Is it time to buy?

October 26, 2008

In this post I will look at whether times like these (when the market has fallen a lot) are good times to invest.

With the recent fall in market values, there are folks suggesting that right now is a good time to invest. There is equally a lot of fear among investors. Warren buffet summed it up well in his article. I want to know whether history suggests that there is anything to be gained from trying to time the market by buying after a fall.

I felt, as usual, that there is no substitute for getting my hands dirty in the data, so I did a little analysis. I tested how the distribution of returns on a S&P 500 investment made in months that follow a fall in the value of the index compare to investment made at any point in time – i.e. can the market be timed?

I have calculated the distribution of annualized returns for an investment in the S&P 500 made under four different scenarios:

  • Any month (baseline)
  • Any month where the current index value is 0%-10% down on the 12-month high
  • Any month where the current index value is 10%-20% down on the 12-month high
  • Any month where the current index value is 20%-50% down on the 12-month high

Note: this is not a 20/20-hindsight analysis. I have not looked back at the data and picked the ‘bottom of the market’ as the investing point. I have used only the data that one would have had available at the point that one made the investment.

Here’s what it looks like for a 5-year investment:

Timing a 5-year investment

Timing a 5-year investment

Your looking at four lines. The black one is the distribution of returns for an investment made at any point in time, the blue for investments made in months where the index value is down 0%-10% on the 12-month high, orange 10%-20% down, red 20%-50% down.  Here what I see:

  1. When the market is down 0% to 10%, its not worth trying to time a 5-year investment
  2. When the market is down 20% to 50%, a 5-year investment will get better returns than one invested at a random point in time, on average.
  3. When the market is down 20% to 50%, it is still possible (but not probable) to lose a lot of money on a 5-year investment. Look at the red bump at -10% – it is from the Great Depression!

What do you see? Are we looking at signal or noise?

I picked a 5-year investment to look at first because my last post suggested that 5 years isn’t really long enough to be confident of returns that out-perform some safer investment options.

Now let’s look at the 10, 20 and 30 year versions of this chart:

Timing a 10-year investment

Timing a 10-year investment

Timing a 20-year investment

Timing a 20-year investment

Timing a 30-year investment

Timing a 30-year investment

Looking at these three charts, I see two things:

  1. For 10-year investments, investing when the market is down 20% to 50% is probably going to produce better returns than a investment at a random point in time, but it’s a close call
  2. For 20-year and 30-year investment there is no significant advantage to investing when the market is down, even by 20% to 50%

What do you see?

So my conclusion *would* be that you can time the market for medium term investments (5-year and 10-year) but not for long term investments (20-year, 30-year). I say ‘would’ because I must caveat all this with the facts that: I’m nothing more than a dabbler at this; I’m probably missing something; if it were this straight forward then why hasn’t the market already self-adjusted for this fact? Then again, Buffett says buy now for the long term, but who amongst us actually is?

If I were to translate this into advice (which this is categorically not, since I am not an advisor) then it would be:

  1. If you’re looking to make a 20 or 30 year investment then JFDI, irrespective of the market conditions
  2. If you’re looking to make a 5 to 10 year investment and you really need the money at the end of that period (i.e. retirement) then be cautious of the S&P 500 overall (at any point in time) and be a little more bullish if you’re investing at a time when the index has seen a 20% to 50% fall in value

WARNING: Details

In this final section I shall deal with the methodology details , and show some charts for comparison to my previous post.

Overall there are three changes in methodology from my previous post, which I want to highlight and compare, so that you can see why these results are different from that post:

  1. The reinvestment of dividends to measure total return
  2. A different data source (now Shiller, previously Yahoo Finance)
  3. A different time range (now Jan 1871 – Jun 2008, previously Jan 1950 to Oct 2008)

1. Dividends

I calculated total return by reinvesting dividends on a monthly basis, as follows:

  • The dividend in month n is used to buy more units of the assett at the month-n price
  • The dividend in month n+1 is paid out on the number of units in month-n including the addition of the units bought with the dividend in month-n
  • The dividend reinvestment happens monthly,  using 1/12 of the annual dividend (the data set has a lot of interpolation in it anyhow)
  • No income tax is paid on the dividend, which would be true of a 401(k) or IRA, but generally not otherwise

The chart below show how the chart from the previous post would have looked with the reinvestment of dividends as detailed above:

Post 1 redux with dividend reinvestment

Results from my previous post redone with dividend reinvestment

2. Different Data Source

I used data provided by Robert Shiller, to whom I’m grateful – you can read about it here. The data has a monthly price and monthly dividend for the ‘S&P 500’ (proxy) from 1871 to June 2008.

I compared the two data sources to each other by repeating the analysis from my previous post  on the new data source. The results were only different in very very minor ways, so we can rest easy..

3. Different Time Range (now Jan 1871 – Jun 2008, previously Jan 1950 to Oct 2008)

The new data source adds data from the years 1871-1941, which is good not only because it increases sample size, but because it includes the Great Depression, to which current times are being compared. The results with these new years look different, but essential tell the same story as the last post – i.e. that a ‘long’ investment probably should 20 or 30 years.  The charts below show the  results from my previous post redone with dividend reinvestment and with the full range of data 1871-2008:

Results from my previous post redone with dividend reinvestment and the full range of data from 1871

Results from my previous post redone with dividend reinvestment and the full range of data from 1871

And for completeness, the chart below shows the results from my previous post redone without dividend reinvestment, but for the full range of data from 1871 to 2008.  Note that the returns look pretty dismal here, and there a good reason: In the years 1871 to 1950 the dividend yields were high (5%+), so by not including it in the calculation of the return,  the majority of the return is missing.

Results from previous post redone without dividend, but with full data range from 1871

Results from previous post redone without dividend, but with full data range from 1871


Distribution of 2010 Index of economic freedom

January 21, 2010

Distribution of scores. Y-axis shows nothing.

Sorry it’s not a histogram, I didnt have time.

There are 3 countries below 30, which are not shown on this chart (Cuba=26.7, zimbabwae=21.4, NKorea=1)

Full data is:

Hong Kong 89.7 Singapore 86.1 Australia 82.6 New Zealand 82.1 Ireland 81.3 Switzerland 81.1 Canada 80.4 United States 78.0 Denmark 77.9 Chile 77.2 United Kingdom 76.5 Mauritius 76.3 Bahrain 76.3 Luxembourg 75.4 Netherlands, The 75.0 Estonia 74.7 Finland 73.8 Iceland 73.7 Japan 72.9 Macau 72.5 Sweden 72.4 Austria 71.6 Germany 71.1 Cyprus 70.9 Saint Lucia 70.5 Georgia 70.4 Taiwan 70.4 Botswana 70.3 Lithuania 70.3 Belgium 70.1 Korea, Republic of 69.9 El Salvador 69.9 Uruguay 69.8 Czech Republic 69.8 Slovakia 69.7 Spain 69.6 Norway 69.4 Armenia 69.2 Qatar 69.0 Barbados 68.3 Mexico 68.3 Kuwait 67.7 Oman 67.7 Israel 67.7 Peru 67.6 United Arab Emirates 67.3 Bahamas, The 67.3 Malta 67.2 Saint Vincent and The Grenadines 66.9 Latvia 66.2 Hungary 66.1 Jordan 66.1 Albania 66.0 Costa Rica 65.9 Trinidad and Tobago 65.7 Macedonia 65.7 Jamaica 65.5 Colombia 65.5 Malaysia 64.8 Panama 64.8 Slovenia 64.7 Portugal 64.4 Romania 64.2 France 64.2 Saudi Arabia 64.1 Thailand 64.1 Turkey 63.8 Montenegro 63.6 Madagascar 63.2 Dominica 63.2 Poland 63.2 South Africa 62.8 Greece 62.7 Italy 62.7 Bulgaria 62.3 Uganda 62.2 Namibia 62.2 Cape Verde 61.8 Belize 61.5 Kyrgyz Republic 61.3 Paraguay 61.3 Kazakhstan 61.0 Guatemala 61.0 Samoa 60.4 Fiji 60.3 Dominican Republic 60.3 Ghana 60.2 Mongolia 60.0 Lebanon 59.5 Burkina Faso 59.4 Morocco 59.2 Croatia 59.2 Rwanda 59.1 Egypt 59.0 Tunisia 58.9 Azerbaijan 58.8 Tanzania 58.3 Nicaragua 58.3 Honduras 58.3 Zambia 58.0 Kenya 57.5 Swaziland 57.4 Bhutan 57.0 Serbia 56.9 Algeria 56.9 Nigeria 56.8 Cambodia 56.6 Vanuatu 56.4 Philippines, The 56.3 Bosnia and Herzegovina 56.2 Mozambique 56.0 Mali 55.6 Brazil 55.6 Indonesia 55.5 Benin 55.4 Gabon 55.4 Pakistan 55.2 Gambia, The 55.1 Senegal 54.6 Sri Lanka 54.6 Yemen 54.4 Malawi 54.1 Cote d’Ivoire 54.1 India 53.8 Moldova 53.7 Papua New Guinea 53.5 Tonga 53.4 Tajikistan 53.0 Niger 52.9 Nepal 52.7 Suriname 52.5 Cameroon 52.3 Mauritania 52.0 Guinea 51.8 Argentina 51.2 Ethiopia 51.2 Bangladesh 51.1 Laos 51.1 Djibouti 51.0 China, People’s Republic of 51.0 Haiti 50.8 Micronesia 50.6 Russia 50.3 Vietnam 49.8 Syria 49.4 Bolivia 49.4 Ecuador 49.3 Maldives 49.0 Sao Tome and Principe 48.8 Belarus 48.7 Equatorial Guinea 48.6 Central African Republic 48.4 Guyana 48.4 Angola 48.4 Lesotho 48.1 Seychelles 47.9 Sierra Leone 47.9 Uzbekistan 47.5 Chad 47.5 Burundi 47.5 Togo 47.1 Ukraine 46.4 Liberia 46.2 Timor-Leste 45.8 Comoros 44.9 Kiribati 43.7 Guinea – Bissau 43.6 Iran 43.4 Congo, Republic of 43.2 Solomon Islands 42.9 Turkmenistan 42.5 Congo, Democratic Republic of 41.4 Libya 40.2 Venezuela 37.1 Burma 36.7 Eritrea 35.3 Cuba 26.7 Zimbabwe 21.4 Korea, Democratic People’s Republic of 1.0

How long is a ‘long term invetsment’ ?

October 25, 2008

I’d been wandering for a while just how long a ‘long term investment’ is.  There’s lots of good stuff written on this, but for me there’s no substitute for getting my hands dirty in data.  So I dusted off Excel and took a look at the numbers. This analysis is not unique, I’m sure.  It’s probably not even entirely accurate. I’m looking forward to hearing about all the ways in which it is flawed, so that I can do v2.

Here are the results (click to get a good look). The method, and a little analysis of the results, are below.

You’re looking at 6 different lines, one for each different ‘investment length’. For example, the blue line shows the distribution of returns on a 1 year investment in the S&P500, taken over all the possible 1 year periods that occurred between Jan 1950 and Oct 2008. The orange line show the distribution of returns on a 30 year investment, which as you’d expect, is much tighter.

A few things stand out for me:

  1. Five years is not a ‘long term investment’, unless you’re willing to accept a fair chance (~25%) of performing at (or well under) a savings account like return (~4%)
  2. Even at twenty years, there is a ~20% chance of getting a return between 2% and 4%, which would be a bit disappointing as an investor, IMO.
  3. Based on the last 58 years of data, it looks like 30 years could be considered ‘long’ (but remember what they say about past performance)

Disclaimer: I’m really not any sort of an expert at this. This is 30 minutes in Excel with data from Yahoo Finance. There are a million nuances that I’m missing.

Of course, this is for investing a lump sum of money at one point in time. Most consumers would actually invest continually over a long period of time, which creates a dollar-cost-averaging effect. Maybe I’ll look at that next..

What does this chart say to you? Let me know in the comments.


I calculated the annualized return by dividing ‘month A closing price’ by ‘month B closing price’. I then raised that number to the power of 1 over the number of years between month A and month B. I then subtracted 1. I then measured frequency of that return by counting the number of occurrences of the return in buckets 2% wide (i.e. count x where: 2%<x<=4%), and dividing by the total number of periods of that length in the test (shown as ‘n’ in the legend). I then plotted the mid-point of that bucket (i.e. 3%) on the horizontal axis, and the corresponding frequency on the vertical axis.

I’m looking forward to hearing your thoughts, and suggestions for v2.