###### CERF Blog

It is well known that one really good way to get extremely rich is to hold a large concentrated position, often as the founder, in the stock of a company that realizes extraordinary success. Another way, generally viewed to be less reliable, is to win the lottery. In a very interesting research report, finance professor Hendrik Bessembinder argues that these two paths are actually very similar. Professor Bessembinder collected data on monthly rates of return on every stock that has traded on an American stock exchange any time over the last 90 years. The total number of such stocks is 25,782 and the total number of monthly observations is 3.52 million (note that very few companies were around for the full 1,080 month period, so that the total number of observation is much smaller than 1,080 times 25,782).

While the average monthly real return is positive, the median return is negative. That is, more often than not, the real monthly return on an individual stock is less than zero. The reason the average is positive is that sometimes there is a large gain (in statistical parlance, the distribution has a positive skew). Stock picking, like playing the lottery, involves lots of small losses and an occasional large gain. This skew holds both for monthly returns and compounded longer-term returns. In fact, the lifetime real return for most companies is negative.

Another result reported by the professor is that the entire cumulative wealth generated by the stock market over the past ninety years, $31.5 trillion, was generated by just 4% of the companies. Thus, if you adopt a strategy of picking individual stocks, you have to be really good to be successful, because only a small fraction of stocks are likely to turn out to be big winners.

I think the main implication of this research, and certainly the author’s main conclusion, is that investors should maximize the diversification in their portfolios. One reason is that diversification reduces the volatility or risk of a portfolio. A second reason, highlighted by this research, is that broad diversification increases the probability that your portfolio will contain at least one or more of the winning companies.

Given that he examined perhaps the most comprehensive data set available on individual stock returns, it is interesting to consider what the professor’s results say about the distribution of stock prices and returns. Surprisingly, the answer is “not much.”

The standard academic assumption is that the natural logarithm of the stock price is normally distributed (this means that the stock price itself is lognormal). Many people have noted that assumption cannot be correct, at least not for daily price moves. The reason is that every once in a while, every few hundred or thousand trading days, there is a very large movement in a stock price, much greater than could occur under the normal distribution. This is the proverbial “ten standard deviation” event. Thus, many sceptics argue that the “true” distribution for stock prices and returns has much fatter tails than the normal.

Unfortunately, the professor’s results don’t shed much light on this issue. His major finding is that stock return distributions are positively skewed, with the degree of skew higher for longer compounding periods and greater volatility. This finding does not imply non-normality; in fact, it arises even if the monthly return distribution is normal (and therefore with zero skew)! To illustrate how this can be, the professor assumes a normal distribution for the monthly return and considers drawing randomly from this distribution and computing compounded returns. He assumes a monthly mean return of 0.8% and various levels of monthly volatility. He considers a range of investment horizons from one year to ten years.

For single stock portfolios, the historical average monthly volatility is about 18%. The simulated results using 18% monthly volatility show only 24% of ten-year returns are positive. The historical average monthly volatility for well-diversified portfolios is more like 6%. The simulated results using 6% volatility show that 72% of returns are positive.

The simulated results broadly mimic the historical data. Both individual stocks and diversified portfolios exhibit positive skew that increases with the compounding period. However, this skew is much greater for individual stocks than for broad market portfolios. This is due to much greater volatility for individual stocks. Individual stocks have a large chance of a negative return, over any compounding period. The key point is that well-diversified portfolios have less volatility and a much greater chance of a positive long-term return. Individual stock picking is playing a lottery, investing in diversified portfolios is not.