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]]>Suppose I asked you to guess what the historical quarterly return measuring back from a random date in the last 50 years. You would answer some number. Now if I told you that the historical return for the quarter starting one day before the chosen date was -40%, would your answer change? This effect is called serial autocorrelation. Even if you believe that quarterly returns from non-overlapping periods are drawn independently from the same normal distribution, returns from overlapping periods are obviously strongly correlated.

Now, treat these rolling returns as sample draws from a distribution and measure the sample mean and variance. If you take independent draws from a normal distribution with this mean and variance, will the sample distribution converge to the historical distribution? No it will not – not even if the real historical distribution over non-overlapping periods was a stationary normal distribution.

It is a bit of work to set up a monte carlo that correctly simulates overlapping returns given the assumption that non-overlapping returns are stationary and normal. Has Welton done this work? There is no way of telling from the sales pitch. But given that they have a financial incentive not to do so, I am skeptical.

]]>There are of course criticisms that can be leveled, but neglecting tail risk does not seem to be one of them.

]]>By the way, you have any proof that Moody’s were assuming lognormal distributions in their models?

]]>Now, we know the physics underlying the transport, we know far less about economics. We do know some things. What Monte Carlo’s allow us to do is determine results from a given set of inputs. If the inputs assumptions are wrong, then the results will be wrong. But, the advantage of Monte Carlos is that we need not make a simplifying assumption just to use the technique than one relying on false assumptions. A good example of this is the value in in hindcasting as a means of training hurricane models.

Ecconomic predictions will always have uncertainties. But, Monte Carlo techniques can utilize every scrap of informaton that is available. One can look at all sorts of patterns, and try to hindcast them with assumptions. That doesn’t guarantee predictive power, but one has a better chance with a model that hindcasts near perfectly than with one that is based on false simplifying assumptions, like normal distributions.

I don’t know the author, but I’d guess that the author is not well versed in modeling.

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