Friday HighlightAug 10 2018

Forrest Gump and the unit depletion fallacy

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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.

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.

Dividends, bond coupons and interest are an extremely important source of long-term returns.

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.

In the case of Apple, it saw its shares split multiple times over its listed history: two for one in each of 1987, 2000 and 2005, and seven for one in 2014 (a 56-fold increase overall).

So, the first part of the explanation for inevitable unit depletion being a fallacy is that it is possible to keep selling units (or fractions of units) and never run out.

However, for investors living off their portfolios to do so successfully does require the second part of the explanation: the value of the units/shares need to grow in price to support future withdrawals from the portfolio. 

Once again, our Forrest example, an admittedly extreme example, demonstrates the power of capital growth in protecting capital.

The 500 shares he sold at the end of 2017 would have netted him a cool $84,615 (£66,205) at the time, based on the share price of $169.23 per share. And his 141,500 remaining shares would have been worth almost $24m at the end of 2017.

None of this should blind investors and advisers to the importance of income generated by portfolios. Dividends, bond coupons and interest are an extremely important source of long-term returns.

But, at the same time, investors and advisers should not ignore the importance of capital growth when designing long-term investment portfolios.

Instead, advisers need to work with clients to understand any biases they may have around selling units if necessary, and to limit the perverse effects of these biases as much as possible so that they can deliver the combination of income and capital growth likely to maximise the risk adjusted total return of client portfolios, and so maximise the chance of meeting client financial goals.

Nic Spicer is portfolio manager and UK head of research at PortfolioMetrix