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What is more important: to buy “low” or to sell “high”?

The correlation between the growth in the JSE Index and the growth in earnings per share.

“Don’t believe everything you think.” – Maxine
“Don’t let your mind wander… it’s too small to be let out on its own.” – Maxine again

We have been happily wasting the days of our lives, researching the following article. So please read the conclusion and then you can soldier on through the research. Our thanks to Simon Fillimore of Independent Securities for providing the data and for making the graphs look pretty and to Eric Lappeman for helping to crunch the numbers.

Let us give you the Conclusion first: In the article that follows we have examined the correlation between the growth in the JSE Index and the growth in earnings per share. We then examined the historical 5-year returns achieved if purchases are made when the PE ratio is low (historically cheap) versus buying when the PE is high and the market is expensive. Then we looked at the relative importance of selling when the market was expensive versus cheap. What is more important – to “buy low” or to “sell high”.

The practical advice from our findings is illustrated in Graph 4. We show the long term relationship between earnings (the red line) and index price (the green line, which tends to fluctuate more than the red line) both based to 100 in 1960. We have added the PE ratio in purple (right hand scale). It shows that the share prices seldom stay high enough for the PE to exceed 17 for very long –either the earnings must grow rapidly or the share price will fall, or the share price will grow at a slower rate than the earnings until the PE drops back to more average levels. Similarly, the PE ratio seldom stays below 12 for very long (but there have been exceptions such as 1975 to 1986 where it kept below 10 despite strong earnings growth and was largely an aftermath of the 1976 riots).

The best we can say is that if one buys when the PE dips below 12 and if one has the fortitude not to sell until there has been a period of strong earnings growth AND the PE rises to about 17, then you have maximised the probabilities of success for the next five years. Note the word “probability” – nothing is guaranteed, and sometimes aberrations occur, but the odds are firmly in your favour if you follow this method.

Currently, the PE of 16x implies that some strong earnings growth will be required to justify current share prices. The analysts are forecasting good growth in earnings for the market as a whole and, in particular, for the big mining shares of Anglo and Billiton, which together, make up over 20% of the market. May they prove correct! Thus the index is no bargain at current levels but always remember, you invest in individual shares, not the Index and the returns mentioned in the article do not include dividends!

Now let us get down to the detail

In the long run, share prices tend to track earnings

Graph 1 shows the long term growth in the JSE Overall Index (the green line) compared with its earnings growth (the red line). We rebased the monthly data to 100 in 1960, which is as far back as this index goes. Our first observation is that over the longer term, the Index seems to track earnings growth very well. The two lines criss-cross each other many times and seldom get far out of alignment. Our second observation is that when they do part, it usually provides a good buying opportunity if the share price is lagging or it is a chilling warning if the share price has run away from the earnings line.

Convincing, but are our eyes deceiving us?

Looking at a long term graph appears comforting and the relationship appears smooth but as Keynes, the famous economist, said, in the long-term we are all dead. Our eyes can play tricks on us so what sins are being hidden within the smooth long term picture? Over the 50 years, the Index rose 331x but earnings rose 228x – and the start date is very important as the index then fell for the next year or two.

Can we benefit from this trend over five years?

Our next step was to inspect the 5 year growth records of both the earnings and the share price. Graph 2 sets out the results.

First take a look at the earnings growth in the red line. We have monthly starting dates from 1960 to July 2005 = 45 years x 12 +6 = 546 starting points. Interestingly, in each of the 546 samples, the earnings always went up over the five years. Of course, the earnings growth was helped by inflation of various rates over the period but that’s a topic for another time. So the red line starts at about 8% growth p.a.. for the five years starting at the beginning of 1960. It drifts down to about 2% in 1966 and then runs up to 20% for 1971 etc.

Then we took a look at the blue line – the share price growth over 5 years hardly ever dips into negative territory. Such a dip took place if you began to invest at the peak of the 1969 boom (see how it stands out in Graph 1) or if you invested in the early 1970’s and got hit by the 1976 riots. There was a close shave if you started in April 1998 – the Index level was hardly any better in 2003. Whenever there has been a drop over five years, the extent has been small, and has usually corrected quite rapidly. Look at the growth if you started in late 1992, the index grew by 30% p.a. for the next five years!

Why don’t price movements correlate strongly to EPS growth over the five years?

For some periods such as 1975 to 1980 and 1983 to 1987, the growth rates appear to be in lockstep but this tight correlation appears to be the exception. Often, the rate of earnings growth is falling while share prices are increasing at faster rates. Or the opposite – earnings are rising but share prices are falling.

We have tried to graph this difference in the green line in graph 2. One would have intuitively expected if one deducted the EPS growth rate from the Index price growth rate, the difference would be in a fairly tight band but the green line shows this is not valid. Visually, the correlation appears poor – the line is all over the place. Sometimes the share prices grow at 10% higher than earnings, normally when share prices are running rapidly. On a few occasions share prices have grown much slower than earnings -by as much as 20% lower. This usually happens when the market plummets but earnings stay the same, or come down only after a delay.

Investor perception – bringing in the PE ratio

Thus, over five year periods, it does not seem as if it is earnings growth that will determine the extent of the movement in the index level. So if it is not the earnings growth driving medium returns, what is? The key change appears to be investor perception, which can be measured by the PE ratio i.e. good performance is mainly dependent on investors paying a higher multiple at the end of five years than they paid at the beginning. Conversely, weak share price growth is mainly due a substantial drop in the PE over the five years.

What is a PE (Price/ earnings) ratio? It is the ratio between the share price and the earnings per share. If the earnings per share are R1 then and the share price is R13, the PE is 13 – about average for the Index as a whole. If the earnings are R1 and the price is R20, then the PE of 20 is expensive. If the PE is under 10, the market is getting very cheap.

So in graph 3 we now again put in the 5 year growth in prices and earnings per share but we add the percentage change in the PE ratio on the right had scale. So take 1981, EPS for the next five years fell to about 8% p.a. yet the share price growth rose to almost 40%. This caused the PE to grow by 200% (from about 5 to 15 as may be observed in graph 4 in the conclusion at the beginning of the article). Thus one might observe that if the share price growth differs greatly to earnings growth, then it is the PE ratio that has changed drastically. Over five years, earnings growth is relatively smooth, it is the share prices that jump around like crazy, so that hints that investors may do well to keep a sharp eye on the PE ratio.

Can the starting PE ratios provide a clue to future returns?

In 2004 we wrote an article on the relationship between starting PE Ratios and five year growth in the index. It is a good time for an update. In table 1 we break the market up into deciles. Starting in 1960, what was the starting PE ratio, and how much did the market rise over the next 60 months. So we can now run it all the way to the Index level of five years ago i.e. July 2005. We thus have 546 samples. So we take the lowest 55 PE ratios and put them into decile 1 and calculate the returns thereon. The results are exactly what you would expect. Buying when the market was historically cheapest resulted in an average annual growth of 26.2% (to which dividends should be added) but the variance was as high as 38.8% p.a. and as low as 14.6%.

The 2nd decile (PE’s between 6.5x and 8.3x) resulted in an average return of 19.2% p.a.

When we get to decile 5, the average has fallen to 11.7% but that included a loss of 0.8% for one of the periods.

In deciles 9 and 10 the average gain falls to 6% but interestingly, the worst losses of 2.9% and 2.7% were not as bad as the 3.6% loss in decile 6 – thus showing that from time to time, strange things can happen at any time, against the odds.

So what we can take away from this table is that normally, but not always, buying when PE’s are low is going to end up in a very good return in five years time while buying when PE’s are high will usually limit the capital gain.

What is more important, selling at the top or buying at the bottom?

So how important is your closing PE in terms of your total return? This time we ranked the table according to what the PE was at the end of five years and worked backwards. What return would you have made when the PE was over 16.7x – decile 10? The average return was 16.3% p.a. over five years for the 10th decile. The worst you did was 9.6% and the best you did was 21.9%. As expected, decile 9 is lower than 15.9% and decile 8 drops to 15.0% but then, unexpectedly there is an increase in deciles 2-4 with decile 3 showing a remarkable 16.5% average return. We went back and checked on decile 3. Although the closing PE’s were low between 8.6x and 9.6x, they were often much higher than the opening PE’s and earnings growth was good in many instances so the good performance here appears to be a bit of a pleasant anomaly.

While it is “common knowledge” that selling when the market is expensive is better than selling when it is cheap, it does not always result in a great return. If the market was expensive 5 years ago and is expensive now, the increase in share price will be limited to the increase in earnings. There is little scope for a positive re-rating if you buy shares when the PE is 17 but obviously, there is a lot more scope if one buys shares when the PE is 10.

In table 3 we show a share that increases earnings per share from R1.00 by 15% per annum to R2.01 in five years time. If you bought it cheaply now on a PE of 10 you would pay R10 for it. If you sell it cheaply in five years on the same PE of 10 then you will make 15% per annum = the growth in earnings. So that is buy low, sell low.

However, if you sell it at the expensive PE of 17 you then receive R34.17 (17x R2.01) for a return of 28% per annum. Buy low, sell high.

However, if you buy high at 17 PE you will pay R17 now and if you sell it on a low PE in 5 years then your return will be just 3%. That’s buy high; sell low.

But if you buy high and sell high, both on a 17 PE, then once again you will make 15%.

So, this table helps to illustrate the point that selling high is important, but not as important as buying low!

* Robert Cowen Investments:


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