Lies, Damned Lies and Percentages

The Mystery of Percentages

Here's a simple warm-up question: you invest $100 in a stock which then rises 20% followed by a drop of 20%. How much is it now worth?

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It's OK, I will give the answer but it really is worth having a stab at your first intuitive response!

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When I used to give a similar question to my students many would smugly blurt out the wrong answer, whereas others were more wary and distrusted such a simple question, rightly suspecting there was a trap lurking in there.

There isn't actually a trap as such, but a realisation that percentages do not work like natural numbers. Percentages are not additive - a 10% rise followed by another 10% rise does not equal 20%. Percentages are multiplicative - this is the reason for the counter-intuitive power of compounding interest in a deposit account, as well as the devastating effect on wealth of long-term inflation. It is this constant battle between these two percentages that can result in voracious greed as everyone wants to beat the market, to make a real positive return on investments.

I cannot hold off answering the initial teaser. A 20% profit would make the initial $100 rise to $120 but then the 20% loss is 20% of the new $120 (not the original $100), which is $24 so that the final total is just $96 - a loss of 4%. We would also get the same result if we had a 20% drop first followed by a rise.

We can now also answer the question in the previous paragraph. A 10% increase will take the total to $110 with a further 10% on the new total bringing the compound interest to $21 and the grand total to $121.

I write about this not to share a lesson in elementary percentages but because in the current situation of volatile stock markets and interest rates a true grasp of percentages will help you ignore some of the more damaging advice meted out by financial advisers and websites.

If we take a working definition of a bear market as a drop of at least 20% from its peak - and therefore the opposite bull market as the mirror image rise of 20% from its bottom - then we can now see that even when we get the bulls waving their flags the market will still be below what it was before the current bear market. And as the percentage swings get larger so does the difference between the false arithmetic adding of percentages and the true multiplication. The US markets are now below 50% from their peaks and such a drop followed by a subsequent 50% rise will leave the markets still losing 25% of their value. A 50% drop requires a 100% rise to get back to par.

Notice here that a 50% rise would be considered a very bullish rally and yet we would still be in bear market territory based on the previous high. Bulls and bears are not absolute positions but are relative descriptions based on the trend from the last turning point. Statistics may lie but so can percentages in the hands of financial pundits desperate for investors.

What do a bull and bear market actually mean?

If you haven't heard the terms bull market and bear market being used then you obviously have never seen or read the financial press. But what do these words really mean?

Astonishingly for such common words they don't actually have any well-defined meanings. A quick search yields a lot of useless dictionary definitions but nothing quantitative. Yes, a bull market is one that is in an upward trend, with a bear market being the opposite. But that seems to be it; purely qualitative definitions. We must be able to do better than this!

According to The Vanguard Group, "While there’s no agreed-upon definition of a bear market, one generally accepted measure is a price decline of 20% or more over at least a two-month period." Indeed that 20% drop from its peak was the definition used on most financial news media as the current markets dropped precipitously. However, Ultra Financial Systems defines it "as a market that loses 15% as measured by a stock market index such as the Standard and Poor's 500 Index (S&P 500) which consists of the stock prices of 500 U.S. corporations." And About.com has this to say on the topic: "A common rule of thumb states that if the market is down 10%, it's a Market Correction, and if it's down 20%, it's a Bear Market. While common, it's not very useful. There is a better way." The site then goes on to list some 12 factors that will help you determine what's going on in the stock market.

So, it seems as if a bear market can be defined by many different parameters, the only thing in common is that prices are heading down. But percentages can give an illusory feeling of what a market is really doing. For example, a 20% drop followed by a 20% rise in no way takes us back to the original peak but rather at 96%, so with another 4% to make up to reach parity. As the percentage swings get bigger the
difference between such peak-to-peak values grows alarmingly - a 50% drop in a stock price followed by a 50% rally will bring the price up to just 75% of the original peak. Indeed a 50% drop in price then requires a 100% increase from this low just to break even. What this means is that our bear or bull markets have to be taken within the context of where we are measuring from.

A bull market that follows a bear market could still be showing a loss compared to that market's previous high. If we take a 20% drop from a high as the start of a bear market then, by symmetry, we should take a 20% rise from its low as the start of a bull market. But as we have shown above, this seems more a matter of semantics than hard mathematics. If a $100 stock drops 50% to a low of $50 and then rallies 20% to $60 then that $60 mark signals the start of a bull market from its low, but as we can see, we are still showing a $40 loss.

So the first lesson is that a bull or bear market is a description that is relative to the last high or last low of the market in question. A new bull market will take a long time to reach a new high compared to the 2007 level. But I think from an investing perspective we can improve on the above definitions. The easiest and best long term indicator is the 200-day moving average on a daily price chart. I have discussed this before but here wish to show how it too can define the current bear market, and it can also be used to define the next bull market.

Any important indicator, whether it is the 200DMA or the 20% market swing level, will show increased volatility at that level as the market participants struggle to figure out if the level will hold or be breeched. These indicators are therefore not precise numbers but have a fuzzy edge to them. As the Vanguard definition warns, their 20% level needs to be broken for "at least a two month period". For an investor, waiting 2 months for confirmation is a long time to be sitting there losing money. The advantage of the 200DMA is that the investor can slowly start to take profits and limit exposure to a bear market.

Taking last Friday's closing prices the S&P 500 was at 756.55 (S&P 500 chart). It's recent low was last Monday, touching 666.79. In just five days this is an increase of 89.76 points, equivalent to 13.5%. A 20% rise would take the S&P 500 to 800. Could we call that the start of a new bull market? In contrast, the 200DMA stands at about 1045, still about 300 points away from the index level and equivalent to a 57% rise from Monday's low. Historically, the 200DMA has been far better for the investor than a random 20% level. When the S&P took a dive last January and all the talk was of a bear market the 200DMA had already been broken during both November and December. The final proof that the market needed oxygen was in May 2009 when the 200DMA proved to be too high to scale and we are now at half of that level - that's half of the May 2009 peak, not the October 2007 all-time high.

The ideas behind bull and bear markets are that they should have long term secular meanings and not be short term indicators to sucker people into buying stocks. They are indicators of trends and not absolute levels. Indeed, the financial press have spectacularly failed to protect investors and report the gravity of this bear market. I expect the corporate news media to start effervescing as we reach the 800 level. Switch them off and just follow the numbers.

Market Noise - 6 March 2009

Market Noise are bookmarks and links to finance and investment stories that I have found interesting or that have warranted a brief comment but have not been expanded to full articles. Market Noise will be a weekly blog post updated as and when I find interesting news.

The Bear Market End is Near... Maybe. Another newsletter sees the end of the pain soon... but perhaps not till the end of 2011!

When to Really Start Buying Stocks and Shares Again

On an almost daily basis some financial website has an article entitled something like “Is it Time to Buy Stocks?” In these times of distress everyone wants to be in at the bottom. But for the investor who has traditionally trusted in managed funds and has little experience in managing his own portfolio this is a highly dangerous strategy. There is a strong case for ignoring all these articles and just looking at the numbers.

This is really written for those people who think that financial markets are complicated and that the whole thing is best left to professionals. The recent fall in global stock markets should have at least made you think that these experts are not really so professional after all. Indeed, for many of them their profits take precedence over yours. Their annual fees are earned whether the fund does well or not. Yes, a well-run highly profitable fund will gain new investors and thereby start on a round of positive feedback. But the art of finding such funds is actually the same as I will describe below.

For those investors with more experience, the thrill and profits from trying to pick the bottom of a market is a genuine driving force. I wish them luck but, as I say above, this isn't primarily written for them. For those who have dutifully put their savings into some kind of investment vehicle and seen those savings dwindle the idea of going it alone can seem daunting. But, I wonder how you initially chose which funds to invest in? Was it from a recommendation from a financial adviser, possibly from your bank or insurance company? There must have been some decision taken right at the beginning. However, since then you have probably lived in the hope that the fund managers know what they are doing.

The point I would like to make is that the transition from a passive investor to an active investor is not so daunting. You don't have to become a trader, watching the markets every day and buying and selling stocks in a frantic attempt to make some profits before the market turns again. I understand that you don't have the time or the inclination to do this, and that as you haven't this would be even more dangerous than doing nothing. But having a look at your portfolio once a week, or even just once a month, is not so much work considering it is after all your money. More importantly, have a look at the charts for each investment. If a page full of numbers makes your head spin then a chart will give you all the information you need to see at a glance if the price is going up or down.

This is where I'd like to introduce one of the most widely used long-term price indicators. Staring at charts of stock prices still won't tell you the future or when to buy or sell. However, adding one simple indicator will make this much clearer. Before doing so let's pull up a chart. There are many websites with financial charts but one of the easiest and free to use is on Yahoo Finance. Just go there and you will see a snapshot of the major stock markets in the world. For the purposes of our example, click on the link to the S&P 500. What I'm about to go through can be used for any stock or share, commodity, investment fund or stock market.

On the main S&P 500 page you will see some basic information about the current day's trading and some news links. What we're really interested in is the chart, so click on that. I think the easiest chart to use at the start is the Basic Tech Analysis one so just click that – the link is on the left column. Along the top row you will see Range and Type options. I actually prefer to look at the candle-stick charts rather than the plain line ones as they also give a sense of the price volatility. So click on Candle in the Type list and you will see the difference. Now let's look at a meaningful range; click on the 1-year chart under Range. Looks ugly, doesn't it! But what is it going to do next? Is it going to take another dive below 800 or hold its nerve and climb back to 1000? None of us knows. Indeed, nobody knows and nobody can tell you for sure. The question “Where is the stockmarket going?” makes work for a lot of writers and pundits but is a question best left for dinner parties and fortune tellers. What you want to know is not what it is going to do but what is it doing right now. The one thing to guide you in your decision to buy or sell is what is the current trend.

To see what the trend is we shall now overlay our first technical indicator – the 200 Day Moving Average. On your chart options you will see one labelled Moving Avg; just click on the 200. You will see a smooth line overlaid on the price chart. This is the running average of the closing prices of the previous 200 days (or 40 weeks). It is one of the primary indicators used by chartists, people who use technical chart analysis on a daily basis. Charts cannot predict the future but they do show the current trend. It will be no surprise to see that the SP500 is currently well below the 200DMA as we are, after all, in a bear market. This is our first clue that it is no time to start buying any stocks at all! As I said before, some of you will get excited by the thought of buying stocks at fire-sale prices but I'm pitching this at those who perhaps have never considered even looking at a technical indicator.

Before we move on, just a few words about using this and other moving averages. The 200-day moving average is used by many as a medium to long-term indicator, showing the trend for possibly one to two years, often longer. It is not in itself a magic wand that will land you untold riches but it is an industry standard. This means that market traders will use this to decide on whether stock prices have finished their current trend and are due for a reversal of fortunes. The fact that so many insiders use this and react to it is one reason why it still works. But unlike secret trading programs this is all in the public domain – you too can profit from it. As you can see, venturing into the world of technical analysis sounds all rather complicated but we haven't even looked at a single equation. It just really isn't that scary.

Right, let's get back to our SP500 chart and zoom out to a 5-year view. Now, looking at a 5 year chart defaults to giving weekly prices rather than daily. On their fully interactive chart you can get a finer view by seeing daily prices for the 5 years. It isn't any more complicated but just has drop-down menus rather than simple clickable links. Anyway, on this particular chart we can see the stockmarket rising from 2004 till the end of 2008. Note how the 200DMA sits below the market during a rally. Also note that the market will sometimes drop down to touch the indicator then bounce off it. In this phase the moving average is known as a support. But look at what happened in the second half of 2007 and especially in January 2008. It looked initially as if this was going to be another bounce off its support but the tumble in January and the failure to break back up above the 200DMA was a dramatic signal that something was very wrong. Those dips below the moving average were signals to start selling. Not all at once, but slowly and with a wary eye if stocks fell further. In May 2008 the S&P 500 tried to rally back up but by now our 200DMA was no longer a support but a resistance level. The failure to break up above this in June 2008 was also another major selling signal. Coming to the present, we see that the S&P 500 is well below its 200DMA and we are well and truly in a bear market. At some point it will rise to meet its 200-day moving average. That could be a few months way, possibly many months away.

As an investor and not a trader you have to think long term and the 200-day moving average is the perfect long-term indicator. Amid the noise and confusion of financial advice you now have one solid technical indicator that gives you a decision making tool independent of personal advice. The 200DMA is not an on-off switch but rather a smooth transition which either confirms the existing trend or starts a reversal of it. As your stock or share or fund starts to approach this moving average is when you should start to be thinking about being active. Back in late 2007 you would have started to sell slowly. There is no shame in selling some stock one month only to buy it back 3 months later at about the same price. These things happen. In January 2008 was a signal to sell some more. And if you were still holding on to all your shares then May 2008 gave you another opportunity to start cashing in the profits of the previous 10 years or so.

For the casual informed investor the 200-day moving average gives a simple indication as to whether we are in a bull or bear market, whether to buy more stocks or sell them. If you are setting aside regular money then there is the temptation to want to invest it immediately. The very simple rule here, with which you won't go far wrong, is that if the price is above the 200DMA then it is safe to buy and if it is below it then it is safe to sell. We have been looking at one particular stockmarket but the technique will work with individual shares and investment funds. Even in a bear market there are some companies that do very well. If you read a recommendation to buy a particular stock then just repeat the above exercise. Yahoo Finance also has charts of all the major stocks and shares. I think this is enough advice for now! I will look at some of the finer points of using this indicator in a future post.

For now, buy stocks if you enjoy gambling!

originally posted on 19 Jan 2009 at Soul Trader Blues.

Markets Hit 12-Year Low - How Significant is this for Stocks?

Markets Hit 12-year Low for only the Third time, but will this be 1974 or 1932?

With US indices breeching their 12-year lows financial journalists and analysts have been reaching for their history books. A long term chart of the Dow reveals that only twice before has the index wiped out 12 years of gains; back in 1974 and 1932.

As everyone in the financial industry is praying that investors will return to the market the focus has been on calculating if these previous retracements can tell us anything about when we are likely to hit this bear market's low. In short, when will this pain end?

"What we found intriguing is that the 12-year lows were breached at a critical juncture in the bear markets," JPMorgan Chase equity analysts gush. In 1932 the April 8 finish came three months before the market hit its bottom, while 42 years later, the Dec. 6 breach marked the exact end of the 1974 low.

So there you have it! The equity pain will - or rather might - be all over within 3 months. Except that having just two data points does not fill me with the same overwhelming confidence as self-interested parties such as JPMorgan Chase. This strikes me as a slightly more sophisticated version of "when is it time to buy shares?" articles.

It is also worth stepping outside the purely US markets, this is after all a global marketplace. The most depressing index by far is surely the Japanese Nikkei. Peaking at around 39,000 in 1990 it now languishes around 7,500: that is a loss of over 80% over a period of almost 20 years and is currently sitting at a level seen in 1981. The "12-year low" is, at least for the Nikkei, a complete irrelevance.

However, stock market indices are all denominated in their local national currency so to accurately compare indices one has to do so using a fixed currency. In 1990 the US Dollar was worth about 140 Japanese Yen; in 2008 the average was about 100 Yen, a loss of about 30%. This is a good time to recall that percentages are multiplicative and not additive. An 80% drop in the index combined with a 30% rise in the currency does not equal an overall drop of 50%, but more like a 74% drop in dollar terms. Even with this adjustment the Nikkei looks in very bad shape.

The fear is that the American and European markets will follow the Japanese, in which case this 12-year low will be consigned to the dustbin of false indicators.