Long term stock market risk
Long term stock market risk
There seems to be some debate as to whether the stock market is truly risky over the long term. This is related to the equity premium argument, and since nobody really knows what will happen, there are people on both sides of the coin. See http://kuznets.fas.harvard.edu/~campbel ... ckrisk.pdf
What surprises me is that neither of these two things have happened:
 If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?
 If instead risk compounds over time the same way returns do, then why does anyone invest in equities in the first place?
What surprises me is that neither of these two things have happened:
 If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?
 If instead risk compounds over time the same way returns do, then why does anyone invest in equities in the first place?
 nisiprius
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Re: Long term stock market risk
I wondered exactly the same thing, and I believe the nonexistence of such investment products proves that, whatever they say, people believe that stocks are risky in the long run. However, I've seen an argumentI probably am not stating it correctly since I didn't agree with itthat says that the problem with such an insurance contract is not that it wouldn't theoretically be profitable, but that the risk/reward characteristics are bad. The insurer would have a high probability of a small return, but only a small returnand only a low probability of a loss, but a huge loss. But to me that's just another way of saying that risk compounds over time!boggler wrote: If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?
Another argument is that the existence of a risk premium proves the risks of stocks in the long run. A clear application of this is to be found in the failed prediction of Dow 36,000 by Glassman and Hassett in their year 2000 book of that title. Their reasoning was perfectly explicit. They said it was a "undeniable historic fact," their words, that
They said in so many words that "The Dow 36,000 theory depends on the risk premium for stocks disappearing," and that "A sensible target date for Dow 36,000 is early 2005, but it could be reached much earlier."
 The truth is that, over the longterm, stocks are no more risky than bonds or Treasury bills, so…
 With this in mind, investors in recent years have begun to act more rationally, bidding up the prices of stocks and driving down the premium they had demanded when they believed stocks were risky, and…
 Soon, prices will rise to where they will be “perfectly reasonable”—around 36,000 on the Dow Jones industrial average.
So, the fact that the Dow did not reach 36,000 at or before early 2005 proves to me that the investors did not believe that "over the long term, stocks are no more risky than bonds."
1) Because many of us, even fraidycats like me, are in fact willing to accept that risk for the likelihood of a higher reward, even though it is only a likelihood. The damage comes when people are led to believe that stock risk declines a lotessentially goes awayover a long term.If instead risk compounds over time the same way returns do, then why does anyone invest in equities in the first place?
2) There's an intermediate position. Saying that "risk compounds over time" is probably an oversimplification, too. The actual content of Jeremy Siegel's waytooinfluential book, Stocks for the Long Run, is that stock prices, over periods of decades, show a characteristic called "mean reversion," meaning there actually is a correcting tendency, and that periods of poor performance are more likely to be followed by good performanceand vice versathan would be the case in a random walk. I think myself this is probably true. The question is: how strong is that tendency and how reliable is it? In any case, the intermediate position is "Risk doesn't go away, and risk does compound over time, but not as fast as if stock prices were a random walk."
3) The way John C. Bogle puts it is in terms of business ownership. He distinguishes investment from speculation. When you own the total market, you are on both sides of every trade and the speculation cancels out, and you are left with the overall investment returns from the growth of U. S. business as a whole. In my own language, because of speculation acting even at the level of the market as a whole, your investment returns are tied to business growth by a Bungee cord, but in the long run, businesses will make money and grow and the far end of the bungee cord is tied to that longterm systematic growthand that growth is faster than the interest rate you can get from a bank account, or that a business is willing to pay for a loan (which is what bonds are).
Last edited by nisiprius on Sat Feb 23, 2013 3:00 pm, edited 3 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Long term stock market risk
I think a lot of the debate has to do with how one defines risk. Many people tend to confuse the math, sometimes intentionally (IMO).
If you look at the return of equities over a oneyear period, in recent history, it has ranged from more than a 30% gain, to more than a 30% loss. In percentage terms, that's a 60% range. If you look at it in terms of the total amount of money you will have at the end of a year, it will range from roughly .65 to 1.35 x your original investmentroughly a factor of two.
If you look over a 10 year period, the annualized returns vary over a somewhat narrower range. From 20002009, they were pretty close to zero (assuming you had TSM, no tilting). From 19901999, the annualized return was something a little more than 15%. So the range of outcomes (in terms of annualized return over the ten year period), has a spread of roughly 20%, compared to 60% for a single year. So it's less risky by that measure.
If on the other hand you look at the ratio of your portfolio's value after ten years between the worst possible case and the best possible case, it's roughly a factor of five, compared to a factor of two for a single year. So the range of outcomes in dollar value increases with time.
Another way of looking at things is the likelihood that your portfolio will have a loss after X years. For the U.S. this is about 30% for a single year, has happened just barely a couple times over ten years, but never over 15 years or more (it has happened in Japan though, so the fact it hasn't in the U.S. doesn't mean the probability is zero). This excludes black swan type events like the government expropriating all equity holdingsthat's a 100%, permanent loss, whether you held the market for a day or a century.
I think people who should know better often pick their choice of which measure of risk they use deliberately to generate the answer they want.
Brad
If you look at the return of equities over a oneyear period, in recent history, it has ranged from more than a 30% gain, to more than a 30% loss. In percentage terms, that's a 60% range. If you look at it in terms of the total amount of money you will have at the end of a year, it will range from roughly .65 to 1.35 x your original investmentroughly a factor of two.
If you look over a 10 year period, the annualized returns vary over a somewhat narrower range. From 20002009, they were pretty close to zero (assuming you had TSM, no tilting). From 19901999, the annualized return was something a little more than 15%. So the range of outcomes (in terms of annualized return over the ten year period), has a spread of roughly 20%, compared to 60% for a single year. So it's less risky by that measure.
If on the other hand you look at the ratio of your portfolio's value after ten years between the worst possible case and the best possible case, it's roughly a factor of five, compared to a factor of two for a single year. So the range of outcomes in dollar value increases with time.
Another way of looking at things is the likelihood that your portfolio will have a loss after X years. For the U.S. this is about 30% for a single year, has happened just barely a couple times over ten years, but never over 15 years or more (it has happened in Japan though, so the fact it hasn't in the U.S. doesn't mean the probability is zero). This excludes black swan type events like the government expropriating all equity holdingsthat's a 100%, permanent loss, whether you held the market for a day or a century.
I think people who should know better often pick their choice of which measure of risk they use deliberately to generate the answer they want.
Brad
Most of my posts assume no behavioral errors.
 jeffyscott
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Re: Long term stock market risk
That appears to have been written in 1999. In the 14 years since this:
Over the past 14 years VTSMX has total cumulative return of 73% and Vanguard short term treasury has cumulative total return of 74%.
http://quote.morningstar.com/fund/chart ... %2C0%22%7D
was written, the realized equity risk premium has been just about 0.In the presence of meanreversion, the strategic benchmark allocation to
equities should not be fixed, but should adjust gradually to changes in the equity
premium. In particular, the equity allocation should be lower at times, such as the
present, when the recent performance of stocks has been spectacular.
Over the past 14 years VTSMX has total cumulative return of 73% and Vanguard short term treasury has cumulative total return of 74%.
http://quote.morningstar.com/fund/chart ... %2C0%22%7D
press on, regardless  John C. Bogle
Re: Long term stock market risk
For one thing, it depends on your risk measure. John Norstad wrote an article Risk and Time that shows how, for a random walk, the range of outcomes increases over time. So he concluded that stocks are more risky over time.boggler wrote:There seems to be some debate as to whether the stock market is truly risky over the long term. This is related to the equity premium argument, and since nobody really knows what will happen, there are people on both sides of the coin. See http://kuznets.fas.harvard.edu/~campbel ... ckrisk.pdf
What surprises me is that neither of these two things have happened:
 If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?
 If instead risk compounds over time the same way returns do, then why does anyone invest in equities in the first place?
Other risk measures may tell a different story.
One of my favorite risk measures is drawdown. Suppose you make a $1000 investment in some risky assets like the stock market. Lets say the expected return is 10% and the volatility is 20%. How much drawdown should you expect with some probability over time?
Using a random walk model with normal distibution similar to Norstad, I calculated the minimum amount you could expect to lose for different holding periods, with 5% probability.
The 5% minimum expected drawdown starts negative and gets larger for a few years. But then it turns up and after about 11 years it crosses zero. A similar analysis with 1% probability showed about 22 years for the min expected drawdown to cross zero.
Assuming a random walk, as time goes on, the chance of seeing an actual loss from stocks, i.e. negative cumulative return, gets less and less. It never goes to zero, but, as long as there is not a total catastrophe, it becomes very unlikely after 20 or 30 years.
Re: Long term stock market risk
Can someone offer an explanation for how risk compounds over time? I believe for compounding there must be some type of mechanism at work. There must be some type of feedback action occuring. If it just means that if you wait long enough, something really bad will occurthat I can can buy.
Re: Long term stock market risk
It depends what definition of "risk" one uses. Is it the variability of the annualized return, or the variability of the final portfolio value? In a random walk model the first will scale with 1/the square root of time, the second will scale with the square root of time. In a practical sense, saying that the variability of the final dollar value of one's portfolio is all that matters neglects the decreasing marginal utility of wealth. For many people, the goal is to reach some minimum level of assets. If a given investment strategy may produce 2x that level, or 20x that level, that looks huge if you assume variance = risk. But in either event the investor won the game; it's just a matter of how much he ran up the score after being assured of victory.TJSI wrote:Can someone offer an explanation for how risk compounds over time? I believe for compounding there must be some type of mechanism at work. There must be some type of feedback action occuring. If it just means that if you wait long enough, something really bad will occurthat I can can buy.
I think a more reasonable way of defining risk for an individual is the probability that they will achieve at least their target. As grayfox says, the longer you remain invested in the market, the less likelihood that equities will have a negative return over that time.
Most of my posts assume no behavioral errors.
Re: Long term stock market risk
Compounding just means that the results at the end of two periods of time are the product of the results for the first period multiplied by the results for the second period.TJSI wrote:Can someone offer an explanation for how risk compounds over time? I believe for compounding there must be some type of mechanism at work. There must be some type of feedback action occuring. If it just means that if you wait long enough, something really bad will occurthat I can can buy.
Consider that returns in a period are either +5% or 5%. The results at the end of one period are a 5050 chance between $10,000 becoming either $10,500 or $9,500
Now at the end of the second period there are four possibilities. We could have +5% after +5%, +5% after 5%, 5% after 5%, and 5% after +5%. The possible results are $9025, $9975, $9975, and $11025. Notice the risk has increased from +/$500 to +/1000. On the other hand, the average outcome is $10,000, which is correct as the average expected return for 5050 +/5% is zero.
In this example the definition of risk half the range between the highest and lowest returns. Notice also, that if risk were measured by how much money could be lost in the worst case, that the answer so far is the same.
If the return distribution is more complex, then the mathematics that must be applied to describe the result is more complex.
Re: Long term stock market risk
Assuming independence, risk compounds exponentially with the square root of the holding period. Therefore, the standard deviation of the annualized return is inversely proportional to the square root of the holding period; the probability of falling 20% below the expected annual return in one year is equal to the probability of falling 5% below the expected annualized return in 16 years.TJSI wrote:Can someone offer an explanation for how risk compounds over time? I believe for compounding there must be some type of mechanism at work. There must be some type of feedback action occuring. If it just means that if you wait long enough, something really bad will occurthat I can can buy.
The reason for this is the law of averages. Suppose you flip a coin N times. As N gets larger, the fraction of heads approaches .5. For example, suppose 40 of your first 100 flips are heads (which is about two standard deviations below the expected 50, and thus happens about 2.3% of the time). The next 100 flips are still expected to be half heads and half tails, so it is most likely that 90 of the first 200 flips will now be heads, and the fraction of heads will have gone from .4 to .45. In 1600 flips, the standard deviation of the number of heads is 20, so there is about a 2.3% chance that you will have fewer than 1560 heads; this is four times the absolute difference that you had with 100 flips, but only 1/4 the percentage difference.
The stock market is usually assumed to work the same way. If the stock market has an 8% annual real return with a 16% annual standard deviation, then the annualized standard deviation in N years is 16% divided by the square root of the number of years. Thus, in 16 years, the standard deviation of annual returns drops to 4%, and there is only a 2.3% probability that the stock market would not keep up with inflation for 16 years (and this has happened). In 25 years, the standard deviation of annual returns drops to 3.2%, so there is a 0.62% chance that the stock market would not keep up with inflation for 25 years (and this has never happened in the US, even including the Depression).
Note that I am assuming independence and normal distributions; this is a standard statistical assumption, but it may not be valid. There are many stock exchanges which lost 100% of their value, and the risk of that happening increases with time.
 jeffyscott
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Re: Long term stock market risk
So I decided to finally learn how to actually post these charts, since the m* linking process fails to retain the specified dates. Here it is:jeffyscott wrote:Over the past 14 years VTSMX has total cumulative return of 73% and Vanguard short term treasury has cumulative total return of 74%.
press on, regardless  John C. Bogle
 nisiprius
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Re: Long term stock market risk
"Risk compounds over time" is a vague phrasenot sure precisely what rmelvey meant by it, but I see two reasonable meanings for it.
First, if, say, you hold an individual bond, and there's 2% chance each year that the bond will default, then there's a 98% chance it will survive. But over 20 years, there's only a 98% * 98% * 98% * ... * 98% = a 66.7% chance of survival.
Second, and this one really bothers me because I "fell for it..." Have you ever seen a chart like this:
I've seen variations on it in many places. It gives the visual appearance that stocks are becoming less risky over longer holding periodsthe bars get shorter and shorter as the holding period increases. Furthermore, the accompanying text often gives that impression, as well. But it's utterly bogus, because the 7.94% and the 17.24% are average annual figures, and if we are interested in what actually happens in our portfolio over 25 years, they need to be compounded out for 25 years. And if 1% expense ratio matters when you compound it for that long, the difference between 7.94% and 17.24% doesn't just matter, it's explosive. It is, in fact, the difference between 6.75X your original investment and 53X your original investment.
Now we get to the everpopular question of how to define risk.
If it's risk of loss, the 1 and 5year numbers show a possibility of loss of money, while 1025 years appear to show that money was never lost. (But if you throw in the old bogeyman inflation, the picture changesinflation, of course, compounds, too. And if you throw in taxes, the effect of giving a percentage of your earnings to the government each year compounds, too).
If it's risk in the sense of not knowing the outcomefluctuationrisk, volatilityrisk, financialeconomics "risk," Knightian "risk," then there's risk even if the lowest number doesn't represent a loss. If it's risk in the sense of not meeting your goals, there's risk as well.
Looking at the last bar, where the average looks to be about 12%: If you are counting on getting 12% average annual returns and you only get 7.94%, i.e. a 3.06% shortfall every year, that's not a small difference. Compounded over 25 years, that means you have only 40% as much money as you planned.
So I think it's reasonable to describe that as "risk compounding," and showing that there is very considerable risk in holding stocks even for periods as long as 25 years.
First, if, say, you hold an individual bond, and there's 2% chance each year that the bond will default, then there's a 98% chance it will survive. But over 20 years, there's only a 98% * 98% * 98% * ... * 98% = a 66.7% chance of survival.
Second, and this one really bothers me because I "fell for it..." Have you ever seen a chart like this:
I've seen variations on it in many places. It gives the visual appearance that stocks are becoming less risky over longer holding periodsthe bars get shorter and shorter as the holding period increases. Furthermore, the accompanying text often gives that impression, as well. But it's utterly bogus, because the 7.94% and the 17.24% are average annual figures, and if we are interested in what actually happens in our portfolio over 25 years, they need to be compounded out for 25 years. And if 1% expense ratio matters when you compound it for that long, the difference between 7.94% and 17.24% doesn't just matter, it's explosive. It is, in fact, the difference between 6.75X your original investment and 53X your original investment.
Now we get to the everpopular question of how to define risk.
If it's risk of loss, the 1 and 5year numbers show a possibility of loss of money, while 1025 years appear to show that money was never lost. (But if you throw in the old bogeyman inflation, the picture changesinflation, of course, compounds, too. And if you throw in taxes, the effect of giving a percentage of your earnings to the government each year compounds, too).
If it's risk in the sense of not knowing the outcomefluctuationrisk, volatilityrisk, financialeconomics "risk," Knightian "risk," then there's risk even if the lowest number doesn't represent a loss. If it's risk in the sense of not meeting your goals, there's risk as well.
Looking at the last bar, where the average looks to be about 12%: If you are counting on getting 12% average annual returns and you only get 7.94%, i.e. a 3.06% shortfall every year, that's not a small difference. Compounded over 25 years, that means you have only 40% as much money as you planned.
So I think it's reasonable to describe that as "risk compounding," and showing that there is very considerable risk in holding stocks even for periods as long as 25 years.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Long term stock market risk
Ok, but if I run the numbers and decide that anything above 5X my original investment will be sufficient, then where is the risk (not the mathematical "risk"the personal risk of me not having enough money)? Let's used annualized numbersVanguard's tendency to quote average numbers annoys me to no end.nisiprius wrote:
I've seen variations on it in many places. It gives the visual appearance that stocks are becoming less risky over longer holding periodsthe bars get shorter and shorter as the holding period increases. Furthermore, the accompanying text often gives that impression, as well. But it's utterly bogus, because the 7.94% and the 17.24% are average annual figures, and if we are interested in what actually happens in our portfolio over 25 years, they need to be compounded out for 25 years. And if 1% expense ratio matters when you compound it for that long, the difference between 7.94% and 17.24% doesn't just matter, it's explosive. It is, in fact, the difference between 6.75X your original investment and 53X your original investment.
Most of my posts assume no behavioral errors.
Re: Long term stock market risk
My intuitive (and nonmathematical) view of risk compounding over time is this: The Dow closed at 14,000 on Friday. I am willing to bet a large sum of money that at close of business day on Monday it will be in the range of 14,000 +/ 200. I would never make that bet on the Dow closing value one year from now, or worse, 5 years from now. It is too risky of a bet.
Re: Long term stock market risk
However, are you willing to bet on the Dow closing above 14,000 at the end of 2038? That is another way of looking at the risk, and the Dow has never declined in a 25year period. The Dow in 2038 might be at 14,000, or at 70,000, or at 350,000, which is a lot of uncertainty, but you may only care about the downside.Higman wrote:My intuitive (and nonmathematical) view of risk compounding over time is this: The Dow closed at 14,000 on Friday. I am willing to bet a large sum of money that at close of business day on Monday it will be in the range of 14,000 +/ 200. I would never make that bet on the Dow closing value one year from now, or worse, 5 years from now. It is too risky of a bet.
(The Dow is not a good measure for this type of risk; it ignores dividends and inflation. If the Dow doesn't change in a year but the stocks pay 3% dividends, you are 3% richer; conversely, if inflation in that year is 5%, you are 2% poorer even with the dividends.)
Re: Long term stock market risk
Thanks for the responses on the subject of compounding and risk. It seems that many have a more expansive view of the term compounding. For many compounding means the same as increasing. I have a more restrictive meaning. And as I thought about this on a rainy Saturday, it seems to me that the development of manias exhibits the more restrictive meaning of compounding. And they can certainly increase risk. Thanks again for the responses.
 nisiprius
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Re: Long term stock market risk
Boggler, TSJ1, the bottom line is that you must do your best to look into the data for yourself and interpret it yourself, using whatever measure of risk is appropriate to you. Do not let anyone else interpret it for you.
You must accept that fact that almost everyone is grinding an axe to some extent, trying to "prove" something about the low or high risk of stocks.
One thing to keep in mind is that there isn't really all that much data. The problem is shown by this chartit's from Jim Otar's book. I would not take the straightline segments seriously (that's letting Otar interpret the data for us!) but the point is that the stock market does show things... bull and bear markets if you like... but sustained periods of nonaverage behavior that can persist for well over a decade. So when you are looking at "a century of data," you may only be looking at eight "things." Not a lot.
Financial data also has an awkward tendency to keep breaking records, to do things that it has never done before, and to break records more often than it "should" (statistical "fat tails.")
You must accept that fact that almost everyone is grinding an axe to some extent, trying to "prove" something about the low or high risk of stocks.
One thing to keep in mind is that there isn't really all that much data. The problem is shown by this chartit's from Jim Otar's book. I would not take the straightline segments seriously (that's letting Otar interpret the data for us!) but the point is that the stock market does show things... bull and bear markets if you like... but sustained periods of nonaverage behavior that can persist for well over a decade. So when you are looking at "a century of data," you may only be looking at eight "things." Not a lot.
Financial data also has an awkward tendency to keep breaking records, to do things that it has never done before, and to break records more often than it "should" (statistical "fat tails.")
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Long term stock market risk
That might be a symptom of the fractal nature of financial markets. Even if we had 1,000 years of data I bet the charts would have large periods of trends that could be broken up into smaller trends that could be broken up into smaller trends and so on...nisiprius wrote:So when you are looking at "a century of data," you may only be looking at eight "things." Not a lot.
Re: Long term stock market risk
TJSI wrote:Thanks for the responses on the subject of compounding and risk. It seems that many have a more expansive view of the term compounding. For many compounding means the same as increasing. I have a more restrictive meaning. And as I thought about this on a rainy Saturday, it seems to me that the development of manias exhibits the more restrictive meaning of compounding. And they can certainly increase risk. Thanks again for the responses.
All the replies on this thread are based on the same concept of applying successive iterations to the most recently achieved value. That is what compounding really means, from its more restricted definition in investing here:
http://www.investopedia.com/terms/c/compounding.asp
Compounding produces exponential growth when the successive iterations are all multiplications by the same number more than one and produces exponential decay when the multiplications are by the same number less than one. When the size and the sign of the multiplier greater or lesser than one is random then future results will be uncertain. What aspect of that uncertainty is of interest will be your definition of risk.
The discussion of the different meanings of risk is misleading as these are just different pieces of information about the same thing. The issue is resolved in the common sense way of deciding what about one's investments one is interested in and then finding which information is informative about that. The question by baw703916 is totally appropriate as one example.
The difficulty with all of this, as pointed out, is that the real world seems to behave in a way that is much messier than these concepts can in practice be used to describe in detail. It is still true that much insight can be gotten into the general behavior.
Re: Long term stock market risk
Well I don't want to touch off a debate on what the meaning of is is. But the compounding of earnings means more than just the multiplication of yearly earnings. In the sense of compounded earnings, it means that earnings are reinvested and generate more earnings. This is the feedback mechanism I mentioned. It is the reinvesting, that gives this meaning to compounding. Many have a wider meaning to the term and just mean increasing without the feedback mechaism.
Re: Long term stock market risk
Yes, that is what I just described, exactly. Earning on earnings is the same thing as multiplying the new balance by the next periods earnings. The new balance is the old principle plus the earnings for the period. In the next period earnings are applied to that new balance. If you add earnings to a principle the new principle is P + E = P * (1 + E/P) = p*(1+r) where r is the rate of earnings. If you repeat that for n periods you get the well known compound growth formula P(n) = P(0) * (1 + r)^n. Compounding is simply repeated multiplication by a factor, which is an algebraic way of expressing earnings on earnings plus earnings on original principal. If r is positive the principle grows exponentially and if it is negative the principle decays exponentially. If the the r in question is returns in a market then r is different in each period and things get more complex. That is where risk comes in.TJSI wrote:Well I don't want to touch off a debate on what the meaning of is is. But the compounding of earnings means more than just the multiplication of yearly earnings. In the sense of compounded earnings, it means that earnings are reinvested and generate more earnings. This is the feedback mechanism I mentioned. It is the reinvesting, that gives this meaning to compounding. Many have a wider meaning to the term and just mean increasing without the feedback mechaism.
Here is a good primer on the subject:
http://www.regentsprep.org/Regents/math ... DecayL.htm
Re: Long term stock market risk
All of these examples seem to be for static portfolios, without ongoing contributions or withdrawals. If we consider a retirement period from which withdrawals must be made to cover living expenses then there is much more risk since market losses to that extent must be realized.
Although most posters here know this already, it is useful to keep in mind that the mere mathematical statement of the probability does not fully match the risk in some real world situations.
Although most posters here know this already, it is useful to keep in mind that the mere mathematical statement of the probability does not fully match the risk in some real world situations.
Re: Long term stock market risk
These graphs assume a gaussian distribution of returns. The red line is the expected value (EV), and each line away from red represents 1 standard deviation. All graphs show the same values (for the curious they happen to be $22 / unit of time for EV and $540 / unit of time for standard deviation  this isn't from the stock market but something else with Gaussian distribution of returns).
The x axis is time and the y axis is $$. Each graph represents a different time period.
So if you notice, the range of the final output is significantly greater over the larger time. But the risk of ruin is also significantly less.
The equation for risk of ruin (the chance of losing all your money at any time in the future) is:
( (1  EV / Std) / ( 1 + EV / Std ) ) ^ ( Total_Money / Standard Deviation ).
There are also equations for losing $X after Y hours, gaining $X after Y hours, or losing $X before reaching $Z, ad infinitum which I can post if others are curious.
The x axis is time and the y axis is $$. Each graph represents a different time period.
So if you notice, the range of the final output is significantly greater over the larger time. But the risk of ruin is also significantly less.
The equation for risk of ruin (the chance of losing all your money at any time in the future) is:
( (1  EV / Std) / ( 1 + EV / Std ) ) ^ ( Total_Money / Standard Deviation ).
There are also equations for losing $X after Y hours, gaining $X after Y hours, or losing $X before reaching $Z, ad infinitum which I can post if others are curious.
Re: Long term stock market risk
Come to think of it, isn't this what an annuity is?boggler wrote:What surprises me is that neither of these two things have happened:
 If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?

 Posts: 189
 Joined: Fri Nov 02, 2007 8:49 am
Re: Long term stock market risk
So then as a young investor making steady contributions the opposite would be true, i.e. much less risk.cbeck wrote:All of these examples seem to be for static portfolios, without ongoing contributions or withdrawals. If we consider a retirement period from which withdrawals must be made to cover living expenses then there is much more risk since market losses to that extent must be realized.
Although most posters here know this already, it is useful to keep in mind that the mere mathematical statement of the probability does not fully match the risk in some real world situations.
Re: Long term stock market risk
The main reason this would not work is Marktomarket accounting, and equity volatility. Even if a 8% return were very likely over the long term, having a standard deviation of + 20 would mean that insurance companies would need to reserve a lot of capital in case the market crashes  i.e. they would have to reserve the delta between the guarantee and the marked to market value of the holdings... and probably a lot more then that for regulatory buffer. So this would be a very capital intensive instrument, and therefore very pricy. So if the long term 8% were likely, and you take 6% of that return to pay for insurance, you are left with a 2% guaranteed return  as an example.boggler wrote: If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?
Re: Long term stock market risk
Quite right. People are trying to explain the basics of an idea. When contributions/withdrawals are involved the mathematics become more intricate. Those issues exactly are what the whole field of retirement models is all about.cbeck wrote:All of these examples seem to be for static portfolios, without ongoing contributions or withdrawals. If we consider a retirement period from which withdrawals must be made to cover living expenses then there is much more risk since market losses to that extent must be realized.
Although most posters here know this already, it is useful to keep in mind that the mere mathematical statement of the probability does not fully match the risk in some real world situations.
However, there is never a "mere" statement of probability. That is just a first step in the whole approach of trying to analyze the problem. And, of course, there are always further uncertainties and considerations. In practice the actual life course of an individual is not so often well fit to any ontheaverage model. This is probably a greater departure from trying to "engineer" a financial lifetime than any extreme events on the financial side. This includes not the least the actual intervention of death at an unknown age that is an insignificant issue on the average but of major significance to the individual when it happens.
Re: Long term stock market risk
Correct. There are even some recent papers that have advocated that young investors not only opt for 100% equity positions but in fact should leverage those positions to increase risk and expected return. That wouldn't be my advice, but just to note that the effect has been noticed.Shireman28 wrote:So then as a young investor making steady contributions the opposite would be true, i.e. much less risk.cbeck wrote:All of these examples seem to be for static portfolios, without ongoing contributions or withdrawals. If we consider a retirement period from which withdrawals must be made to cover living expenses then there is much more risk since market losses to that extent must be realized.
Although most posters here know this already, it is useful to keep in mind that the mere mathematical statement of the probability does not fully match the risk in some real world situations.
Re: Long term stock market risk
Thanks for this. This is a helpful illustration of how the idea plays out. Your disclaimer that this is not necessarily the data for any actual investment is fine. John Norstad, whom we sometimes cite here, offers a similar article about risk and time in the same vein.assumer wrote:These graphs assume a gaussian distribution of returns. The red line is the expected value (EV), and each line away from red represents 1 standard deviation. All graphs show the same values (for the curious they happen to be $22 / unit of time for EV and $540 / unit of time for standard deviation  this isn't from the stock market but something else with Gaussian distribution of returns).
The x axis is time and the y axis is $$. Each graph represents a different time period.
So if you notice, the range of the final output is significantly greater over the larger time. But the risk of ruin is also significantly less.
The equation for risk of ruin (the chance of losing all your money at any time in the future) is:
( (1  EV / Std) / ( 1 + EV / Std ) ) ^ ( Total_Money / Standard Deviation ).
There are also equations for losing $X after Y hours, gaining $X after Y hours, or losing $X before reaching $Z, ad infinitum which I can post if others are curious.
The important point to note is that given a specified form of distribution (Gaussian in this case, but it does not have to be to mollify those who object to not fat enough tails) and the parameters that specify a specific Gaussian distribution, namely the mean and standard deviation, then all of the information one wants to know can be extracted if one is clever enough with the math. That is why statements that standard deviation is not risk are misleading. Once risk as standard deviation is given, all the other notions of risk can also be computed from it, if enough work is done.
As with all statistical modelling, the accuracy of the results in describing the real world can be a tough problem. The insight gained from the idea about how things work is invaluable if a person has not comprehended it before.
Re: Long term stock market risk
Indeed. The graph itself is meant to show the trend. Standard deviation itself does not define risk. But for me what defines risk are things such as "what are the chances I might not achieve $X after Y years", or "what are the chances I will lose $X after Y years" or "what are the chances I will lose $X before getting $Z", or "how many years do I have to stay invested before I have a 95% chance of achieving $X, with a 10% chance of losing $Z"dbr wrote:Thanks for this. This is a helpful illustration of how the idea plays out. Your disclaimer that this is not necessarily the data for any actual investment is fine. John Norstad, whom we sometimes cite here, offers a similar article about risk and time in the same vein.assumer wrote:These graphs assume a gaussian distribution of returns. The red line is the expected value (EV), and each line away from red represents 1 standard deviation. All graphs show the same values (for the curious they happen to be $22 / unit of time for EV and $540 / unit of time for standard deviation  this isn't from the stock market but something else with Gaussian distribution of returns).
The x axis is time and the y axis is $$. Each graph represents a different time period.
So if you notice, the range of the final output is significantly greater over the larger time. But the risk of ruin is also significantly less.
The equation for risk of ruin (the chance of losing all your money at any time in the future) is:
( (1  EV / Std) / ( 1 + EV / Std ) ) ^ ( Total_Money / Standard Deviation ).
There are also equations for losing $X after Y hours, gaining $X after Y hours, or losing $X before reaching $Z, ad infinitum which I can post if others are curious.
The important point to note is that given a specified form of distribution (Gaussian in this case, but it does not have to be to mollify those who object to not fat enough tails) and the parameters that specify a specific Gaussian distribution, namely the mean and standard deviation, then all of the information one wants to know can be extracted if one is clever enough with the math. That is why statements that standard deviation is not risk are misleading. Once risk as standard deviation is given, all the other notions of risk can also be computed from it, if enough work is done.
As with all statistical modelling, the accuracy of the results in describing the real world can be a tough problem. The insight gained from the idea about how things work is invaluable if a person has not comprehended it before.
Given the parameters used to define the distribution (however you define it  Gaussian, nonparametric, fattailed Gaussian, etc.) one can define the equations answering the questions (the Gaussian equation for Risk of Ruin is one simple one, but I have many others). So standard deviation itself might not mean anything, but rather the probable range of results after Y years, with 95% confidence or whatever. But your point is a good one, that the inputs themselves might not define risk, but rather can answer the questions you want answered in terms of probabilities.
Re: Long term stock market risk
Agreed. It might be the most helpful thing is to ban the word "risk" from the conversation and instead just talk about things such as "What are the chances my wealth will fail to exceed $X after thirty years?" or "What are the chances I will run out of money trying to spend $x from a starting portfolio of $y for z years?" The point is that instead of trying to define risk in order to ask a question and then arguing that said definition is not really what risk is, why not just ask and answer the question (as you do)?assumer wrote:
Indeed. The graph itself is meant to show the trend. Standard deviation itself does not define risk. But for me what defines risk are things such as "what are the chances I might not achieve $X after Y years", or "what are the chances I will lose $X after Y years" or "what are the chances I will lose $X before getting $Z", or "how many years do I have to stay invested before I have a 95% chance of achieving $X, with a 10% chance of losing $Z"
Given the parameters used to define the distribution (however you define it  Gaussian, nonparametric, fattailed Gaussian, etc.) one can define the equations answering the questions (the Gaussian equation for Risk of Ruin is one simple one, but I have many others). So standard deviation itself might not mean anything, but rather the probable range of results after Y years, with 95% confidence or whatever. But your point is a good one, that the inputs themselves might not define risk, but rather can answer the questions you want answered in terms of probabilities.
Re: Long term stock market risk
That is similar to the plot I made here for a hypothetical investment with return ~ N(.10,.20^2)assumer wrote:These graphs assume a gaussian distribution of returns. The red line is the expected value (EV), and each line away from red represents 1 standard deviation. All graphs show the same values (for the curious they happen to be $22 / unit of time for EV and $540 / unit of time for standard deviation  this isn't from the stock market but something else with Gaussian distribution of returns).
The x axis is time and the y axis is $$. Each graph represents a different time period.
So if you notice, the range of the final output is significantly greater over the larger time. But the risk of ruin is also significantly less.
This shows the 5% quantile which I think must be the same as the orange 2 standard deviation on your chart. The zero crossing point is at 130 months, which means that at 130 months (10.83 years), 5% of the possible outcomes had balance < 0, i.e. a loss. Which is the same as saying 95% did not have a loss. And at about 22 years, only 1% showed a loss, or 99% did not show a loss.
I found this calculator that shows percentages of times the S&P outperformed some return over various time periods.
http://dqydj.net/investmentsandreturns/
Putting in 0% and not adjusted for inflation, shows 96.78% positive for 10 years and 100% positive for 20 years. So the historical is fairly close to a simple randomwalk model.
There are other factors, so you could make a more detailed model. For instance, monthly stock returns have fat tails, which would make it more worse. But then there is also mean reversion which would make it better.
To summarize, if your risk measure is the chance of showing a loss, it definitely decreases over longer periods like 10, 20 or 30 years.
Re: Long term stock market risk
Yes agreed. If risk is the chance of loss (or some % loss), that decreases over time. If your risk is the absolute range of results (in terms of $), that increases over time. I prefer the former.grayfox wrote:To summarize, if your risk measure is the chance of showing a loss, it definitely decreases over longer periods like 10, 20 or 30 years.
Re: Long term stock market risk
It had occurred to me (but I've never expressed it mathematically) that the higher your savings rate, the more investment risk you are able to tolerate (financially, leaving aside the psychological aspect). Of course this is at odds with what many investors (individual and institutional) do, which is to try to use loading up on risk as a substitute for an inadequate savings rate.dbr wrote:Correct. There are even some recent papers that have advocated that young investors not only opt for 100% equity positions but in fact should leverage those positions to increase risk and expected return. That wouldn't be my advice, but just to note that the effect has been noticed.Shireman28 wrote:So then as a young investor making steady contributions the opposite would be true, i.e. much less risk.cbeck wrote:All of these examples seem to be for static portfolios, without ongoing contributions or withdrawals. If we consider a retirement period from which withdrawals must be made to cover living expenses then there is much more risk since market losses to that extent must be realized.
Although most posters here know this already, it is useful to keep in mind that the mere mathematical statement of the probability does not fully match the risk in some real world situations.
Brad
Most of my posts assume no behavioral errors.
Re: Long term stock market risk
Well stated. I agree with both of you.assumer wrote:Yes agreed. If risk is the chance of loss (or some % loss), that decreases over time. If your risk is the absolute range of results (in terms of $), that increases over time. I prefer the former.grayfox wrote:To summarize, if your risk measure is the chance of showing a loss, it definitely decreases over longer periods like 10, 20 or 30 years.
Brad
Most of my posts assume no behavioral errors.
Re: Long term stock market risk
If the risk is lower over time and everyone agrees, then 2000 and 2008 reflecting real life have no bearing on overall life since 20 years worth of continued market growth will make everything just fine.
But since the risk of loss is known at the inception of an allocation and can happen at any time, the use of algorithm after algorithm and regression from the age of dinosaurs does little to provide a consistency of reward to the consumer who needs money to live on.
The issue is really anticipating the seriousness of an economy and the risk to wealth. Everyone replying in this blog knew of the impact of the inverted yield curve and how the economy relates to GDP.
Standard deviation goes down over time but the risk of loss goes up. And that is what controls. Of course if the advisor/consumer relies on some formula and avoids current scenarios which they have never been taught about you have the current economic stupidity all around.
Errold Moody, PhD MBA MSFP LLB BSCE
Life and Disability Insurance Analyst
Registered Investment Adviser
But since the risk of loss is known at the inception of an allocation and can happen at any time, the use of algorithm after algorithm and regression from the age of dinosaurs does little to provide a consistency of reward to the consumer who needs money to live on.
The issue is really anticipating the seriousness of an economy and the risk to wealth. Everyone replying in this blog knew of the impact of the inverted yield curve and how the economy relates to GDP.
Standard deviation goes down over time but the risk of loss goes up. And that is what controls. Of course if the advisor/consumer relies on some formula and avoids current scenarios which they have never been taught about you have the current economic stupidity all around.
Errold Moody, PhD MBA MSFP LLB BSCE
Life and Disability Insurance Analyst
Registered Investment Adviser
Re: Long term stock market risk
I really don't understand what you are getting at here: "the risk of loss goes up". I think it had been made pretty clear by a number of posts in the thread using both historical examples and modeling results that the probability of having a net loss (as in the current value is less than the original investment) decreases with time. If on the other hand you mean the probability that there will be a severe bear market at some point during the holding period, then yes, that obviously increases with time. But in spite of two major bear markets, an investment made into TSM in 2000 is worth more today (with reinvestments) than it was 13 years ago.efmoody wrote:Standard deviation goes down over time but the risk of loss goes up. And that is what controls.
"That is what controls" I'm really confused; what does it control?
Crashes are part of the financial landscape. Someone who can't deal with that has no business investing in equities.
Most of my posts assume no behavioral errors.
Re: Long term stock market risk
Typically you assume that stocks follow a random walk. So the expected value of the price at time t equals the value at time t1. And the actual value at time t will be the price at t1 plus some error term e. This means that:TJSI wrote:Can someone offer an explanation for how risk compounds over time? I believe for compounding there must be some type of mechanism at work. There must be some type of feedback action occuring. If it just means that if you wait long enough, something really bad will occurthat I can can buy.
E(pt) = E(et) + E(et1) + E(et2) ... + E(pt=0)
And because the et are uncorrelated:
Var(pt) = Var(et) + Var(et1) + Var(et2) ... + Var(et=1)
Because we assume that each et has the same constant variance (homoskedasticity), the Var(pt) = c * t where c is that constant. So the further out in time you go, the greater your variance. Specifically, variance increases proportional to time, and standard deviation increases proportional to the squareroot of time.
So there's no feedback, it's just a consequence of the assumed mathematical properties of stock prices.
 nisiprius
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Re: Long term stock market risk
No, because insurance companies aren't allowed to invest in stocks. They aren't even allowed to invest in junk bonds, but a company called Executive Life Insurance Company managed to pull the wool over the regulators' eyes and do so, and became insolvent in 1991; I'm pretty sure the biggest insolvency in U. S. history.boggler wrote:Come to think of it, isn't this what an annuity is?boggler wrote:What surprises me is that neither of these two things have happened:
 If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: Long term stock market risk
Maybe I need to reread the Berkshire Hathaway annual report.nisiprius wrote: insurance companies aren't allowed to invest in stocks.
Most of my posts assume no behavioral errors.
 nisiprius
 Advisory Board
 Posts: 36682
 Joined: Thu Jul 26, 2007 9:33 am
 Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.O. Henry
Re: Long term stock market risk
I trust you're joking. In case you are not, there is a company named Berkshire Hathaway which is "A diversified company with major interest in GEICO, life insurance, annuity sales and sales of jewelry." Among the things it owns is an insurance company named Berkshire Hathaway Group. I assume it's domiciled in Nebraska and subject to Nebraska laws. I'm not a lawyer or an insurance expert, but Google quickly finds me:baw703916 wrote:Maybe I need to reread the Berkshire Hathaway annual report.nisiprius wrote: insurance companies aren't allowed to invest in stocks.
Nebraska Revised Statute 445138
There's a lot of other stuff, such as 445112. Minimum quality ratings and I admit I don't understand what I'm reading, but if you can find anything that says they can use stocks to meet claims obligations I'd like to see it. I'm pretty sure all they are allowed to invest in is investmentgrade bondsand cash.(1) An insurer may invest in:
(a) Bank certificates of deposit, banker's acceptances, or corporate promissory notes with a remaining term of no more than one year; and
(b) Shares, interests, or participation certificates in any management type of investment trust, corporate or otherwise, registered under the Investment Company Act of 1940, as amended, as a diversified openend investment company, that invests solely in such investments as described in subdivision (1)(a) of this section.
(2) Any investment in corporate promissory notes authorized under subdivision (1)(a) of this section shall have a 1 or 2 designation from the Securities Valuation Office. If the Securities Valuation Office does not rate the investment in question but does rate an obligation of the obligor having a priority equal to or lower than the investment in question, the insurer may apply such rating to the investment. If the Securities Valuation Office does not rate the investment in question or an outstanding obligation of the obligor having a priority equal to or lower than the investment in question, the investment shall have a minimum shortterm quality rating of P2 by Moody's Investors Service, Inc., A2 by Standard and Poor's Corporation, or the corresponding investment grade rating from any nationally recognized statistical rating organization recognized by the Securities Valuation Office. If the obligor of an investment is authorized by, established by, or incorporated under the laws of Canada or any province thereof and the Securities Valuation Office does not rate the investment in question, the minimum quality rating shall be R2 by the Dominion Bond Rating Service, A1 by the Canadian Bond Rating Service, or the corresponding rating of any successor organization approved by the director.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

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Re: Long term stock market risk
OK this is quite different from the UK I believe.nisiprius wrote:No, because insurance companies aren't allowed to invest in stocks. They aren't even allowed to invest in junk bonds, but a company called Executive Life Insurance Company managed to pull the wool over the regulators' eyes and do so, and became insolvent in 1991; I'm pretty sure the biggest insolvency in U. S. history.boggler wrote:Come to think of it, isn't this what an annuity is?boggler wrote:What surprises me is that neither of these two things have happened:
 If there truly is less risk over the long term, why is there no fund akin to a stable value fund, but for a very long period of time and based on equities rather than bonds. If the stock market is expected to return, say, 8% every year on average, can't someone simply get an insurance wrap contract to allow long term investors to have stable long term returns over time?
In the UK if they meet minimum solvency requirements (ie bonds, primarily, as assets) then they can invest the surplus in real estate and equities.
Unit linked policies (ie where the performance is not tied to insurance company policy profits) can invest in virtually anything. Equities. Property. etc.
Solvency II is the new global regulation on insurance companies. Tightens up on what counts as solvency.
Re: Long term stock market risk
I don't understand all of it either, but it looks to me like part 445141 allows some investment in stocks.nisiprius wrote:I trust you're joking. In case you are not, there is a company named Berkshire Hathaway which is "A diversified company with major interest in GEICO, life insurance, annuity sales and sales of jewelry." Among the things it owns is an insurance company named Berkshire Hathaway Group. I assume it's domiciled in Nebraska and subject to Nebraska laws. I'm not a lawyer or an insurance expert, but Google quickly finds me:baw703916 wrote:Maybe I need to reread the Berkshire Hathaway annual report.nisiprius wrote: insurance companies aren't allowed to invest in stocks.
Nebraska Revised Statute 445138There's a lot of other stuff, such as 445112. Minimum quality ratings and I admit I don't understand what I'm reading, but if you can find anything that says they can use stocks to meet claims obligations I'd like to see it. I'm pretty sure all they are allowed to invest in is investmentgrade bondsand cash.(1) An insurer may invest in:
(a) Bank certificates of deposit, banker's acceptances, or corporate promissory notes with a remaining term of no more than one year; and
(b) Shares, interests, or participation certificates in any management type of investment trust, corporate or otherwise, registered under the Investment Company Act of 1940, as amended, as a diversified openend investment company, that invests solely in such investments as described in subdivision (1)(a) of this section.
(2) Any investment in corporate promissory notes authorized under subdivision (1)(a) of this section shall have a 1 or 2 designation from the Securities Valuation Office. If the Securities Valuation Office does not rate the investment in question but does rate an obligation of the obligor having a priority equal to or lower than the investment in question, the insurer may apply such rating to the investment. If the Securities Valuation Office does not rate the investment in question or an outstanding obligation of the obligor having a priority equal to or lower than the investment in question, the investment shall have a minimum shortterm quality rating of P2 by Moody's Investors Service, Inc., A2 by Standard and Poor's Corporation, or the corresponding investment grade rating from any nationally recognized statistical rating organization recognized by the Securities Valuation Office. If the obligor of an investment is authorized by, established by, or incorporated under the laws of Canada or any province thereof and the Securities Valuation Office does not rate the investment in question, the minimum quality rating shall be R2 by the Dominion Bond Rating Service, A1 by the Canadian Bond Rating Service, or the corresponding rating of any successor organization approved by the director.
Also, as an example away from Nebraska, http://www.northwesternmutual.com/about ... 294692.pdf indicates that Northwestern Mutual has 12% of its assets in equities (though about a third of that is in real estate which they classify as equities even though some of us might not).
Re: Long term stock market risk
Certainly Berkshire Hathaway the holding company owns stocks. Now maybe the rule applies specifically to regulated subsidiaries in the insurance area (as was the case where *we think* that even if AIG had gone bankrupt, that wouldn't have necessarily meant that all the regulated insurance companies would have gone out of business.nisiprius wrote:I trust you're joking. In case you are not, there is a company named Berkshire Hathaway which is "A diversified company with major interest in GEICO, life insurance, annuity sales and sales of jewelry." Among the things it owns is an insurance company named Berkshire Hathaway Group. I assume it's domiciled in Nebraska and subject to Nebraska laws. I'm not a lawyer or an insurance expert, but Google quickly finds me:baw703916 wrote:Maybe I need to reread the Berkshire Hathaway annual report.nisiprius wrote: insurance companies aren't allowed to invest in stocks.
Nebraska Revised Statute 445138There's a lot of other stuff, such as 445112. Minimum quality ratings and I admit I don't understand what I'm reading, but if you can find anything that says they can use stocks to meet claims obligations I'd like to see it. I'm pretty sure all they are allowed to invest in is investmentgrade bondsand cash.(1) An insurer may invest in:
(a) Bank certificates of deposit, banker's acceptances, or corporate promissory notes with a remaining term of no more than one year; and
(b) Shares, interests, or participation certificates in any management type of investment trust, corporate or otherwise, registered under the Investment Company Act of 1940, as amended, as a diversified openend investment company, that invests solely in such investments as described in subdivision (1)(a) of this section.
(2) Any investment in corporate promissory notes authorized under subdivision (1)(a) of this section shall have a 1 or 2 designation from the Securities Valuation Office. If the Securities Valuation Office does not rate the investment in question but does rate an obligation of the obligor having a priority equal to or lower than the investment in question, the insurer may apply such rating to the investment. If the Securities Valuation Office does not rate the investment in question or an outstanding obligation of the obligor having a priority equal to or lower than the investment in question, the investment shall have a minimum shortterm quality rating of P2 by Moody's Investors Service, Inc., A2 by Standard and Poor's Corporation, or the corresponding investment grade rating from any nationally recognized statistical rating organization recognized by the Securities Valuation Office. If the obligor of an investment is authorized by, established by, or incorporated under the laws of Canada or any province thereof and the Securities Valuation Office does not rate the investment in question, the minimum quality rating shall be R2 by the Dominion Bond Rating Service, A1 by the Canadian Bond Rating Service, or the corresponding rating of any successor organization approved by the director.
Now BRK's biggest insurance operations are in 1) reinsurance, and 2) Geico (mostly auto insurance). Reinsurance is a very different animal, and I just read an article about a "clever" hedge fund scheme to set up a reinsurance company in Bermuda, which could then reinvest their reserves back in the hedge fund (with a more favorable tax treatment, of course). This may be objectionable on several levels, but an insurance company investing in a hedge fund is the aspect I wanted to call attention to. As for Geico, in the neverending speculation about who Buffett's successor might be, it was pointed out at some point that Geico has its own investment portfolio which is not managed directly by Buffett. I got the impression that said portfolio includes stocks...
Finally, Buffett often refers to "float" from insurance operations and the effective cost of capital for his company. The way he words things it certainly doesn't give the impression that said float is walled off from the rest of BRK's finances. That's why I said I may need to reread a report or two.
Brad
Most of my posts assume no behavioral errors.
Re: Long term stock market risk
So... is it too late to take you up on that bet?Higman wrote:My intuitive (and nonmathematical) view of risk compounding over time is this: The Dow closed at 14,000 on Friday. I am willing to bet a large sum of money that at close of business day on Monday it will be in the range of 14,000 +/ 200. I would never make that bet on the Dow closing value one year from now, or worse, 5 years from now. It is too risky of a bet.
Re: Long term stock market risk
Boggler wrote: 
People invest in stocks because stocks have the potential to provide attractive returns precisely because they are risky. The risk premium is the required potential return agreed upon by a consensus of investors to take the chance of making some money vs losing money. The premium varies with time and perception of risk, and there does seem to be some correlation to the P/E or P/E10 ratio. In recent years it appears that investors have been willing to accept a lower premium for the risk they take.
Are stocks riskier over long periods of time? I think you have been given good replies on this by other posters, but I just wanted to offer a view point that's a bit different. Are stocks less risky in the long run? The first thing to note is that the long term is made up of a series of short terms, none of which will resemble the long term average.
Here is what William Coaker, CFP, CIMA, says you will encounter in your investment journey:
Note too that I used a loss of 50%, and that follows the socalled rule of thumb that you can lose 50% of assets invested in stocks in a market crash, but there is absolutely nothing that says losses must stop at 50%. Stocks are riskier than that.
Another frightful thing you might encounter near retirement is an unfavorable sequence of returns. That can have a major effect on your plans. Finally, there is no rule that you must invest all your savings in stocks. My suggestion would be to nvest in stocks, i.e. capitalism, but use some prudence regarding the potential of risk.
Also note that the paper you linked takes on more meaning knowing when it was written  1999.
Paul
Good question and one rarely ever considered by new investors.If instead risk compounds over time the same way returns do, then why does anyone invest in equities in the first place?
People invest in stocks because stocks have the potential to provide attractive returns precisely because they are risky. The risk premium is the required potential return agreed upon by a consensus of investors to take the chance of making some money vs losing money. The premium varies with time and perception of risk, and there does seem to be some correlation to the P/E or P/E10 ratio. In recent years it appears that investors have been willing to accept a lower premium for the risk they take.
Are stocks riskier over long periods of time? I think you have been given good replies on this by other posters, but I just wanted to offer a view point that's a bit different. Are stocks less risky in the long run? The first thing to note is that the long term is made up of a series of short terms, none of which will resemble the long term average.
Here is what William Coaker, CFP, CIMA, says you will encounter in your investment journey:
Ask yourself why stocks are risky in the short term and why no one recommends stocks for short term goals. The answer is because the money may not be there when you need it, and that is because stocks are volatile in the short term. Consider if you need $10,000 for something in 5 years and you put it all in stocks and you lose $5,000 (50%) in year 4. Now consider you need to fund retirement in 30 years and in year 29 you lose half ($500,000). The market does not care that you've saved for 28 years, it only plays by short term possibilities. As you now know from John Norstad's work, the dispersion of possible total asset value widens with time. This is very different than the dispersion of annualized returns getting smaller.Investment professionals often tell clients, “I think the S&P 500 will be up 10 percent next year,” and clients like to hear that. But it almost never happens. From 1926 to 2004, the S&P 500 rose between 8 percent and 14 percent in only six years, an 8 percent occurrence. In fact, just 25 times in 79 years the S&P 500 returned between 0 percent and 20 percent, which is only 32 percent of the time. That means the index has been more than twice as likely to lose money or gain more than 20 percent than to experience returns between 0 percent and 20 percent.
Note too that I used a loss of 50%, and that follows the socalled rule of thumb that you can lose 50% of assets invested in stocks in a market crash, but there is absolutely nothing that says losses must stop at 50%. Stocks are riskier than that.
Another frightful thing you might encounter near retirement is an unfavorable sequence of returns. That can have a major effect on your plans. Finally, there is no rule that you must invest all your savings in stocks. My suggestion would be to nvest in stocks, i.e. capitalism, but use some prudence regarding the potential of risk.
Also note that the paper you linked takes on more meaning knowing when it was written  1999.
Paul
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.
Re: Long term stock market risk
Yes please. It would also be helpful if you can illustrate with an example. (I tried using EV $22 Sd $540, but I don't know what you used for Total money to produce these graphs).assumer wrote:
The equation for risk of ruin (the chance of losing all your money at any time in the future) is:
( (1  EV / Std) / ( 1 + EV / Std ) ) ^ ( Total_Money / Standard Deviation ).
There are also equations for losing $X after Y hours, gaining $X after Y hours, or losing $X before reaching $Z, ad infinitum which I can post if others are curious.
Can it be used with % such as: Expected return 5% per year, Annual Sd 15% ?
Re: Long term stock market risk
Great thread guys.
Consider if I have accumulated enough to see me through retirement and I'm content to deposit mostly in inflation bonds. I might estimate that I'm unlikely to live another 30 years, but would like some insurance to cover beyond 30 years should I outlive that expectation. Equally I'd like to leave an inheritance. I might look at small cap value (SCV) stocks and see that since 1927 there's be no 30 year period of less than 8% real annualised and based on that deposit 10% into buy and hold SCV and deposit the remainder 90% into a 30 year inflation bond ladder. If 30 years later that 8% real annualised growth rate is provided by SCV then the 10% original investment grows to 100% of the original investment amount in inflation adjusted terms. If however after 29 years 364 days SCV halve in value then by 30 years it might not have met its growth objective.
In view of that risk I might opt to alternatively invest the 'growth' element maybe in something like 22% SCV, 14% gold, 64% bonds and perhaps estimate that that has a 4% annualised real reward expectancy  and as such I should deposit 30% initially into that, and invest the remainder 70% in inflation bonds (i.e. 30% investment in 4% real annualised for 30 years grows to 100% of the original (approximately)).
For the former with 90% initially deposited into inflation bonds to support 30 years of income, I have 3% each year income being provided. For the latter with 70% in inflation bonds I have 2.33% each year income. That 0.66% difference in income amounts might make little difference to my own living standard, which is pretty well secured for the next 30 years. The risk of opting for the 10% initial investment all in SCV compared to investing 30% in a more diverse asset allocation is carried by my kids (or if I live beyond 30 years).
After 29 years, with most of the 'income' pot having been spent and just the remainder 'growth' pot remaining, the risk of all of that growth pot being in SCV is higher than having the growth pot invested more diversely. A single outlier event such as 2008/9 could significantly impact the final 30 year result.
I'd suggest its fractal and the potential risk/rewards for longer term are the same as for shorter periods. Opt for higher risk and the rewards might be significantly greater, but at the risk of returns being significantly less than expected. Opt for a more conservative choice and the range of outcomes are more centralised. Single outlier events that induce sizeable moves down (or up) can impact longer term results as equally as they do shorter term results.
Why invest in stocks  because they're a means to diversify. How safer are the alternatives individually?pkcrafter wrote:Boggler wrote: Good question and one rarely ever considered by new investors.If instead risk compounds over time the same way returns do, then why does anyone invest in equities in the first place?
People invest in stocks because stocks have the potential to provide attractive returns precisely because they are risky. The risk premium is the required potential return agreed upon by a consensus of investors to take the chance of making some money vs losing money. The premium varies with time and perception of risk, and there does seem to be some correlation to the P/E or P/E10 ratio. In recent years it appears that investors have been willing to accept a lower premium for the risk they take.
Are stocks riskier over long periods of time? I think you have been given good replies on this by other posters, but I just wanted to offer a view point that's a bit different. Are stocks less risky in the long run? The first thing to note is that the long term is made up of a series of short terms, none of which will resemble the long term average.
Here is what William Coaker, CFP, CIMA, says you will encounter in your investment journey:Investment professionals often tell clients, “I think the S&P 500 will be up 10 percent next year,” and clients like to hear that. But it almost never happens. From 1926 to 2004, the S&P 500 rose between 8 percent and 14 percent in only six years, an 8 percent occurrence. In fact, just 25 times in 79 years the S&P 500 returned between 0 percent and 20 percent, which is only 32 percent of the time. That means the index has been more than twice as likely to lose money or gain more than 20 percent than to experience returns between 0 percent and 20 percent.
Ask yourself why stocks are risky in the short term and why no one recommends stocks for short term goals. The answer is because the money may not be there when you need it, and that is because stocks are volatile in the short term. Consider if you need $10,000 for something in 5 years and you put it all in stocks and you lose $5,000 (50%) in year 4. Now consider you need to fund retirement in 30 years and in year 29 you lose half ($500,000). The market does not care that you've saved for 28 years, it only plays by short term possibilities. As you now know from John Norstad's work, the dispersion of possible total asset value widens with time. This is very different than the dispersion of annualized returns getting smaller.
Note too that I used a loss of 50%, and that follows the socalled rule of thumb that you can lose 50% of assets invested in stocks in a market crash, but there is absolutely nothing that says losses must stop at 50%. Stocks are riskier than that.
Another frightful thing you might encounter near retirement is an unfavorable sequence of returns. That can have a major effect on your plans. Finally, there is no rule that you must invest all your savings in stocks. My suggestion would be to invest in stocks, i.e. capitalism, but use some prudence regarding the potential of risk.
Consider if I have accumulated enough to see me through retirement and I'm content to deposit mostly in inflation bonds. I might estimate that I'm unlikely to live another 30 years, but would like some insurance to cover beyond 30 years should I outlive that expectation. Equally I'd like to leave an inheritance. I might look at small cap value (SCV) stocks and see that since 1927 there's be no 30 year period of less than 8% real annualised and based on that deposit 10% into buy and hold SCV and deposit the remainder 90% into a 30 year inflation bond ladder. If 30 years later that 8% real annualised growth rate is provided by SCV then the 10% original investment grows to 100% of the original investment amount in inflation adjusted terms. If however after 29 years 364 days SCV halve in value then by 30 years it might not have met its growth objective.
In view of that risk I might opt to alternatively invest the 'growth' element maybe in something like 22% SCV, 14% gold, 64% bonds and perhaps estimate that that has a 4% annualised real reward expectancy  and as such I should deposit 30% initially into that, and invest the remainder 70% in inflation bonds (i.e. 30% investment in 4% real annualised for 30 years grows to 100% of the original (approximately)).
For the former with 90% initially deposited into inflation bonds to support 30 years of income, I have 3% each year income being provided. For the latter with 70% in inflation bonds I have 2.33% each year income. That 0.66% difference in income amounts might make little difference to my own living standard, which is pretty well secured for the next 30 years. The risk of opting for the 10% initial investment all in SCV compared to investing 30% in a more diverse asset allocation is carried by my kids (or if I live beyond 30 years).
After 29 years, with most of the 'income' pot having been spent and just the remainder 'growth' pot remaining, the risk of all of that growth pot being in SCV is higher than having the growth pot invested more diversely. A single outlier event such as 2008/9 could significantly impact the final 30 year result.
I'd suggest its fractal and the potential risk/rewards for longer term are the same as for shorter periods. Opt for higher risk and the rewards might be significantly greater, but at the risk of returns being significantly less than expected. Opt for a more conservative choice and the range of outcomes are more centralised. Single outlier events that induce sizeable moves down (or up) can impact longer term results as equally as they do shorter term results.

 Posts: 6019
 Joined: Mon Jan 03, 2011 9:40 am
Re: Long term stock market risk
I used to be one that believed stocks were riskier in the long run until I ran the actual numbers comparing 2 different type of investors one would see in the real world (not the stupid 100% SP500 vs. 100% cash anaylsis that everyone likes to use).
I looked at 2 types of investors: One that is 80/20 and another that is 50/50. Equities were sp500 or DJ (don't remember which) and bonds were 10 yr. treasuries. I looked at them in every rolling period from 1926 current. I looked at 5, 10, 15 yr.,and 20 year periods. Here is the data:
5 year rolling: 80%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <20% the balanced portfolio
10 year rolling: 85%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <15% the balanced portfolio
15 year rolling: 95%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <5% the balanced portfolio
20 year rolling: 98%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <2% the balanced portfolio
Now folks will come up and say that this is "just" the history from 1926 current and will say the last 80+ years of data is not useful. Instead they will throw out ideas that have NO DATA to support their claims. It is up to the investor to see what the data means to them. It is simple you either invest with the PROBABILITIES (within a 1 or 2 S.D. outcome) which would have you higher in equites OR the POSSIBILITY of something bad happening (the 2+ S.D. outcome) which would put you in a more balanced portfolio.
Now the folks on here love to quote Norstad's article (I never understood why as I find it poorly written and not surprised is not mentioned by ANYONE other then his friends on Bogleheads) which says there is no time diversification effect with equities. That is funny because my data crunching above I think CLEARLY shows that is not true when the data is looked at differently.
My opinion, there are MANY folks suffering from recency bias where stocks have been doing poorly at the same time bonds have done very well making folks think why take on the extra risk when the difference in returns have been so close or blatantly in favor of bonds. Also, there are many on here that are in the deaccumulation mode for which they are right high volatility is NOT desirable as on HAS to draw money out of the portfolio.
Good luck.
Good luck.
I looked at 2 types of investors: One that is 80/20 and another that is 50/50. Equities were sp500 or DJ (don't remember which) and bonds were 10 yr. treasuries. I looked at them in every rolling period from 1926 current. I looked at 5, 10, 15 yr.,and 20 year periods. Here is the data:
5 year rolling: 80%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <20% the balanced portfolio
10 year rolling: 85%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <15% the balanced portfolio
15 year rolling: 95%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <5% the balanced portfolio
20 year rolling: 98%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <2% the balanced portfolio
Now folks will come up and say that this is "just" the history from 1926 current and will say the last 80+ years of data is not useful. Instead they will throw out ideas that have NO DATA to support their claims. It is up to the investor to see what the data means to them. It is simple you either invest with the PROBABILITIES (within a 1 or 2 S.D. outcome) which would have you higher in equites OR the POSSIBILITY of something bad happening (the 2+ S.D. outcome) which would put you in a more balanced portfolio.
Now the folks on here love to quote Norstad's article (I never understood why as I find it poorly written and not surprised is not mentioned by ANYONE other then his friends on Bogleheads) which says there is no time diversification effect with equities. That is funny because my data crunching above I think CLEARLY shows that is not true when the data is looked at differently.
My opinion, there are MANY folks suffering from recency bias where stocks have been doing poorly at the same time bonds have done very well making folks think why take on the extra risk when the difference in returns have been so close or blatantly in favor of bonds. Also, there are many on here that are in the deaccumulation mode for which they are right high volatility is NOT desirable as on HAS to draw money out of the portfolio.
Good luck.
Good luck.
"The stock market [fluctuation], therefore, is noise. A giant distraction from the business of investing.” 
Jack Bogle
Re: Long term stock market risk
For those easily bored by math, skip this postVerde wrote:Yes please. It would also be helpful if you can illustrate with an example. (I tried using EV $22 Sd $540, but I don't know what you used for Total money to produce these graphs).assumer wrote:
The equation for risk of ruin (the chance of losing all your money at any time in the future) is:
( (1  EV / Std) / ( 1 + EV / Std ) ) ^ ( Total_Money / Standard Deviation ).
There are also equations for losing $X after Y hours, gaining $X after Y hours, or losing $X before reaching $Z, ad infinitum which I can post if others are curious.
Can it be used with % such as: Expected return 5% per year, Annual Sd 15% ?
For this particular instance I used a pool of $10,000.
Here are the inputs:
Long term
Pool: $10,000
Long Term Goal: $20,000
EV: $22 / time period
Standard Deviation: $540 / time period
Short term
Short term time periods: 10
Short term pool: $2,000
Short term goal: $3,000
Short term results: $650
Here are the outputs:
Long Term
Risk of Ruin (probability of losing $10,000 ever):
=( ( 1  EV / Std ) / ( 1 + EV / Std ) ) ^ ( Pool / Std )
= ( ( 1  22 / 540 ) / ( 1 + 22 / 540 ) ) ^ ( 10000 / 540 ) = 22%
Long Term Goal (probability of reaching $20,000 ever):
=EXP( EV / Var *(Goal  Pool ) )*SINH( EV / Var * Pool )/ SINH( EV / Var * Goal )
=EXP( 22 / 540^2 * ( 20000  10000 ) ) * SINH( 22 / 540^2 * 10000 ) / SINH( 22 / 540 * 20000 )
= 82%
where EXP( x ) is e^x and SINH( x ) is the hyperbolic sinusoidal equation.
Probability of losing $10,000 before reaching $20,000:
= 100%  82% = 18%
Short Term
Short Term EV:
= EV * Time_Periods
= $22 * 10
= $220
Short Term Std:
= Std * sqrt( Time_Periods )
= $540 * sqrt( 10 )
= $1710
Short term risk of ruin (probability of losing $2,000 within 10 time periods):
= CUMNORM( (Short_Term_Pool  Short_EV )/ Short_Std ) + EXP( 2 * Short_EV * Short_Term_Pool / Short_STD^2 ) * CUMNORM( (Short_Term_Pool + Short_EV ) / Short_STD )
where CUMNORM is the cumulative normal distribution, or "NORM.DIST( x, 0, 1, TRUE)" for "x" in excel.
= (excel formula)
NORM.DIST( (2000  220 )/ 1710 ), 0, 1, TRUE ) + EXP( 2 * 220 * 2000 / 1710^2 ) * NORM.DIST( ( 2000 + 220 ) / 1710, 0, 1, TRUE )
= 21%
Probability of losing $2,000 before reaching $3,000 sometime within 10 time periods:
= EXP( EV / Std^2 * Short_Term_Pool ) * ( SINH( Short_EV / Short_Std^2 * ( Short_Term_Goal  Short_Term_Pool ) ) / SINH( EV / Std * Short_Term_Goal )  Short_Term_Std^2 / ( Short_Term_Goal )^2 * (Summation) )
Okay this one you need to do some tricky math to get the final "Summation" term. Now here's where I have to admit that these equations are from my blackjack days. The equation for how to get the summation is on page 137 of the mathematicallyheavy book "Blackjack Attack, 3rd edition", which I don't have offhand right now. The reason is that there is not a closedform solution of this equation, and you have to estimate it with a seriesexpansion.
Regardless, the "Summation" term for this particular situation is 336.
The final probability ends up being 19%. Private message me if you want more information on these timeconstrained, shortterm goal, equations, and I'll see if I can dig up that old book. It's in my excel sheet already so I haven't referred back to the book in a while.
There is also an equivalent equation for "Probability of Reaching $3,000 before losing $2,000 within 10 time periods", for which there is also not a closed form solution, but it ends up being 60%.
Therefore, the "probability of always being between $0 and $3,000 for all 10 time periods" is 100%  19%  60% = 21%.
I'm sure the investment banking institutions also have all these equations and use them frequently to estimate risk and return, but I don't know much about the industry.
Surprisingly or not, these equations are for a very simple distribution (Gaussian, or Normal). When you start getting to nonGaussian distributions coming up with closedform equations for these situations is nearimpossible. I'm sure montecarlo simulations would be better suited for such a task, and coding it would actually be pretty straightforward.
Not without modification.Can it be used with % such as: Expected return 5% per year, Annual Sd 15% ?
This assumes a CONSTANT expected value and standard deviation (in terms of $) over the time periods. This is not directly applicable for a constant percentage gains, in which the EV (in terms of $) is nonconstant. The equations would need some fudging to account for that, which I don't have time to do right now.
I've veered way off topic here, but my original point regarding the variance over time holds, when you consider how the graph I posted expands over time, but also the risk of ruin decreases over time.
Re: Long term stock market risk
You say stocks are not risky in the long run, but does your data suggest they are risky in the short term? If so, what do you consider short term? Your data shows that 80% of the time the 80/20 outperforms and when it doesn't there is only <20% of the time it underperforms more than the 50/50 portfolio. That makes it sound like even at 5 years an 80/20 portfolio isn't all that risky.staythecourse wrote:I used to be one that believed stocks were riskier in the long run until I ran the actual numbers comparing 2 different type of investors one would see in the real world (not the stupid 100% SP500 vs. 100% cash anaylsis that everyone likes to use).
I looked at 2 types of investors: One that is 80/20 and another that is 50/50. Equities were sp500 or DJ (don't remember which) and bonds were 10 yr. treasuries. I looked at them in every rolling period from 1926 current. I looked at 5, 10, 15 yr.,and 20 year periods. Here is the data:
5 year rolling: 80%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <20% the balanced portfolio
10 year rolling: 85%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <15% the balanced portfolio
15 year rolling: 95%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <5% the balanced portfolio
20 year rolling: 98%+ of the time the 80/20 outperformed and the times it didn't it underpeformed AT WORST <2% the balanced portfolio
Now folks will come up and say that this is "just" the history from 1926 current and will say the last 80+ years of data is not useful. Instead they will throw out ideas that have NO DATA to support their claims. It is up to the investor to see what the data means to them. It is simple you either invest with the PROBABILITIES (within a 1 or 2 S.D. outcome) which would have you higher in equites OR the POSSIBILITY of something bad happening (the 2+ S.D. outcome) which would put you in a more balanced portfolio.
Now the folks on here love to quote Norstad's article (I never understood why as I find it poorly written and not surprised is not mentioned by ANYONE other then his friends on Bogleheads) which says there is no time diversification effect with equities. That is funny because my data crunching above I think CLEARLY shows that is not true when the data is looked at differently.
My opinion, there are MANY folks suffering from recency bias where stocks have been doing poorly at the same time bonds have done very well making folks think why take on the extra risk when the difference in returns have been so close or blatantly in favor of bonds. Also, there are many on here that are in the deaccumulation mode for which they are right high volatility is NOT desirable as on HAS to draw money out of the portfolio.
Good luck.
Good luck.
Paul
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.