Options for fixed payouts

How much in monthly payouts are you seeking?

How long is "long term" for you?

Can you talk about how much risk you can tolerate? E.g. I think a financial planner or various asset allocations could set you up with a stock and bond portfolio that yield 3% ($1000/month) right now, with low risk to principal for a

20-year-period, and a very strong likelihood that the principal will grow. The monthly payment could grow, too, via selecting stocks with records of dividend growth.

Short term CD's are paying over 5% now, with no risk to principal.

Exactly my point in the exchange above. Why on earth would anyone even suggest a portfolio yielding 3% which is inherently riskier than a CD or MM yielding 1-2% more?

Elizabeth Richardson

wrote

Historical data also indicates that, for long periods, there is no risk to principal with stocks. Also, "the volatility of stocks decreases more rapidly than the volatility of either bonds or T-bills. For holding periods longer than 20 years, a fully diversified stock portfolio is on average less volatile than either a bond portfolio or a T-bill portfolio... [T]his is even more true when the results are adjusted for inflation."

See also (chart on page 11)

(United Kingdom data, Table 1)

These two sources seem to disagree. The first has some major typos and shows no data: "If for example the anticipated rate of return for a portfolio is 10% per year (0.85% per month) with a standard deviation of

2.71 the reality is that the rate of return will be somewhere between 3.56% and -1.86% per month two-thirds of the time, and between 6.27% and

-4.57% per month one-third of the time. There is a one-in-six chance that the monthly return will be below -1.86%."

The second disagrees with itself as well as the first when it looks at real data, "If I look at quarterly US data for the period since World War II, I get a somewhat different picture... The annualized standard deviation of a T-bill strategy is about 1.5% over a quarter and 3% over

25 years... with stock market risk measured at 16% for short-term investors and... 8% for 25-year investors." It seems this dude's model may have been useful for showing some long vs. short term investing strategy differences, but his own data contradicts your statement above, doesn't it?

-Will

The paragraph from which the quotation above cites Jeremy Siegel (_Stocks for the Long Run_).

snip excerpt from a different section of the site above. It might go to credibility, but it does not address my quotation above. I am not sure that the numbers in the excerpt you gave are that far off, anyway. My quick review says no. I hesitate to do a complete analysis of that excerpt, because it strays from the main disagreement we are having.

I suspect "stock market risk" here is not meant to be synonymous with "stock market standard deviation." That 8% for 25-year investors sure does not seem like an SD.

You are welcome to seek sources which assert as you appear to claim: The long term volatility of investment grade bonds is lower than than for stocks.

Forgive me, it's been more than 15 years since I took statistics... I believe the above analagy and the two posts which follow are comparing Oranges to the performance of the Buffalo Bills...

"anticpated return of a portfolio is 10%" OK so far... "standard deviation of 2.71" OK so far... my understanding would be

2.71 is the number of units (percentage points in this case) which the 10% will change 75% of the time (so 75% of the time the returns are between 7.29 and 12.71%). The 75% if the bell curve type deal... .85% per month- why use this number?- it is 10%/12 months, but the assumption that all months have an "equal return" or "equal contribution to return" is a little much. "the reality is that the rate of return will be somewhere between 3.56% and -1.86% per month two-thirds of the time, and between 6.27% and

-4.57% per month one-third of the time. There is a one-in-six chance that the monthly return will be below -1.86%"- this is just BAD MATH. If the .85 % per month is used, the standard deviation of 2.71 would also needed to be divided by 12 (for deviation per month) correct?

I am an Engineer by degree, so any business types with a larger knowledge than me can pick this apart (and feel free to show me the error of my ways), but to me the error appears in how one determines the deviation and to which numbers the deviation applies to.

The reason bonds have a higher "long term" volatility than stocks is that returns will be confined in most probability to between 3-8% per year for bonds. Just guessing at these for what I would expect if I invested in bonds. However the change in returns would be "higher percentages" of the overall return. 1 basis point difference for a bond returning 8% is 12.5 (1%/8%.5%). One basis point for a stock returning 20% is a much less percentage of the overall return (5%,

1%/20%=5%). CD's have an even more restricted return (probably between 0-5%), so a 1% change in return for a CD is an even higher volatility than for bonds or stocks.

The primary goal of investing is probably overall return. Volatility is something used to measure the principal value of the portfolio changing from year to year and is often used to measure risk of the principle.

The goal of adding bonds is to reduce volatilty of the portfolio, even if the bond returns in and of themselves are more "volatile". Same with CDs. They are used primarily to keep the principal value of a portfolio "relatively constant".

"jIM" wrote quoting what I think must be a partial rough draft of a book

Whence with some caveats, a monthly SD of 2.71/sqrt(12) 0.78 is often assumed.

Correcting bad math and improving upon arguably poor presentation, I think they meant to write something more like {the reality is that the monthly rate of return will be somewhere between 0.07% and 1.63% per month 68% of the time. There is about a one-in-six chance that the monthly return will be below 0.07%.}.

I think the authors were just trying to point out the hazard of using "average returns" of stocks. They want people to understand short term volatility.

Short term volatility of returns, AFAIC.

Indeed, but in what context? I haven't read the book...

As Jim and Joe have pointed out, this is way bad math (technical term).

Hmm, the paper is littered with areas where he uses the terms synonymously, e.g paragraphs 1 and 2 on page 5. He sure implies this in the section I quoted. What do you think he means?

I think your sources (the ones that can do math better than me) do this just fine.

-Will

That may be, and it's a worthy goal. But Flipping from monthly returns and SD to Annual, and then posting wrong results either through typos or miscalculation, is only going to further the belief that this topic is simply not to be understood. Seems to me, your post as copied here, is the most understandable view of this topic (the topic is that SD shrinks over longer time spans, right?);

copy of Elle's SD chart------------ It shows that the average returns for all time periods are about 10% per year. But the SDs vary a great deal.

Time Period, SD

1 year, 18% ( = good chance of having a large negative return) 5 years, 8% ( = much less chance of a large negative return) 10 years, 5% ( = tiny chance of a negative return) 15 years, 4% (worst annualized return was +1%) 20 years, 3% (worst annualized return was +3%) 25 years, 3% (worst annualized return was +5%) 30 years, 2% (worst annualized return was +5%)

"joetaxpayer" wrote

You're right, and Will is right. It's a shabby piece. I surfed that whole site more and became increasingly displeased. Still, I am not yet sure whether that quotation I provided is off the mark. I suspect it is consistent with Siegel's _Stocks for the Long Run_ theses, as implied subsequently in the piece.

It shrinks for stocks, yes, but I think the bigger point of contention is what it does for bonds. After a lot of searching, I can't turn up a whole lot on this, even though it seems like something worth really driving home to long term financial planners of all stripes. (Even less on housing volatility is available.) Maybe it's obvious? Jim's comments on why he expects bond volatility to rise the longer the term may be right on the money. Also, I agree factoring in inflation makes the volatility differences between stocks and bonds even greater as the term gets longer.

The main theme is that an all-stock allocation is superior for the long run, risk-wise and return-wise.

We do not agree about what my sources state. What would be more helpful to this discussion is if you produced fresh sources that explicitly state what you seem to claim: That the standard deviation of bond returns for long terms is lower than that for stocks.

Well, the sources I'll cite are not necessarily fresh. First, there is my previous quote about *actual market data* from

Then I'll direct you to the Monte Carlo simulation on the site you cited: Run it for stocks over 20 years, and then for bonds over 20 years. Compare the widths of the bell curves (which is described by the standard deviation). You'll find the bond curve to be considerably narrower.

-Will

"Will Trice" wrote

Go to the custom setting. Manually put in the fixed bond's settings of 6% return and 7% standard deviation. Compare in a second window to the bond setting, using 5 years and 20 years. This software is extrapolating somehow from the short-term volatilities and not indicating long term SDs derived from historical data. All it is demonstrating is a reversion to the mean with enough 'rolls of the dice' ( years of stock or bond returns), which is what one would expect from a Monte Carlo simulation. As usual I did not cite this link in support of the point you imply.

Not sure I follow you here. I used the custom setting as you suggest above, and not surprisingly, it gives more-or-less the same answer.

As to reversion to the mean, this is what you would expect over the long term. Why do you think SDs get narrower over long time periods?

-Will

I thought the inflation thing might be worth investigating so I've been playing around with Shiller's data at:

Using the long bond data in his spreadsheet, I constructed an index (I'm unable to locate any freely available bond index data that contains more than 10 years worth of values) and computed 30 year annualized returns and volatilities, with and without adjusting for inflation, for both long bonds and the S&P.

Here's what I turned up:

S&P (dividend adjusted) Nominal 30 year average annualized return: 9.2% Standard deviation: 2.23% Real 30 year average annualized return: 6.47% Standard deviation: 1.72%

Long Bonds Nominal 30 year average annualized return: 4.6% Standard Deviation: 1.9% Real 30 year average annualized return: 2% Standard deviation: 1.3%

Keep in mind that using a bond index approach like this artificially increases volatility because it does not allow for holding bonds until maturity.

I did the same for home returns using Shiller's data at:

With this we have:

Home prices Nominal 30 year average annualized return: 3.4% Standard deviation: 1.7% Real 30 year average annualized return: 0.27% Standard deviation: 1%

Thus showing that stock risk > long bond risk > home risk, defining risk as the standard deviation on 30 year annualized returns.

As always, check my math...

-Will

"Will Trice" wrote Re the site

and long term volatilities of stocks and bonds> Not sure I follow you here. I used the custom setting as > you suggest above, and not surprisingly, it gives > more-or-less the same answer. Right, not exactly the same, because the Monte Carlo trials vary somewhat on each run. All the software is doing, I bet, is dividing the SD for the short periods by sqrt(long period/short period) and generating the random distribution of the same using MC trials. The software assumes, somewhat misleadingly, that stock and bond returns comport to a random distribution. The result is that the site above is contrived and says nothing about whether the actual long term volatility of bonds is below that of stocks.

Regardless, my "tunnel vision" post of a day or so ago offers an explanation of why the relation between stock and bonds' long term volatilities is probably moot and so one cannot easily find anything credible and truly dispositive on either your claim or my claim.

If this were true then it would not be a Monte Carlo simulator. Instead, each pass will take n random draws against a Gaussian distribution for the n year simulation, each draw using the input average and standard deviation (i.e. the single year arithmetic average and the standard deviation of that average). It will then calculate the total return using all the draws and dump the result in one of the histogram bins on the chart. Rinse, repeat. After many passes like this the histogram chart will fill out (that's why you see it grow). No need to divide by the square-root of anything, although doing this would avoid having to use the Monte Carlo simulator.

Well, they do. It just may not be Gaussian, or known, or stable. If you recall from a thread a while back, I'm a big proponent of not using Gaussian distributions when modelling short-term returns. But even the biggest fat-tail distribution guru admits that, long-term, the distributions of asset returns gets to be pretty darn Gaussian. And even short-term, Gaussian distributions are useful for gross modelling.

In an earlier post I showed results from actual data that this is indeed the case.

Sorry, I don't know which post you're referring to, but why don't you believe the published data that you cited? Namely, the Campbell paper, "Strategic Asset Allocation". He talks about actual data in the second-to-last paragraph on page 6.

-Will

Because of quotations like the following, the truth about the relationship between stock and bond long term volatilities remains to me an exploration.

"Research shows clearly that over periods of 20 years or more, stocks are no more risky -- in fact, less risky -- than bonds or Treasury bills." -- Congressional Testimony, James K. Glassman, 1998

"It is widely known that stock returns, on average, exceed bonds in the long run. But it is little known that in the long run, the risks in stocks are less than those found in bonds or even bills." -- Siegel, as quoted by Glassman above.

"Siegel notes that the risk inherent in stocks never disappears no matter how long you are invested. What does diminish over time is the risk of holding stocks versus that of bonds. The relative risk of stocks is below that of bonds. Over long periods of time, stocks were more stable than would have been expected from their year-to-year volatility. However, that was not true for bonds. Stocks, being claims on real assets, respond much better to inflation risk."