# Doubling time and the Rule of 72

CIO Global Blog

16 Jul 2019

With the S&P 500 recently hitting another major milestone—passing 3,000 for the first time—it gives us a good opportunity to investigate one intriguing characteristic of investing: "doubling time." Fig. 1 shows approximately how long it has taken for S&P 500 index to double—a median of about 9.2 years. Of course, index gains are only one part of an investor's expected return. When you include the collection and reinvestment of dividends to get total returns, as in Fig. 2, the S&P 500's historical doubling time drops significantly to a median of just 5.7 years.

Unfortunately, longer doubling times are one consequence of lower expected returns going forward. Calculating doubling time usually involves some tricky arithmetic, but fortunately we have a useful rule of thumb, the "Rule of 72," to provide an estimate. It's an easy calculation: divide 72 by the expected return, and the result it the approximate number of years it would take to double your initial investment.

For example, our equilibrium total return Capital Market Assumption (CMA) for US large-cap stocks is 7.2%, and 72/7.2% = 10 years. For a portfolio with an expected return of about 5%, this would work out to a doubling time of about 14.4 years, but taking enough risk to add 1% to annual returns would cut the doubling time to about 12 years, an average.

Strictly speaking, the Rule of 72 only works if you're assuming a static portfolio, with no spending or additional savings. But that doesn't mean it can't be used for "living portfolios." For investors in their working years, savings can significantly accelerate doubling times; for example, adding 2% of your portfolio's value each year is mathematically the same as adding 2% to returns, as long as you can sustain this proportion over time (not a bad goal). The calculation for investors in retirement is a little less fun; if you are spending more than your expected return, you can use the net spending rate to calculate a "half life" for the portfolio (the approximate time for your investment's value to fall by 50%); for example 72/-4% = 18 years.

## Figure 1 - "I love you 3,000!"

UBS, Bloomberg, as of 15 July 2019

## Figure 2 - Dividends help with doubling

UBS, Bloomberg, as of 15 July 2019

#### Author:

Justin Waring, Investment Strategist Americas, UBS Financial Services Inc. (UBS FS)