phase, more income is fixed, and portfolios are smaller and shorter-lived, so that inflation's effect on expense levels becomes disproportionally greater than its effect on income). I could be all wet here, but it seems like existing MC tools understate portfolio or living standard risk when they use real returns and constant inflation vs using nominal returns and varying inflation.

The issue is, as always, a matter of computational power. If we use nominal returns and varying inflation we add an extra state variable and double the amount of time it takes to generate Monte Carlo results. Each new state variable, approximately, doubles the amount of time it takes to get results from the previous number of state variable.

I would have to let Larry speak to the question of accuracy, but as to the question of MC being optimistic (again, I'm not enough of an economist to know if MC is or isn't optimistic by it's nature), that's exactly why we allow you to alter your consumption patterns and why the default consumption pattern is cautious rather than aggressive.

Best,

Dick

Hi Larry,

In September 2009 you mentioned we should look for more comments from you on this important issue shortly. I have'nt been able to find any comments subsequently posted by you adressing log normal distrbutions and tail risk. Please share your current thinking about whether,how and when this issue will be addressed.

Also, please comment on whether you are or will consider adding a feature so that ESPlanner calculates and reports based on user supplied parameters the impact on portfolio sustainability of early in retirement sequential portfolio losses. Perhaps a feature based on Moshe Milevsky's "Sequence-of-Return Downside Exposure (SORDEX) Ratio" or something conceptually similar? http://www.ifid.ca/pdf_newsletters/PFA_2009APR_BlackSwan.pdf

Thanks.

Kind regards,

John

From: Laurence Kotlikoff
Hi Yaron, Thanks for raising this. It's an issue I'm thinking about and hope to be able to deal with formally in a future update. The issue is what's the best way to incorporate tail risk and whether we really know that the jointly distributed log normal is really off the mark with respect to tail risk. I intend to raise this issue with several experts in finance in the next week or so, one of whom won the Nobel prize for work in finance, so he's as good as it gets. So look for some more comments on this issue from me shortly. best, Larry

2009-09-27 16:28