## Range of Outcomes for Different Stock/Bond Allocations

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Topic Author
Langer83
Posts: 5
Joined: Wed Aug 19, 2015 12:46 pm

### Range of Outcomes for Different Stock/Bond Allocations

I'm hoping to find a good resource that shows the range of outcomes for different stock and bond allocations over different time periods. For example, say I have \$1 million now and a 60/40 stock-bond split, what would be the range of expected balances in 1, 2, 5, 10, and 20 years (Say the 10th , 50th, and 90th percentile, but other ranges would work). What about for an 80/20 allocation? This could be an online calculator of some sort where users could input values, or it could be a table/graph in an existing resource. I could translate rates of returns into dollars if that's what's available. I guess it would probably be based on Monte Carlo simulations, but any sort of analysis would work.

I've looked around a bit and the existing data I've seen do give me a real intuitive sense of what I'm gaining in security by giving up some returns. The annual standard deviation of returns doesn't mean much to me, and the best/worst year on record for different allocations also doesn't mean much to me.

Any help would be great appreciated. Thanks!
dbr
Posts: 36362
Joined: Sun Mar 04, 2007 9:50 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

That is a good question though I am not aware of a calculator that comes to mind.

But why does the standard deviation of annual returns not mean anything to you? It is the first cut answer to the question.

Come to think of it though, you could go to a program like FireCalc, enter zero spending, and select a portfolio from the assets it does allow you to use. The output is a chart of what would have happended over the next n years to that investment had it been made in any of a hundred odd years in the past. This is like MC except that the various runs are based on the actual history of past years. Maybe other retirement planners can output the information using zero spend. Some are MC based and some are historical periods based.
M B
Posts: 198
Joined: Mon Jul 11, 2011 5:58 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

These (esp. figures), although not quite designed for it, may provide some answers:
http://mathieu.bouville.name/finance/wh ... erm-start/
http://mathieu.bouville.name/finance/ri ... -term.html
dbr
Posts: 36362
Joined: Sun Mar 04, 2007 9:50 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

M B wrote:These (esp. figures), although not quite designed for it, may provide some answers:
http://mathieu.bouville.name/finance/wh ... erm-start/
http://mathieu.bouville.name/finance/ri ... -term.html

It might help the OP if you could explain the methodology by which those charts are produced. I am thinking of the issue about why he thinks standard deviation of returns doesn't relate, etc.
rca1824
Posts: 719
Joined: Tue Jun 03, 2014 9:33 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

Langer83 wrote:I'm hoping to find a good resource that shows the range of outcomes for different stock and bond allocations over different time periods. For example, say I have \$1 million now and a 60/40 stock-bond split, what would be the range of expected balances in 1, 2, 5, 10, and 20 years (Say the 10th , 50th, and 90th percentile, but other ranges would work). What about for an 80/20 allocation? This could be an online calculator of some sort where users could input values, or it could be a table/graph in an existing resource. I could translate rates of returns into dollars if that's what's available. I guess it would probably be based on Monte Carlo simulations, but any sort of analysis would work.

I've looked around a bit and the existing data I've seen do give me a real intuitive sense of what I'm gaining in security by giving up some returns. The annual standard deviation of returns doesn't mean much to me, and the best/worst year on record for different allocations also doesn't mean much to me.

Any help would be great appreciated. Thanks!
Like this?

worst

Code: Select all

``````equity       1      2      5     10     20
0%  -11.1%  -3.3%  -0.4%   0.8%   1.6%
20%  -10.8%  -6.2%   0.6%   3.2%   3.5%
40%  -19.1% -13.4%  -2.2%   2.9%   3.6%
60%  -27.3% -20.6%  -5.4%   1.8%   3.5%
80%  -35.6% -27.9%  -8.9%   0.3%   3.1%
100%  -43.8% -35.2% -12.7%  -1.7%   2.4%
``````
median

Code: Select all

``````equity       1      2      5     10     20
0%    3.4%   3.3%   4.2%   4.0%   3.9%
20%    5.7%   5.4%   5.4%   5.2%   5.1%
40%    8.4%   7.8%   7.3%   6.8%   7.6%
60%   10.4%   9.9%   8.7%   8.4%   9.0%
80%   13.1%  10.2%  10.0%   9.4%  10.7%
100%   14.5%  12.0%  10.6%   9.9%  11.7%
``````
best

Code: Select all

``````equity       1      2      5     10     20
0%   32.8%  25.0%  19.5%  13.7%  10.7%
20%   30.3%  25.0%  19.6%  14.5%  11.8%
40%   29.0%  24.9%  19.6%  15.3%  13.3%
60%   32.9%  25.7%  20.1%  16.0%  14.8%
80%   42.7%  34.0%  24.2%  17.3%  16.2%
100%   52.6%  42.2%  28.3%  20.1%  17.7%
``````
Monthly or yearly movements of stocks are often erratic and not indicative of changes in intrinsic value. Over time, however, stock prices and intrinsic value almost invariably converge. ~ WB
livesoft
Posts: 76846
Joined: Thu Mar 01, 2007 8:00 pm

### Re: Range of Outcomes for Different Stock/Bond Allocations

Close to what you want, but probably not exactly:

http://paulmerriman.com/fine-tuning-you ... tion-2014/
This signature message sponsored by sscritic: Learn to fish.
bigred77
Posts: 2042
Joined: Sat Jun 11, 2011 4:53 pm

### Re: Range of Outcomes for Different Stock/Bond Allocations

I LOVE playing with these tools. Bear in mind this data references fairly strong small and value tilts, as wells as a hefty slub of international in their portfolios:

https://www.ifa.com/portfolios/60
kolea
Posts: 1322
Joined: Fri Jul 11, 2014 5:30 pm
Location: Maui and Columbia River Gorge

### Re: Range of Outcomes for Different Stock/Bond Allocations

It is fun to play with numbers but you have to be aware that the key parameters (bond interest, dividend rate, inflation rate) all vary a lot so the real interesting thing to look at is the envelope of returns over a wide variety of the above parameters. I used to like to tweak one parameter (like inflation) while holding the rest constant to see what the sensitivity is to that one parameter. In general it is a bad idea to try to use these simulations as a prediction of anything, but I think it is useful to see where the portfolio sensitivities lie and what a change in AA does to those sensitivities.
Kolea (pron. ko-lay-uh). Golden plover.
grayfox
Posts: 5569
Joined: Sat Sep 15, 2007 4:30 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

Langer83 wrote:I'm hoping to find a good resource that shows the range of outcomes for different stock and bond allocations over different time periods. For example, say I have \$1 million now and a 60/40 stock-bond split, what would be the range of expected balances in 1, 2, 5, 10, and 20 years (Say the 10th , 50th, and 90th percentile, but other ranges would work). What about for an 80/20 allocation? This could be an online calculator of some sort where users could input values, or it could be a table/graph in an existing resource. I could translate rates of returns into dollars if that's what's available. I guess it would probably be based on Monte Carlo simulations, but any sort of analysis would work.

I've looked around a bit and the existing data I've seen do give me a real intuitive sense of what I'm gaining in security by giving up some returns. The annual standard deviation of returns doesn't mean much to me, and the best/worst year on record for different allocations also doesn't mean much to me.

Any help would be great appreciated. Thanks!
If you know the portfolio mean and sd, can you not use the 68-95-99.7 Rule to estimate those percentile ranges as +/-1, 2 and 3 sd''s from the mean?

https://en.wikipedia.org/wiki/68–95–99.7_rule

Also, rca has a pretty good table. However, if you want the Total Return, or how much money you end up with, you will have to compound it out over the number of years. to get to the actual values. Why not just use that table?
rca1824
Posts: 719
Joined: Tue Jun 03, 2014 9:33 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

grayfox wrote:
Langer83 wrote:I'm hoping to find a good resource that shows the range of outcomes for different stock and bond allocations over different time periods. For example, say I have \$1 million now and a 60/40 stock-bond split, what would be the range of expected balances in 1, 2, 5, 10, and 20 years (Say the 10th , 50th, and 90th percentile, but other ranges would work). What about for an 80/20 allocation? This could be an online calculator of some sort where users could input values, or it could be a table/graph in an existing resource. I could translate rates of returns into dollars if that's what's available. I guess it would probably be based on Monte Carlo simulations, but any sort of analysis would work.

I've looked around a bit and the existing data I've seen do give me a real intuitive sense of what I'm gaining in security by giving up some returns. The annual standard deviation of returns doesn't mean much to me, and the best/worst year on record for different allocations also doesn't mean much to me.

Any help would be great appreciated. Thanks!
If you know the portfolio mean and sd, can you not use the 68-95-99.7 Rule to estimate those percentile ranges as +/-1, 2 and 3 sd''s from the mean?

https://en.wikipedia.org/wiki/68–95–99.7_rule

Does standard deviation have much meaning in this case? Stock returns aren't a normal distribution. That's why I like to use "best" and "worst" returns to get a sense of the range. There's also something wrong with the standard deviation calculation with bonds .. 20-year bond holdings have more variance than 20-year stock holdings, and I know that can't be right. I think it's because interest rates have changed so much since 1926. A better model would be to just assume bonds will return their current yield, but stocks will follow the same kind of random walk. I'm working on a Monte Carlo simulator next. The problem is bond returns are NOT iid because their terminal value is predetermined upon purchase - only stocks are a random walk. I think a more nuanced model would treat current interest rates as the semi-random walk, then derive the sequence of bond returns from the sequence of interest rates. Has anyone done that in their Monte Carlo?
grayfox wrote:Also, rca has a pretty good table. However, if you want the Total Return, or how much money you end up with, you will have to compound it out over the number of years. to get to the actual values. Why not just use that table?
Like this?

Terminal \$ values per initial \$

worst

Code: Select all

``````equity       1      2      5     10     20
0%    0.89   0.94   0.98   1.08   1.37
20%    0.89   0.88   1.03   1.37   2.01
40%    0.81   0.75   0.89   1.33   2.04
60%    0.73   0.63   0.76   1.20   1.98
80%    0.64   0.52   0.63   1.03   1.83
100%    0.56   0.42   0.51   0.84   1.60
``````
median

Code: Select all

``````equity       1      2      5     10     20
0%    1.03   1.07   1.23   1.47   2.15
20%    1.06   1.11   1.30   1.66   2.71
40%    1.08   1.16   1.42   1.93   4.30
60%    1.10   1.21   1.52   2.24   5.65
80%    1.13   1.21   1.61   2.45   7.66
100%    1.15   1.25   1.66   2.57   9.16
``````
best

Code: Select all

``````equity       1      2      5     10     20
0%    1.33   1.56   2.44   3.60   7.58
20%    1.30   1.56   2.44   3.87   9.28
40%    1.29   1.56   2.45   4.15  12.15
60%    1.33   1.58   2.50   4.43  15.76
80%    1.43   1.80   2.96   4.94  20.20
100%    1.53   2.02   3.48   6.25  26.02
``````
Monthly or yearly movements of stocks are often erratic and not indicative of changes in intrinsic value. Over time, however, stock prices and intrinsic value almost invariably converge. ~ WB
dbr
Posts: 36362
Joined: Sun Mar 04, 2007 9:50 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

Peersonally I think stock behavior is sufficiently wild that presuming any "standard" statistical distribution for the behavior is going to be very approximate. That said, using standard deviation as information does not presume the assumption of a normal distribution, and thinking so is a mistake. It may not be a mistake to recognize that doing elsewise may not improve the prediction. Also people sometimes seem to think that standard deviation of annual returns does not tell you about the end point of years, but actually it does as annual SD contains the information for extrapolating multi year results. A problem is making more assumptions about independence vs serial correlation, and so on.

Regarding MC simulations. To run them you have to assume statistical distributions from which to draw the parameters for the runs. You are now back exactly where you were with the same problem except that the problem is now hidden to the observer. That is the reason that some people have advocated the historical periods approach. Places that has been done are in FireCalc, CFireSim, and in Jim Otar's retirement optimizer.
pkcrafter
Posts: 14965
Joined: Sun Mar 04, 2007 12:19 pm
Location: CA
Contact:

### Re: Range of Outcomes for Different Stock/Bond Allocations

Here is another chart you should look at.

John Norstad: Risk and Tme. See chart at bottom of article.

Be careful with data, your performance may vary.

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.
grayfox
Posts: 5569
Joined: Sat Sep 15, 2007 4:30 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

rca1824 wrote: Like this?

Terminal \$ values per initial \$

worst

Code: Select all

``````equity       1      2      5     10     20
0%    0.89   0.94   0.98   1.08   1.37
20%    0.89   0.88   1.03   1.37   2.01
40%    0.81   0.75   0.89   1.33   2.04
60%    0.73   0.63   0.76   1.20   1.98
80%    0.64   0.52   0.63   1.03   1.83
100%    0.56   0.42   0.51   0.84   1.60
``````
median

Code: Select all

``````equity       1      2      5     10     20
0%    1.03   1.07   1.23   1.47   2.15
20%    1.06   1.11   1.30   1.66   2.71
40%    1.08   1.16   1.42   1.93   4.30
60%    1.10   1.21   1.52   2.24   5.65
80%    1.13   1.21   1.61   2.45   7.66
100%    1.15   1.25   1.66   2.57   9.16
``````
best

Code: Select all

``````equity       1      2      5     10     20
0%    1.33   1.56   2.44   3.60   7.58
20%    1.30   1.56   2.44   3.87   9.28
40%    1.29   1.56   2.45   4.15  12.15
60%    1.33   1.58   2.50   4.43  15.76
80%    1.43   1.80   2.96   4.94  20.20
100%    1.53   2.02   3.48   6.25  26.02
``````
Yes, I think that is more usable. E.g. it shows that \$1 invested 100% in stocks for 5-years has ended up with losing half your money or multiplying times 3.5. A wide range of outcomes has been observed over any length of time.

This is a great chart. Investors should study it, understand it and memorize it like schoolchildren memorize the times table.
Topic Author
Langer83
Posts: 5
Joined: Wed Aug 19, 2015 12:46 pm

### Re: Range of Outcomes for Different Stock/Bond Allocations

Thanks so much! Lots of good info here. I need to through all the links here to investigate.

rca - Your second set of tables is pretty much exactly what I was looking for. Do you have a link to where the original data was calculated? I'd just like to see the source, so I know the years of analysis and other details on the data they used for the analysis. I'm assuming these are nominal returns? I'd love inflation-adjusted returns, but nominal data works.

The reason standard deviation of annual returns doesn't mean much to me is that I'm not particularly concerned about one year outcomes. At the very least, I'd like to better see how gaining more stability in the short-term costs me in long-term performance. Looking at annual standard deviations and expected long-run returns is like comparing 1-year volatility with very long-term returns. What about 2-5 years? That's probably more important to me. A lot of retirees have cash to cover 1-3 year bad years of returns, but poor returns over a longer time period are a more serious risk. What about 10 years? My understanding is that performance over the first ten years of retirement goes a very long-way in predicting whether your portfolio will last you for the rest of your life, so 10 year returns are important. etc.
dbr
Posts: 36362
Joined: Sun Mar 04, 2007 9:50 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

Langer83 wrote:
The reason standard deviation of annual returns doesn't mean much to me is that I'm not particularly concerned about one year outcomes.
The long term is the compounded result of a sequence of one year returns. This means the one year outcomes are also the long term outcome, not in actual number but in the needed information. That doesn't mean the actual calculation is easy to do with accuracy or that further considerations don't have to be taken into account, but I think you may be misunderstanding the significance of knowing the standard deviation of annual returns.

An example of the principle is on this page. While Norstad's example is simplistic it should supply an appreciation of the idea:

rca1824
Posts: 719
Joined: Tue Jun 03, 2014 9:33 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

Langer83 wrote:Thanks so much! Lots of good info here. I need to through all the links here to investigate.

rca - Your second set of tables is pretty much exactly what I was looking for. Do you have a link to where the original data was calculated? I'd just like to see the source, so I know the years of analysis and other details on the data they used for the analysis. I'm assuming these are nominal returns? I'd love inflation-adjusted returns, but nominal data works.

The reason standard deviation of annual returns doesn't mean much to me is that I'm not particularly concerned about one year outcomes. At the very least, I'd like to better see how gaining more stability in the short-term costs me in long-term performance. Looking at annual standard deviations and expected long-run returns is like comparing 1-year volatility with very long-term returns. What about 2-5 years? That's probably more important to me. A lot of retirees have cash to cover 1-3 year bad years of returns, but poor returns over a longer time period are a more serious risk. What about 10 years? My understanding is that performance over the first ten years of retirement goes a very long-way in predicting whether your portfolio will last you for the rest of your life, so 10 year returns are important. etc.

I want to use Shiller's data to go back to 1870 but he only has treasury yields not treasury returns. These are nominal returns but you could also download CPI data and adjust them. When comparing BETWEEN stocks and bonds, it doesn't matter whether you use nominal or real. The optimum is still the optimum. Although I imagine it is informative to know whether your investments are losing purchasing power or not if that's your goal instead.

Your intuition about ignoring annual returns is partially correct. It makes more sense to look at rolling N-year periods where N is your horizon. Because stock returns tend to mean revert over time, they're not a perfect random walk. Volatility is reduced significantly (but not completely) by holding longer since most of the speculative return component washes out, leaving only volatility in intrinsic returns, which is less than the combined volatility of the two which drive short-term volatility to such extremes. Nearly every market downturn is followed up above average growth. The problem with looking at N year periods is the number of samples gets smaller. When N=30, you only have 3 completely independent data points going back to 1926. So you can't place too much faith in the result. Like Jack Bogle I like to look at decades. So I use N=10 for my "long run" returns. 10 is long enough to mitigate speculation but short enough to avoid sampling error problem.

Annual returns do matter in the case of rebalancing. The fact that stocks and bonds have negative correlation on annual basis helps rebalancing which is why the efficient frontier has that neat bulge in the middle. If you don't rebalance, then you just get a straight line between stocks and bonds which is inferior to the portfolio that rebalances to buy low sell high and therefore get more returns for less risk.
Monthly or yearly movements of stocks are often erratic and not indicative of changes in intrinsic value. Over time, however, stock prices and intrinsic value almost invariably converge. ~ WB
Topic Author
Langer83
Posts: 5
Joined: Wed Aug 19, 2015 12:46 pm

### Re: Range of Outcomes for Different Stock/Bond Allocations

I want to use Shiller's data to go back to 1870 but he only has treasury yields not treasury returns. These are nominal returns but you could also download CPI data and adjust them. When comparing BETWEEN stocks and bonds, it doesn't matter whether you use nominal or real. The optimum is still the optimum. Although I imagine it is informative to know whether your investments are losing purchasing power or not if that's your goal instead.
This is great. I love playing around with Excel spreadsheets and will post my own analysis here if I find the time to get around to it.

One question - The NYU link has data for both 3-month Treasuries and 10-Year T-bonds. Not surprisingly, the volatility/returns of those two types of securities are dramatically different. I wouldn't want to use just one of them in my analysis, but I'm not sure how to split them up. I'm leaning towards a 50/50 split or 2/3 10-Year bonds and 1/3 Treasuries. What do you think? Right now, the average effective duration on Vanguard's Total Bond Market fund is 8.0 years.
rca1824
Posts: 719
Joined: Tue Jun 03, 2014 9:33 am

### Re: Range of Outcomes for Different Stock/Bond Allocations

Langer83 wrote:

I want to use Shiller's data to go back to 1870 but he only has treasury yields not treasury returns. These are nominal returns but you could also download CPI data and adjust them. When comparing BETWEEN stocks and bonds, it doesn't matter whether you use nominal or real. The optimum is still the optimum. Although I imagine it is informative to know whether your investments are losing purchasing power or not if that's your goal instead.
This is great. I love playing around with Excel spreadsheets and will post my own analysis here if I find the time to get around to it.

One question - The NYU link has data for both 3-month Treasuries and 10-Year T-bonds. Not surprisingly, the volatility/returns of those two types of securities are dramatically different. I wouldn't want to use just one of them in my analysis, but I'm not sure how to split them up. I'm leaning towards a 50/50 split or 2/3 10-Year bonds and 1/3 Treasuries. What do you think? Right now, the average effective duration on Vanguard's Total Bond Market fund is 8.0 years.
I think using the 10 year treasury bond rate will be a good enough proxy for total bond market. If anything the higher effective duration will make it perform better in the analysis. Short term treasuries are like cash so they drag a portfolio down too much. Actually I've gotten best results with long term treasuries VUSUX with high-equity portfolios need more interest rate risk to balance out.
Monthly or yearly movements of stocks are often erratic and not indicative of changes in intrinsic value. Over time, however, stock prices and intrinsic value almost invariably converge. ~ WB