# The Mayfly and Methuselah

Our perception of the world is shaped by our lifespan. Some creatures live to see just one sunset, others live for thousands of years. We now expect to live around 80 years and we invest for about half of that time. But some people invest like Mayflies rather than taking the long-term view. It turns out that investing over the long-term has considerable benefits.

A Mayfly lives at most a few days in its adult form. But during that time it moves from life underwater to life on the wing and mates. A Mayfly will witness a single sunrise and a single sunset.

A bristlecone pine tree in the US was found to be almost five thousand years old. This tree was a sapling during the Early Bronze Age before the founding of the Old Kingdom in Egypt. It was named Methuselah.

Let's look at the US stock market from these two different points of view: a Mayfly that lives for just one day, and Methuselah that looks at markets over decades. Each of the five graphs below looks over different time-scales. The top graph looks at the size of returns over the space of one week. You can see that sometimes these returns, when annualised, are as high as 200% or more, but they also range down to -100%. In other words, **the Mayfly is gambling**. 57% of the time the Mayfly wins, but 43% of the time he loses.

As we increase the period of time over which we invest to a month (21 trading days) the returns look less spread out. Less spread out means more certain. And now the returns are positive 60% of the time. Longevity seems to be good for investment!

If we space out our returns over one year (252 trading days) the story improves again. Returns are positive 74% of the time. Over a decade returns are positive 90% of the time and **over 40 years returns are always positive**.

Of course there is a catch. While the Mayfly sometimes got huge returns Methuselah didn't. The average annualised return for Methuselah was just 7%. But remember that Methuselah will earn this compound rate over a very long period of time, such that 7% over 40 years earns about 1400%. Subtracting 2% for inflation that's still around 600% cumulative return. But what's best about Methuselah's return is that it is much less uncertain than the outcomes for the Mayfly.

## What The Mayfly Sees

The reason why the Mayfly is gambling is because of it's short lifespan. The return on stocks turns out to be a combination of two things:

**Drift**: Long-term upward drift linked to earnings growth and economic growth**Seasonality**: There is a small amount of seasonality in market price movements**Noise**: Short-term unpredictable fluctuations in price driven by daily trading called volatility.

We can break down the S&P 500 into these three components graphically. First we convert the monthly S&P 500 returns since 1960 onto a log scale, then we perform some statistical analysis, and here are the results. The original data is the top panel, then we see the small seasonal variations over the course of a year, then the very strong long-term upward drift, and finally the noise that is left over.

Over the lifetime of the Mayfly share prices are driven by both upward drift and by daily volatility. However the factor which dominates is noise because of the way drift and noise scale with time. We can easily show this by working out how much markets drift over the course of one day. The long-term growth of equity markets historically has been around 7% per year. However during the Mayfly's lifetime of a single day the size of that drift is just 1/252nd of 7% which is just 0.03% (there are 252 trading days per year).

*Drift is all but invisible to the Mayfly*

Volatility is the typical daily percentage variation in price. For an index like the FTSE 100 or the US S&P 500 this is usually around 20% per year. But volatility scales differently to growth - it depends on the square root of time because it behaves like a random walk. So in a single day the volatility of a stock index is one "square root of 252"th of 20%. The square root of 252 is about 16 so the typical daily price movement due to volatility is around 1.3% which is an order of magnitude bigger than drift which was 0.03%.

*For the Mayfly volatility is 45 times bigger than upward price drift*

## What Methuselah Sees

For a creature that thinks over longer time-scales markets look completely different. Let's use a decade as an example. Over the space of ten years the price will move up thanks to the 7% drift by a little under 100%. Volatility on the other hand scales as the square root of time so that will be 63% (20% times the square root of 10).

*For Methuselah drift over a decade is one and a half times bigger than volatility*

As we increase the time-scale the dominance of drift over volatility grows greater. If we consider forty years the drift return jumps up to 1400% while the volatility only increases to 126% and now the drift growth exceeds volatility ten-fold. In engineering terms we might say that **for long-term investors the signal to noise ratio improves**.

## Conclusion

It is easy to see that if we invest over the long-term we can look through market noise to ride the long-term growth of earnings. Returns using Methuselah's approach may not be spectacular, but they have been very consistent over the last century for the US and the UK.

There are some caveats. Firstly we suffer from behavioural problems that make us deviate from the patience of Methuselah. Noise in the financial press about initial coin offerings and tech unicorns easily draw us into the Mayfly mentality of chasing short-term fads promising spectacular returns. Secondly long-term upward drift due to growing corporate earnings is slowing down. This is due to a variety of factors, such as an ageing global population and a lack of innovation that truly increases economic productivity. This means that a long-term return of 5% or 6% might now be more realistic.

One of the most valuable assets we have as investors is time. Given our long and increasing lifespan we should capitalise on this time wealth and behave like Methuselah not a Mayfly.

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