From Chapter 10: Raddr 3, Gummy 2, Bogle 0?
Posted: Sun Jun 06, 2004 9:20 am
Chapter 10 was John Bogle's discussion On Reversion to the Mean. I had looked forward to reading it and, unfortunately, built up my expectations much too high. The reason that I put the question mark after Bogle's score is that he did draw attention to the Fundamental Return of stocks.
You can visit Gummy's site or look at his CD to learn about the details of the Dividend Discount Model and its adaptations, such as the Gordon equation.
Assume that an investment produces dividends grows at a steady rate and that the price that people are willing to pay for the (current) value of that income stream remains steady.
Then, approximately, the price paid for a particular investment will grow at a rate = the initial dividend yield + the growth rate of the dividends.
If the payout ratio of dividends remains constant, the growth rate of dividends and earnings are exactly the same. If the payout ratio varies slowly, the growth rate of dividends is approximately the same as the growth rate of earnings, but not exactly the same. If the payout ratio varies slowly, a reduction in the payout ratio will increase the retained earnings and will tend (or, at least, should tend) to result in the faster growth of earnings. The net effect, ideally, is that the dividend growth rate increases (at least, partially), which offsets (to some extent) the effect of the reduction in the payout ratio. [I know of no convincing set of assumptions that would cause everything to end up being exactly the same mathematically.]
Because (real) earnings growth rate (with earnings averaged over 5 to 10 years) has been well behaved while the (real) dividend growth rate has been erratic, the equation for price growth is frequently written as:
The price paid for a particular investment will grow at a rate = the initial dividend yield + the growth rate of the earnings.
John Bogle refers to this as the Fundamental Return of stocks. He adds a speculative term because people are willing to pay different prices at different times for the same stream of income. He approximates the effect by using the price to earnings ratio (P/E) at the beginning and at the end of a period.
In its final form, John Bogle presents his mathematical model of the total return from stocks as:
The total return of stocks = the initial dividend yield + the growth rate of the earnings + the speculative return = the Fundamental Return + the Speculative Return.
What constitutes a fair price for an income stream is what people are able and willing to pay. What constitutes the number to use over the long-term is what people have been able and willing to pay for it over many years. That is, the average long-term Speculative Return should be zero. If the prices that people have been able and willing to pay for stocks had been dominated by a long-term trend instead of fluctuating, the model would have been modified to take that into account. [Demographics is a factor that probably influences the Speculative Return that has not been treated separately. That may change in the future.]
Mathematically, the key set of assumptions are that earnings growth has been reasonably steady and that the Speculative Return has been dominated by fluctuations instead of a long-term trend.
A better way to state this, consistent with what Gummy has mentioned, is that the total return of stocks = the Fundamental Return + a human factor that varies with time.
The Effect of Medium-Term Cycles
Many of the effects that John Bogle describe show nothing more than the presence of long-term cycles that are best explained in terms of human perceptions. If fluctuations dominate trends so that something similar to a mean exists, the comparisons that John Bogle makes cannot help but show a tendency to revert to a mean almost by definition. As more data are collected, they define a new mean.
The first set of comparisons that John Bogle made were in terms of relative fund performance ranked by quartiles from one decade to the next. Consider this alternative to his Reversion to the Mean explanation. Imagine that each fund had its own average (or mean) performance throughout the time period and that superimposed upon each was its own, large fluctuating component. Those funds that were in the top quartile in the first decade should be among the better funds that also were near their peak upward fluctuations. In the following decade, their fluctuating components would not be as favorable and, in some cases, would be unfavorable. The performance of the group during the second decade should be reduced, not because the steady component had diminished, but because circumstances were not all happening in each group member's favor at the same time. The initial separation into quartiles is what caused the observed result. The key requirement is that a large, possibly dominating, fluctuating component is present.
It would be one thing if the top quartile and the bottom quartile consistently changed places. They did not. If they had, a stronger assertion would have made sense: that the means were all the same and that all of the differences were only momentary fluctuations.
One type of behavior shows up consistently. Poor performance often persists. Most frequently, this is related to fees. In some cases, however, it is the result of a special kind of skill: consistently making bad investment choices.
Medium-Term Cycles
There can be many explanations as to why we should expect to see medium-term cycles.
One factor is the amount of time it takes to discern that a particular investment approach is doing better than alternatives. There is a lot of apparently random year-to-year fluctuation in the market in general. Unless an approach is spectacularly successful, which is unlikely, in takes several years as a minimum to show convincingly that there is improvement.
Another factor is that any advantage will diminish as more and more people become aware of it. It can take a long time and it may not disappear completely. With time, however, people will look instead to other factors and a relative advantage can reemerge.
I will mention here my concern about investment style differences. Many people are more willing than I to assume that they will persist.
The most important factor, I imagine, is the common learning experience of each generation. Few people who lived through the Great Depression were ever entirely comfortable in owning stocks. Few people who lived through the stagflation of the 1970s feel comfortable in holding something without an inflation hedge such as low or medium interest, fixed rate long-term bonds. Many who started in the late 1980s and in the 1990s are as emotionally attached to equity investments as survivors of the Great Depression were attached to bonds.
Raddr 3, Gummy 2
Raddr's precise definition of Reversion to the Mean is a new finding and it is meaningful. The volatility of the stock market has decreased more rapidly than if it were purely random. That is, the variance has fallen faster with time than 1/N, where N is the number of years (and the standard deviation has fallen faster than 1/[the square root of N] ).
Gummy has discussed the more traditional Reversion to the Mean issue in quite a bit of detail. He has shown that Reversion to the Mean makes little sense unless you treat it as a separate human factor, not as a mathematical theorem.
Have fun.
John R.
You can visit Gummy's site or look at his CD to learn about the details of the Dividend Discount Model and its adaptations, such as the Gordon equation.
Assume that an investment produces dividends grows at a steady rate and that the price that people are willing to pay for the (current) value of that income stream remains steady.
Then, approximately, the price paid for a particular investment will grow at a rate = the initial dividend yield + the growth rate of the dividends.
If the payout ratio of dividends remains constant, the growth rate of dividends and earnings are exactly the same. If the payout ratio varies slowly, the growth rate of dividends is approximately the same as the growth rate of earnings, but not exactly the same. If the payout ratio varies slowly, a reduction in the payout ratio will increase the retained earnings and will tend (or, at least, should tend) to result in the faster growth of earnings. The net effect, ideally, is that the dividend growth rate increases (at least, partially), which offsets (to some extent) the effect of the reduction in the payout ratio. [I know of no convincing set of assumptions that would cause everything to end up being exactly the same mathematically.]
Because (real) earnings growth rate (with earnings averaged over 5 to 10 years) has been well behaved while the (real) dividend growth rate has been erratic, the equation for price growth is frequently written as:
The price paid for a particular investment will grow at a rate = the initial dividend yield + the growth rate of the earnings.
John Bogle refers to this as the Fundamental Return of stocks. He adds a speculative term because people are willing to pay different prices at different times for the same stream of income. He approximates the effect by using the price to earnings ratio (P/E) at the beginning and at the end of a period.
In its final form, John Bogle presents his mathematical model of the total return from stocks as:
The total return of stocks = the initial dividend yield + the growth rate of the earnings + the speculative return = the Fundamental Return + the Speculative Return.
What constitutes a fair price for an income stream is what people are able and willing to pay. What constitutes the number to use over the long-term is what people have been able and willing to pay for it over many years. That is, the average long-term Speculative Return should be zero. If the prices that people have been able and willing to pay for stocks had been dominated by a long-term trend instead of fluctuating, the model would have been modified to take that into account. [Demographics is a factor that probably influences the Speculative Return that has not been treated separately. That may change in the future.]
Mathematically, the key set of assumptions are that earnings growth has been reasonably steady and that the Speculative Return has been dominated by fluctuations instead of a long-term trend.
A better way to state this, consistent with what Gummy has mentioned, is that the total return of stocks = the Fundamental Return + a human factor that varies with time.
The Effect of Medium-Term Cycles
Many of the effects that John Bogle describe show nothing more than the presence of long-term cycles that are best explained in terms of human perceptions. If fluctuations dominate trends so that something similar to a mean exists, the comparisons that John Bogle makes cannot help but show a tendency to revert to a mean almost by definition. As more data are collected, they define a new mean.
The first set of comparisons that John Bogle made were in terms of relative fund performance ranked by quartiles from one decade to the next. Consider this alternative to his Reversion to the Mean explanation. Imagine that each fund had its own average (or mean) performance throughout the time period and that superimposed upon each was its own, large fluctuating component. Those funds that were in the top quartile in the first decade should be among the better funds that also were near their peak upward fluctuations. In the following decade, their fluctuating components would not be as favorable and, in some cases, would be unfavorable. The performance of the group during the second decade should be reduced, not because the steady component had diminished, but because circumstances were not all happening in each group member's favor at the same time. The initial separation into quartiles is what caused the observed result. The key requirement is that a large, possibly dominating, fluctuating component is present.
It would be one thing if the top quartile and the bottom quartile consistently changed places. They did not. If they had, a stronger assertion would have made sense: that the means were all the same and that all of the differences were only momentary fluctuations.
One type of behavior shows up consistently. Poor performance often persists. Most frequently, this is related to fees. In some cases, however, it is the result of a special kind of skill: consistently making bad investment choices.
Medium-Term Cycles
There can be many explanations as to why we should expect to see medium-term cycles.
One factor is the amount of time it takes to discern that a particular investment approach is doing better than alternatives. There is a lot of apparently random year-to-year fluctuation in the market in general. Unless an approach is spectacularly successful, which is unlikely, in takes several years as a minimum to show convincingly that there is improvement.
Another factor is that any advantage will diminish as more and more people become aware of it. It can take a long time and it may not disappear completely. With time, however, people will look instead to other factors and a relative advantage can reemerge.
I will mention here my concern about investment style differences. Many people are more willing than I to assume that they will persist.
The most important factor, I imagine, is the common learning experience of each generation. Few people who lived through the Great Depression were ever entirely comfortable in owning stocks. Few people who lived through the stagflation of the 1970s feel comfortable in holding something without an inflation hedge such as low or medium interest, fixed rate long-term bonds. Many who started in the late 1980s and in the 1990s are as emotionally attached to equity investments as survivors of the Great Depression were attached to bonds.
Raddr 3, Gummy 2
Raddr's precise definition of Reversion to the Mean is a new finding and it is meaningful. The volatility of the stock market has decreased more rapidly than if it were purely random. That is, the variance has fallen faster with time than 1/N, where N is the number of years (and the standard deviation has fallen faster than 1/[the square root of N] ).
Gummy has discussed the more traditional Reversion to the Mean issue in quite a bit of detail. He has shown that Reversion to the Mean makes little sense unless you treat it as a separate human factor, not as a mathematical theorem.
Have fun.
John R.