“Market Mis-timing”: a study of the distribution of returns from the S&P 500 1950-2012

March 26th, 2012

Nick Hays

Dhaka, Bandladesh

No prizes here for “most catchy blog title”. However I hope this short article does exactly what it says on the tin.

This topic is an area of some interest to me because although I remain fascinated by the daily movements of markets and short-term trading, I am also an advocate of a conservative, long-term approach to investing.

While both strategies have their merits, my research has led me to conclude that for the average retail investor, the long-term ‘buy-and-forget’, index investment approach is by far the preferred approach.

This assertion will be the subject of an upcoming series which I am in the process of writing. In the meantime, this article examines one variable of the ‘buy-and-hold’ investment strategy: time horizon. In other words, how long the investor commits to locking up his funds.

A common fear amongst retail investors is buying at the ‘wrong’ time, or as I am calling it ‘market mis-timing’. Simply put, we are afraid that we may buy at the top of the market and just as the bull is running out of steam.

This fear is entirely rational when you consider recent history. For example, a buy-and-hold investor who bought the S&P 500 index at the peak of the dotcom bubble in March 2000 would have been sitting on paper loss for the next 7 years, and would still be nursing a negative return even today, 12 years later. That is a compounded annual return of -1.4% (including dividends, but before adjusting for inflation).

However, looked at from a longer-term perspective and the picture appears very different. From 1965-2011 the S&P 500 gave a buy-and-hold investor a compounded annual return of +9.2% (including dividends, before inflation).

The fact is that over the very long term, stocks have historically been a reliable source of positive returns for patient investors who were willing to accept a level of volatility and periods of negative returns.

While past performance is no indicator of future returns, I am a firm believer in the power of mean reversion in data sets that are sufficiently large and long-term in nature.

If we believe that the stock market’s positive trend remains intact over the very long-term, then intuitively we understand that the longer the period we are willing to lock our money up in the market, the less we need to worry about the risk of buying at the ‘wrong’ or ‘right’ time. The logical conclusion of this is that a theoretical ‘infinite’ time period would reduce the risk to the absolute minimum. (In fact it’s an oft-quoted fact that Warren Buffett’s preferred stock holding period is “forever”). Obviously in the real world we cannot entertain an ‘infinite’ holding period - eventually investors want the money back so that they can consume, hence a practical time horizon must be selected.

Put another way, there is a trade-off between, on the one hand, the risk of “market mis-timing” and on the other the time value of money – the opportunity cost of locking up our money for extended periods of time.

In summary, my aim is to quantify and estimate the appropriate minimum holding period for a buy-and-hold index investor. Note the “appropriate minimum holding period” is defined here as the period which adequately reduces the spread of the investor’s expected returns, as measured by the standard deviation. I have used the S&P 500 as an illustrative example, examining holding periods of 1 through 10 years commencing on every trading day within the period 3^rd January 1950 - 5^th March 2012.

The result is in line with what we intuitively know to be true. The below chart shows that the longer the holding period, the less extreme the distribution in potential returns:

As you can see, the standard deviation of returns declines quite gradually between the 4-10 year holding periods. However below 4 years, the volatility increases significantly, at which point the relationship starts to take on an exponential characteristic.

I am quite confident that if I were to examine other broad stock indices, or if I expanded the number of holding periods examined, e.g. between 1 month and 20 years, the pattern would look the same as above.

Using this as a guide, a minimum holding period of 4 years appears to offer a reasonable level of protection from volatility of returns while still being a ‘realistic’ time horizon for the average investor. 4 years is the point on the chart where the curve begins to flatten – that is to say that 4 years is the point of diminishing incremental benefit from longer holding periods.

Longer holding periods obviously offer greater protection, and investors must weight this benefit against the opportunity cost of locking up the money for a longer period.

Expressing the same data another way, the below chart shows the maximum, minimum and average (arithmetic mean) of returns for the same holding periods:

 

The idea for this chart I borrowed from Michael Keppler’s “Risk is not the same as Volatilty”. It neatly illustrates the relative risk/reward profiles of various holding periods.

As you can see, an investor with a time horizon of 1 year could have earned returns of anywhere between -49% and +69%. An investor with a 10 year horizon would have reduced the spread, with the minimum being at -6.5% and the maximum being +18%.

Note however that regardless of the holding period, over the 1950-2012 period the average return is quite consistent, fluctuating only between 8.5% (1 year) and 7.1% (years 4 and 6-10)

The Long and the Short?

Almost by definition, the average retail investor cannot consistently time the market to avoid buying at the ‘wrong time’. If this is accepted, then the average retail investor must accept the unknown risk of whether they are buying at the top of the cycle, the bottom, or somewhere in between.

S&P data from 1950-2012 suggest that an investor with a time horizon of only 1 or 2 years must accept a wide range of potential returns.

To reduce the uncertainty of future returns, the retail investor must extend his minimum holding period, weighing this against the opportunity cost / time value of money. The data indicate a holding period of 4 years as a potentially optimum point in this trade-off, though pin-pointing the actual optimum level would require an assumption to be made on the time value of money.

(Reduced time value of money due to unusually low interest rates - such as those seen today - would push the optimum period further out, as an investor would gladly 'pay' the extra required to reduce the potential return spread).