A Statistical Approach to the Australian All Ordinaries

Buy low, sell high - like motherhood and apple pie, but what is high and what is low?

The answer to this question can be narrowed down by taking a statistical approach to analysis of the recent history of the Australian All Ordinaries.

Excel has a function which allows you to create a percentile analysis of a series of data. This can be applied to a series like the results of calculation of the percentage difference between the All Ords today compared to say 2 months, 1 year and any other number of periods ago. It can also be applied to a series of the volatility, or degree of overbought/sold compared to a benchmark such as the 200 day simple moving average.

The results of that percentile function can then be graphed using Excel's built in graphing functions.

You can then read any piece of data against the chart to determine where in the historical context the point lies. What percentile does it fall within? What percentage of historical results were higher or lower?


Here is the result of percentile analysis of the All Ordinaries growth performance for various rolling periods using index data starting from 1984.

If we know the 1 year growth as at today we can compare to a chart to determine the percentile within which that level of1 year growth would lie. Excel will, for each point on the chart, tell you the percentile number and the level of 1 year growth. For 12 September 2011 the 1 year growth rate was determined from the my table of calculations to be negative 11.9%. From a similar chart to that above that was determined to be in the 13th percentile of 1 year growth. In other words, from 1984 to 2010 the 1 year growth rate was higher 88.1% of the time. But 11.9% of the time it was worse and that can mean a lot worse, but generally not lasting for more than a year.

From the chart above we can see that about 75% of the time there is positive growth in the stock market. Compare that to the chart near the bottom of the Japanese Nikkei over a similar period. It has had positive growth only about 35% of the time.

You can also look at the results for a day that was a historical high or low to determine whether the results for today look like previous highs or lows compared to medians and averages (two other Excel functions) of the available past results.

What do market bottoms look like?

Here is the result of my analysis of major falls in the market since 1984.

This chart is quite straight forward other than that I have assumed at present that we had a bottom on 9 August 2011. This is on the verge of being proven wrong as I write on 12 September.

The top section of the table shows the Average, Median, Minimum and Maximum of the results shown in the bottom half of the table.

The bottom half of the table shows the characteristics of a number of market bottoms. It can be seen that the market on 9 August 2011 was within the ranges of results that in the past have been a market bottom, but not at the extreme bottom of those ranges for the one and two year growth rates in particular.

Summarising the Outcomes.

The results of the various periods of growth (and moving averages) that I monitor can be summarised into a "dashboard" which shows both the percentages and the percentile of historical growth within which that percentage falls.

From the top half of the above Dashboard we can see that the market has virtually no evidence of an uptrend at present. All of the moving averages I monitor are pointing down (last 3 days total is less than previous 3 days total) and for all but 10/30 all moving average pairs/crosses indicate that the market is falling.

However from the middle of the dashboard we can see that the market is in the worst 20 percentiles of being:
1. Most oversold against 200 day sma
2 Having most negative growth in 2 months and
3. being most volatile (as it is during bear markets including around market bottoms).


Towards the bottom of the dashboard we can see the actual levels of growth over the periods I monitor, compare them to the median and see the percentiles within which todays results fall.

This analysis is subject to the usual caveat of the past not predicting the future. Also, given the size of the stock market boom to October 2007 and fall to March 2009 there is a chance that in future these curves will shift so that the types of negative growth now will be more common (ie in higher percentiles) as they are now in the Japanese market (which I have also analysed) because of the falls from the undoubted bubble top in 1990. Having said that, the odds of the market showing higher rates of growth in future would normally be regarded as quite strong, while the chances of significant further falls would be regarded as real but significantly less than the chances of rises.

If we look at a chart of 1 year growth from 1985 to 2010 we will see that more negative growth is quite rare and has not lasted all that long in the past.

Could this be a top?

We know that we are below April 2011 levels so it is not a top, but lets look at what markets tops look like in terms of growth. As you will see is that the current market does not look anything like any of our past market tops in terns of historical growth.

Since 1984 the market has never had a top without 2 Month and 1, 2 and 5 year growth being positive. Generally all periods show positive growth. At the present time, no period of growth is positive and all periods of growth are substantially below the median levels of past market tops. It doesn't look anything like a top.

What Strategy To Follow?

There is little point in buying when there is virtually no evidence of any sustained market upturn, even if the market is within a range often associated with market bottoms and with various growth periods being at relatively low percentiles.

My strategy is that now and lower provides a time of probable buying opportunity but there is no point buying a falling market. Work out what you will accept as signalling a likely/possible market uptrend and how to stage your commitment to that uptrend, but be prepared to cut positions in the case of any emerging uptrend being a bear market rally.

Two bits of folklore to remember in this regard are:
1. first loss is best loss
2. the (up)trend is your friend (until it ends).

This strategy is informed by the analysis and results of John Hussman. He was guided mainly by economic fundamentals and value compared to historical outcomes. This helped him identify the unsustainable high of the market in 2007. However he missed virtually all the 2009/early 2010 rally because he was unwilling to look at price trends and how low the growth percentiles were in historical terms.

A note about the Japanese experience.

Japan has three lessons for us. First, money can be made in a market post the bursting of a bubble if timing is good, which is why looking at the trends is important. Second, what appear to be lowish percentiles in a market characterised as a sustained bull market will be average percentiles in a post bubble market with tough demographics, which is why not getting too carried away based only on the percentiles is also important - wait for the emergence of a trend. Third, time in the market is not a guarantee of a positive return if you buy at an extreme market top, which October 2007 may have been.

We see from this chart both that the top growth percentiles are literally off the chart because of the extreme bubble of 1990 and that about 65% of the time each period of growth monitored had negative growth as a result of the protracted readjustment of the market from the 1990 bubble during which the Nikkei has fallen about 80% from its all time high.

Conclusion.

By looking at the percentiles resulting from a statistical analysis we can know whether we are buying near a possible top or bottom and tailor our risk management accordingly.

By looking at indicators of existing trends such as the direction or crosses/pairs of moving averages we can judge whether we would be buying/selling into an up/downtrend.

The goal of course is to buy near a bottom but only into what is likely to be an uptrend but to accept the possibility of whipsawing and losses through reversal of the trend.

We can reduce the risks of whipsawing by staging our commitment to a new up or down trend or, having bought near a very likely low based on our percentile analysis, we can choose to ride it out in the hope and with the likelihood that our losses will be smaller than most other investors and eliminated during the next uptrend.