Share Sleuth: Time to measure performance more accurately

Richard Beddard explains why he's changing the way the performance chart is presented as the portfolio approaches its 10th anniversary.

This month, I have refrained from trading, although I might have added shares in Anpario (LSE:ANP) had I realised the portfolio had enough cash to add a small holding. The company briefly strayed into value territory and now sits right on the cusp by my estimation. Like Porvair (LSE:PRV), Anpario has been on my watch list for many years.

Moreover, like Porvair, the single factor holding me back from adding shares in Anpario has been its valuation, so it is slightly galling that when the opportunity arose, I did not check I had the firepower to follow through! Hopefully I will have another opportunity to buy shares in Anpario.

This month, I will address a change to the presentation of this article. From now on, the vertical scale on the performance chart will be a logarithmic scale instead of the arithmetic scale we have been using.

Before I explain why, a caveat. I do not dwell on the performance of the portfolio because I do not believe short-term movements in the value of investments are correlated with long-term outcomes. This is why the Dogs of the FTSE strategy, regularly covered by Money Observer, works. Previous losers are often future winners. Anything less than 10 years is short-term to me, and were it not for the fact that readers are interested in Share Sleuth’s performance, I would not include the chart, or even generate it.

On 9 September, though, the Share Sleuth portfolio hits a significant milestone. It will be 10 years old, which means the chart will become somewhat meaningful. It will tell us whether I have been a better or worse investor than average, which brings me back to logarithmic scales.

Why scale matters

To show you how an arithmetic scale distorts performance charts I would like you to join me in a demonstration. The link will take you to a web page with a chart of the Dow Jones Industrial Average, a venerable US stockmarket index. Now un-tick the boxes above the chart that say "Log-scale" and "Inflation-Adjusted".

This chart shows the index level on an arithmetic scale, and you should see a curve that gets steeper and steeper as time goes on, typical of long-term stock market charts.

It goes right back to 1914, and includes the Wall Street Crash, the most dramatic stock market event of the 20th century. In the two years following 1929, the Dow fell by over 90%. Can you see it on the chart? In the 1920s, the line is almost flat.

That is odd, because the much smaller 40% declines of the dotcom bubble after 2000 and the 50% decline during the financial crisis of 2008 are easy to pick out.

Now click the log scale box. The true picture comes into focus. The Wall Street Crash is restored to its rightful place, and the long-term growth of the stock market is almost a straight line, not an exponential curve.

The reason for the difference is the scale. An arithmetic scale goes up in equal increments, so the distance from two to four is the same as the distance from four to six.

A logarithmic scale goes up in equal multiples, so the distance from two to four is the same as the distance from four to eight (both have doubled).

The logarithmic scale keeps movements of the index in proportion. The more whatever we are charting goes up and the longer it goes up for, the bigger the discrepancy between the two scales.

To show the difference, we have put both an arithmetic scale and a logarithmic scale on the Share Sleuth chart and plotted its performance twice. The differences are more subtle than the Dow example, but they are already apparent.

If the portfolio continues to grow, the distortions of the arithmetic scale would get worse, which is why we have changed it.

Log scale paints truer picture

Source: interactive investor   Past performance is not a guide to future performance

Missed adding Anpario

Notes: No new additions. Transaction costs include £10 broker fee, and 0.5% stamp duty where appropriate. Cash earns no interest. Dividends and sale proceeds are credited to the cash balance. £30,000 invested on 9 September 2009 would be worth £111,780 today. £30,000 invested in FTSE All-Share index tracker accumulation units would be worth £64,432 today. Objective: To beat the index tracker handsomely over five-year periods.

Source: SharePad, 3 April 2019