Distribution of Returns

Taking monthly data for the past 25 years (end of August 1990 to end of July 2015) we created a histogram to show the dispersion of returns broken down into 1% chunks (with a “catch-all” for excesses greater than +10% or -10%. The data below shows the output for the FTSE 100.

To assist the reading of the data, there have been two individual calendar months where the FTSE100 lost between 7% and 8% - September 1990 and October 1997. Correspondingly, there have been 3 periods when the market rose by between 9% and 10% in a single month – April 1992, September 1997 and April 2003.

In analysing the data a little deeper you will see that the greatest number of occurrences falls within the +2% to +3% range (38 in count and 12.67% of the total number of observations) followed by the 0% to +1% (35 and 11.67% respectively) and finally +3% to +4% (33 and 11%). Being as the data covers 25 years’ worth of information, there are 300 observations in the chart above.

• The largest monthly gain over the past 25 years was 10.98%
• The largest monthly loss over the time period was –12.86%

The average monthly return for the past 25 years is 0.7390%, but for the mathematically driven of you out there, the median number is 0.9978. 61.67% of the observations have a return of greater than 0%, meaning in a roundabout way that 4 months in 10 have been negative. What the data doesn’t tell you though is the “quantum” of the up months and down months. For instance, if, on average the market under investigation was up 9 months in 10, averaging 0.50% per month, but the average of the one negative month was -6%, then the “odds are good, but the goods are odd” and this would probably be an asset worth avoiding!

One of the reasons for creating and observing these charts (and we can run these charts for tens of thousands of instruments – both indices and funds) is to get a greater understanding for the characteristics of them. When running this analysis over different time periods (for instance 3 month, 6 month, annual intervals and so on) you get different outputs and different observations. All investments are volatile, but having the courage of conviction to see through the short-term market movements can help reduce costs in managing portfolios through not panic selling or FOMO buying (FOMO being “Fear Of Missing Out”). Charts like this are really useful to provide to clients – both experienced and inexperienced alike to inform, educate and remind them that markets with risk do not deliver consistent returns. A monthly average of 0.73% certainly looks incredibly attractive compared to cash returns at the moment, but it can come with wealth warnings – there certainly haven’t been ANY occasions in the past 25 years where cash deposits have lost 10% or more in a month (in full honesty, when looking at a similar chart using the Halifax £10k deposit rate, there haven’t been any negative period AT ALL over the past 25 years).

Correspondingly, when looking to the highs and using cash as the investment of choice, there haven’t been the big positive numbers either. In the 300 observations over the past 25 years, 296 of them are between 0% and 1%. 4 have been between 1% and 2%.

Although in essence, the numbers for cash look safe, and the month over month chart as shown at the top of this paper looks quite volatile, one thing that isn’t shown is the compounding effect of returns on investment performance. “Compound Interest is the 8th Wonder of the World” so said Albert Einstein “he who understands it earns it, he who doesn’t pays it” and this is borne out in the chart below. Volatility of returns can be your friend - assuming you invested £10,000 in the FTSE 100 and placed £10,000 on deposit, the difference in 25 year returns is staggering – a “buy and hold” strategy with dividends reinvested have turned the cash pot to £17,994.27 and the FTSE 100 investment has grown to £71,039.52

When returns are consistently low, the corresponding compounding number is low and the impact of it is low. The effectiveness of compounding is low. When you add a little volatility and risk to the numbers, the compounding effect is higher, the returns higher and the effectiveness of compounding higher.