Diversifying your portfolio reduces volatility and improves compound average returns. Portfolio theorists dream of finding risky asset classes with low correlation to known risky asset classes. However, author William J. Bernstein argues that correlations between asset classes have been rising. He explains why this is so in his book Skating Where the Puck Was: The Correlation Game in a Flat World , the second book of his four part Investing for Adults series. One of the side effects of rising correlations is that everything tends to crash at once. We are moving toward “a cohort of nearly identically behaving asset class drones.” “When everyone owns the same set of risky asset classes, the correlations among them will trend inevitably toward 1.0.” Bernstein asks “Will things really get that bad?” The surprising answer is “We are, in fact, already there; further, it’s always been that bad. Yes, international REITs were a wonderful diversifying asset, but the ordinary globally...

We tend to look at investment returns one year at a time. Most investment models treat each year’s returns as independent of previous years. But this isn’t actually true. A decade of returns in the real world doesn’t look the same as 10 independent single years strung together. Here I look at 10- and 20-year returns of different stock/bond mixes based on historical data. As usual, it is easiest to get U.S. returns data. I found S&P 500 returns and 10-year Treasury bond returns from 1928 to 2013 at NYU Stern . I got historical CPI figures from Robert Shiller . This gave me 86 years of U.S. stock and bond real (inflation-adjusted) returns. From these returns I created 5 portfolios with different stock/bond mixes: 0/100, 25/75, 50/50, 75/25, and 100/0. With the mixed portfolios, I rebalanced to the target percentages once per year. Then I calculated rolling 10- and 20-year returns. For each period, I calculated the compounded average annual real return. Everything I’ve...

It is well-known that stock returns do not follow the normal distribution that is commonly used to analyze returns. Less well known is that the returns from one year to the next are not independent; there are small correlations. A consequence of these correlations is that the riskiness of stocks grows slower than simple models predict. Jeremy Siegel made this observation in his book Stocks for the Long Run . I found this result so remarkable that I decided to investigate myself. I grabbed Robert Shiller’s historical U.S. stock returns and made some calculations. Over the past 100 years, U.S. stock market returns have had a standard deviation of 19.0%. If the returns of each year were independent of each other, we’d expect this standard deviation to grow by the square root of the number of years. So, after 25 years, we expect the standard deviation of total returns to be 5 times higher, or 95%*. For each time period from 1 to 40 years, I calculated the standard deviation o...

There is no shortage of advice out there on how to find the right balance between the asset allocation that makes people comfortable (low volatility, but low return), and the asset allocation that makes people money (high return, but high volatility). I’m going to suggest a possible different approach for novice investors. Disclaimer: I do not recommend the following strategy in any way. These are just ideas to chew on. Think for yourself. Because high returns and high volatility go hand-in-hand, we’re advised to seek the most risk we can handle while still able to stick to an investment plan and sleep well at night. The most nervous investors end up with low returns either because they have few risky investments or because they bail out of their risky investments at the worst possible time. Even not so nervous investors can have these types of problems. Toss in some unreasonably high mutual fund MERs, and the end result is that their long-term savings grow to less than ha...

Long-time reader, Gene, asked the following good question. “Have you considered making a pseudo index fund by buying perhaps 15 large-cap stocks from each of Canada and the USA that would mimic an index? Not ideal for a growing portfolio, but for a relatively-stable account, and low commissions, it could save money on fees. Drawbacks are that it would be harder to increase or decrease holdings, and the savings wouldn't be huge over already inexpensive ETFs.” Gene is right that a carefully-run stable portfolio of stocks can cost less in fees than index ETFs. However, an important issue is how well such a portfolio would track its index. For an answer here, I turn to Meir Statman’s paper How Many Stocks Make a Diversified Portfolio ? Table 1 of this paper shows how the standard deviation of portfolios varies with the number of stocks you own. At this point, I need to diverge to a topic that few investors understand well: volatility losses. Consider a very simple example. In...

Few investors understand how volatility in investment returns costs them real money. I did some simulations to try to explain where the lost money goes. In the hypothetical land of Volatilia, half of stocks return -70% each year and the other half return +80%. The problem for investors is that which stocks get each return changes randomly from year to year. There are a million active investors who each pick one stock every year and pile all of their savings into it. There are another million investors who use an index fund that owns all stocks in equal dollar amounts. Assuming that all investors add $5000 per year to their savings, each index investor will end up with $634,200 after 40 years. Mathematically inclined readers will realize that the active investors will end up with the same average result, but there will be winners and losers. On the surface, it seems like there is no real cost to trying the active route. You could end up with more money or less money, but the...

Dan Hallett accused mutual fund critics of missing the big picture when they focus their criticism on high MER costs. His main point is not so much that MERs are not a problem but that there are other important ways that investors lose money. He claims that one of these ways that investors lose money is due to a volatility drag that comes with periodic investments or dollar-cost averaging (DCA). I’ve done a couple of experiments and can’t find any evidence that this volatility drag exists. In fact, DCA has a slight edge over lump-sum investing. Hallett explains volatility drag as follows: “You’ve no doubt scratched your head at why a portfolio’s long-term performance hasn’t quite lived up to expectations. It’s likely that volatility drag is one of the big culprits. ... If a mutual fund reports a 7 percent 10-year rate of return, for example, the only way to have achieved that precise result was to invest at the beginning of that period, hold for the full decade and have no buy...

Nassim Taleb gets much credit for popularizing the idea that big economic events, so-called “black swans,” occur more frequently than standard economic theory predicts. The initial work was actually done by the “father of fractals,” Benoit Mandelbrot . Physicists have studied detailed market data and have now concluded that Mandelbrot was right .   The bigger the market move we contemplate, the lower the chances that it will happen. However, these probabilities shrink much more slowly than standard economic theory predicts. In standard economic theory based on the normal distribution, if a move has a 1 in 1000 chance of happening, a move twice as large has less than a 1 in a billion chance of happening. In Mandelbrot’s model as confirmed by the physicists, the bigger move has about a 1 in 8000 chance; each doubling in move size reduces the odds by 8 times. For conditions of low market volatility, standard theory and Mandelbrot’s model agree fairly well, but when it comes t...

Most commentators agree that the stock portion of our portfolios should consist of many stocks in order to reduce volatility. Where they disagree is on how many stocks are needed to be adequately diversified. Over the years, the trend has been for the recommended minimum number of stocks to rise. I have an explanation for this trend. In 2009 Tom Bradley wrote "While a portfolio of 20 stocks and a few government bonds were just fine for our parents a generation ago, it’s probably not enough today." Why would the minimum number of stocks we should own change over time? With each stock you add to a portfolio, the volatility tends to decrease. However, the amount of benefit drops off as the number of stocks rises. Adding a second stock gives a big reduction in volatility, but adding a 101st stock doesn't reduce volatility much. For indexers, there is no such thing as too much diversification as long as the cost of ownership (fund MERs) stays low. So, an index in...

A reader, Seth, asked the following question about taking a bearish position in the market: “I read your article on leaky leveraged ETFs . I have invested less in these products in the volatile markets. Other than put options or shorting a stock like the SPY (risk of call back and paying out dividend disbursements), do you know of other ways to take a bearish position on the indexes? Are all bear ETFs calculated on compounded daily percent?” There are other ways to bet against the market, including selling call options and investing in bear funds, but I can’t recommend them. Selling naked calls on the hunch that the market may be going down can lead to big losses if you’re wrong, and the various bear funds don’t perform well on average through all types of markets. All the bear ETFs I’ve looked at rebalance daily and suffer from volatility losses. The bear funds I’ve seen try to make money by picking individual stocks that they expect to drop in price. These funds don’t reba...

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. In a previous post, I showed how the average real return in the U.S. stock market from 1926 to 2000 is 9.3%, but that this translated into a compounded real return of only 7.4% . The reason for this difference is the volatility of the returns. Let’s go for a better understanding of the cost of volatility without any advanced math. A Simple Example Suppose that you have $10,000 invested for two years. In the first year you lose 10%, and the next year you make 10%. It might seem at first that you have your $10,000 back, but that isn’t exactly right. After the first year you were down to $9000, and then in the second year you earned 10% on that $9000 to get a total of $9900. In the end you lost 1% of your money. However, the annual returns were -10% and +10% for an average return of 0%. The lost 1% over the two years is not due to a negative e...

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. When giving out investing advice, many authors report long-term average stock returns, but the numbers seem to differ from one author to the next. Surely, we have lived only one history. Some differences can be explained by the authors studying different time periods or different baskets of stocks. However, there is another reason for differences that relates to how the average is calculated. In Chapter 6 of Worry-Free Investing , Zvi Bodie and Michael Clowes discuss U.S. stock returns from 1926 to 2000. They give real returns , which means the returns after inflation is subtracted out. Based on the historical data, they calculate the average yearly real return on stocks to be 9.3%. But, others say that the long-term real return on U.S. stocks is 7%. This may not look like a big difference, but if you play around with one of the many free reti...

For investors who can’t stomach the volatility of investing 100% of their long-term savings in stocks, the usual advice is to put some fraction of savings into fixed income investments. Another approach is to use stock options to protect against large losses. Suppose that an investor Irene has $100,000 that she wishes to invest mostly in large U.S. stocks, but is nervous about losing money. One approach for Irene is to just put all of her savings into the S&P 500 (which is sitting at 900.80 as I write this) and live with the volatility. The following chart shows the returns for Irene across a range of possible outcomes in the S&P 500. We’ll focus on her results as of June 2010, a little over a year from now. It’s the lower left hand corner of this chart that worries Irene. The thought of losing that much money is scary. One solution is for Irene to put some money (say 30%) into fixed-income investments. The following chart compares the all-stock approach to the 70...

The Million Dollar Journey had an article yesterday about Horizons BetaPro ETFs. These Exchange-Traded Funds (ETFs) are designed to give investors double exposure to certain indexes. This means that if you are invested in their S&P/TSX 60 ETF and the index goes up by 1% one day, the ETF should go up by 2%. They also offer a bear version of each ETF where a 1% rise in the index gives a 2% drop in the bear ETF. Obviously, the owners of the bear ETFs are hoping for the index to drop. Let’s focus on the ETF based on the S&P/TSX 60 index, which is based on the biggest companies in Canada. If the TSX 60 goes up by 10% one year, you’d expect the corresponding Horizons BetaPro ETF (ticker symbol HXU) to go up by 20% that year. But, that’s not how it works. For example, in its first year, HXU returned 13.28% and the TSX 60 rose 9.19%. If we double the TSX 60 return, we find that there is a 5.1% gap. What causes this 5.1% gap? I tried reading the prospectus, but like most such do...

It’s hard to see the steady rise of the stock market on a day-to-day basis because of the volatility of prices. Whether you focus on the long-term increase in prices or the short-term volatility determines whether you are an investor or a trader. Let’s suppose that the stock market is expected to rise 10% per year with volatility of 20%. The volatility (or standard deviation) has a precise mathematical meaning, but let’s just say that it creates a return range of 10% plus or minus 20%, or from -10% to +30%. In most years the market return will be in this range. Because there are about 250 trading days per year, you’d think that we could divide these numbers by 250 to get a range for each day of -0.04% to +0.12%, but volatility doesn’t work this way. From experience we know that daily market movements are very often outside this range. The problem with this thinking is that volatility partially cancels out over time. A big rise followed by a big drop may leave the stock price unchanged....

Most commentators agree that we should include some bonds in our long-term investments. My quest for a reasonable analysis to support this conclusion continues. Previously, I have discussed the ideas of Gordon Pape and Morningstar on this subject. I’m starting to feel like I’m in some sort of boxing match. So, let’s do it right: “In this corner ... Roger C. Gibson, esteemed author of ‘Asset Allocation: Balancing Financial Risk’ now in its fourth edition. He’s a well-respected expert whose ideas have been endorsed by Sir John M. Templeton and Don Philips, Managing Director, Morningstar.” “And in this corner ... some guy who figured out how to use Blogger.” Oh well. I lose on the credibility meter. My only chance is that people actually think about the arguments. Gibson does an impressive amount of analysis and explains many important concepts clearly. When it finally comes time to figure out an optimal asset allocation, he tosses in an interesting assumption about our tolera...

Here is a bonus post today in case you’re not following the book review. Your reaction to a game show scenario can reveal important information about your attitudes as an investor. It can even tell you what mix of investments are appropriate for your portfolio. Let’s get right to it. You are playing Deal or No Deal and you are down to two amounts: one penny and a million dollars! What is the minimum offer you would accept from the banker? For those not familiar with this game show, here is the situation. You are about to toss a coin. If it comes up tails, you get nothing (and lose nothing). If it comes up heads, you get a million dollars. Just before you toss, someone offers you a sum of money to give up your chance to toss for the million dollars. What is the minimum such offer you would accept? It turns out that your answer depends on how rich you are. Bill Gates would likely accept an offer of half a million dollars, but not much less. However, someone in a despera...

In a previous post , I showed how the average real return in the US stock market from 1926 to 2000 is 9.3%, but that this translated into a compounded real return of only 7.4%. The reason for this difference is the volatility of the returns. Let’s go for a better understanding of the cost of volatility without any advanced math. A Simple Example Suppose that you have $10,000 invested for two years. In the first year you lose 10%, and the next year you make 10%. It might seem at first that you have your $10,000 back, but that isn’t exactly right. After the first year you were down to $9000, and then in the second year you earned 10% on that $9000 to get a total of $9900. In the end you lost 1% of your money. However, the annual returns were -10% and +10% for an average return of 0%. The lost 1% over the two years is not due to a negative expected return; it is due to the volatility of the returns. The average return is 0%, but the compounded return is about -0.5% per year. Anoth...