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Forrest Gump and the unit depletion fallacy

Forrest Gump and the unit depletion fallacy

The popularity of constructing portfolios to generate a certain natural yield owes a lot to investors’ fear of selling units. 

There is still a widespread belief among investors living off their portfolios that they shouldn’t sell shares in their portfolio or units of mutual funds they hold, because if they do they’ll eventually ‘run out’ of shares/units, and thus money.

So, they invest in high yielding instruments (no matter how risky), never sell anything and live off any dividends, coupons and interest generated by the portfolio.

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However, this fear of selling units is misplaced and results from the confusion of capital - how much an investor has invested - with the number of securities or units of funds that an investor holds.

It turns out that while protecting capital, the number of units/shares multiplied by their price, is very important, this isn’t at all the same as not selling units.

Investors can quite easily go on selling units and never run out because neither the price of those units, nor even the stock of units, is actually ‘fixed’ over time. If this sounds a bit confusing, then it’s here that a film example can help illuminate things.

The 1994 Oscar-winning film, Forrest Gump, has a short scene in it where Forrest opens a letter of thanks from Apple after his former military commander and business partner, Lieutenant Dan, invests some of the profits from the Bubba Gump Shrimp Company in what Forrest takes to be ‘some kind of fruit company’.

For our example, let’s ignore the film timeline slightly (for purists the investment would have been pre-IPO in the 1970s).

Instead, let’s assume the investment had been just for Forrest and was in 10,000 shares of Apple at its IPO price of $22 in December 1980.

Let’s also assume that Forrest had decided to sell 500 shares in each of the 37 Decembers since then for him and his son, Forrest Jr, to live off.

How many shares would Forrest have now? Surely none, as he’d been continually selling and would by now have run out.

Actually, by mid-2018 he would have sold a total of 18,500 shares, or 8,500 more than he had originally purchased. And he would still be left with 141,500 shares. 

The solution to this paradox lies in the fact that unit quantity isn’t really ever ‘fixed’. Units of a mutual fund can be traded fractionally, which means it’s possible to keep selling portions of units without running out.

While shares can’t be traded fractionally and need to be traded in whole numbers, the number of shares held can change without buying or selling due to share splits or, less frequently, reverse splits.

A share split is simply where a share previously worth £100 becomes two shares worth £50 or four shares worth £25 due to a corporate action, while a reverse share split is, unsurprisingly, the opposite.