The Manhattan Paradox, or Why Volatility Kills

Many thinks to my friend Sam for sending the Q2 commentary by Michael C. Litt of Arrowhawk Capital Partners. The paper has now been published at PIonline.

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In 1626, Peter Minuit, operating on behalf of the Dutch West Indies Company, paid US$23.70 (60 Dutch Guilders) in beads to the Canarsee Indians for the island of Manhattan. The lesson on compounding goes something like this: If the Canarsee had invested the proceeds at 5% per annum, their beads would be worth US$3.25 billion today. At the 7.5% actuarial assumed rate of return used by many pension plans, the reinvested value becomes US$1.15 trillion. . . . There are two problems with this type of expected future value analysis. First, the geometric rate of return assumption implies no risk, or zero volatility in the return stream. Second, there are no withdrawals factored into the ending value. As we shall see, the influence of these two considerations is very relevant to the experience of a long-term investor.
Assume for a moment that the Canarsees’ actual investment had a 5% “expected return” and 7.5% volatility, with no periodic withdrawals of capital. By generating 1,000 Monte Carlo simulations over the ensuing period, assuming a normal probability distribution for returns, one can determine a mean and distribution for the outcomes. It turns out that the tribe’s fortunes would have been quite varied. In the 50th percentile, or median case, the Canarsee end up with US$913 million. In two out of 1,000 scenarios – the best and worst cases – they end up with either US$109 billion or just US$4.6 million. In the former case, the Canarsee would have wealth just exceeding the combined total of Bill Gates and Warren Buffett, perhaps resulting in a tribal leader joining those two for lunch at Piccolo Pete’s Restaurant. In the latter case, the Canarsee could just afford a classic six-room apartment on Central Park West with a view of the park and the Thanksgiving Day parade. Thus, over long periods, portfolio volatility has a great deal of impact on the power of compounding. The median level of ending wealth in the volatile case is over 70% lower than the wealth produced in the non-volatile 5% geometric return assumption (i.e. US$913 million vs. US$3.25 billion). Volatility has significant impact on the expected value of assets over time.

Those roller coaster rides have very, very long-term consequences.


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  1. why do these academic bozos write like this? parables about 3 indian tribes? jargon galore? Why don’t they just present their message as directly and simply as possible? I’m reading David Swenson’s book about individual investing (Uncommon Success) and it is SO direct and devoid of BS that it stands out !

      • And they can’t imagine you would understand without a parable or an analogy.

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