Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

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bh7
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Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

Excluding TIPS for the moment...

Here a rolling 10 year returns from 1871-2015, both real and nominal, with portfolios comprised of S&P 500 and 10 year treasury bonds.

Code: Select all

        ---------REAL----------   --------NOMINAL---------
  AA     Mean       SD    Worst     Mean       SD    Worst
  0%    2.52%    3.90%   -7.20%    4.77%    2.90%    0.77%
 10%    3.08%    3.78%   -6.58%    5.34%    2.79%    1.47%
 20%    3.60%    3.70%   -5.99%    5.87%    2.75%*   2.07%
 30%    4.10%    3.68%*  -5.44%    6.36%    2.79%    2.63%*
 40%    4.56%    3.71%   -4.92%    6.83%    2.92%    2.61%
 50%    5.00%    3.79%   -4.42%    7.27%    3.12%    2.48%
 60%    5.40%    3.94%   -3.96%    7.67%    3.38%    2.15%
 70%    5.77%    4.13%   -3.54%    8.05%    3.70%    1.36%
 80%    6.11%    4.38%   -3.27%*   8.39%    4.06%    0.33%
 90%    6.42%    4.67%   -3.28%    8.70%    4.46%   -0.77%
100%    6.70%    5.01%   -4.35%    8.98%    4.90%   -1.95%
30/70 had best worst nominal returns, but 80/20 actually had best worst real returns. That's a 50% shift in AA just by shedding the money illusion.

A risk averse investor might choose 50/50 if focusing on optimizing nominal returns, but actually 80/20 if optimizing real returns.

If only there was TIPS data going back to 1871, then we could get some real answers to the best allocation. Though the current TIPS yields are not very reassuring, so if they ever were generous in the past, they're certainly not right now.
Last edited by bh7 on Mon Sep 07, 2015 12:49 pm, edited 1 time in total.
retiredjg
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Re: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by retiredjg »

Here are a few old threads and articles that address your question.

http://www.bogleheads.org/forum/viewtopic.php?p=538014

http://www.rickferri.com/blog/investmen ... own-bonds/

http://www.marketwatch.com/story/why-bo ... -10?page=1
100% bond portfolio have done much worse than 100% equity portfolios.
There are also times when the reverse is true. Sometimes for a decade or more.
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bh7
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Re: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

retiredjg wrote:Here are a few old threads and articles that address your question.

http://www.bogleheads.org/forum/viewtopic.php?p=538014

http://www.rickferri.com/blog/investmen ... own-bonds/

http://www.marketwatch.com/story/why-bo ... -10?page=1
100% bond portfolio have done much worse than 100% equity portfolios.
There are also times when the reverse is true. Sometimes for a decade or more.
You're confusing ex-ante with ex-post.

Sure, there are some years when bonds had less ex-post risk than stocks, but you don't know which those years will be ex-ante. The only thing you can do as an investor is optimize your ex-ante strategy. You bet on the asset that has the highest ex-ante probability of winning and/or lowest probability of losing money. Stocks win on both fronts.

The point of that statement is that bonds are actually riskier than stocks. An investor with infinite risk aversion, who can't choose TIPS, would have been best off with 80/20, contrary to popular belief.

The reason is because over the long run, bonds carry extreme inflation risk. Whereas the risk of stocks tends to diminish in the long run as the market reverts to its mean return.

Bonds for the short run; stocks for the long run.
lack_ey
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by lack_ey »

Any idea how this would fall out globally or internationally?

A lot of country bonds got pretty much wiped out by hyperinflation in the 20th century (though stocks didn't do much better). It may or may not be more appropriate to use post-WW2 data.

Also, if there really is very high inflation, there may be defaults or strange new rules or accounting on TIPS.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by nisiprius »

And now that we've excluded TIPS "for the moment," can we please include them again? Because they do exist now, even if they do complicate the simplistic argument that you cannot keep up with inflation except with stocks.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

nisiprius wrote:And now that we've excluded TIPS "for the moment," can we please include them again? Because they do exist now, even if they do complicate the simplistic argument that you cannot keep up with inflation except with stocks.
Good point. I started with the basic 3-fund portfolio that holds stocks and nominal bonds, and showed that nominal bonds are quite risky over the long run due to inflation risk which can exceed equity risk. So what I've achieved so far is not to find the best portfolio, but just to show a severe flaw with the traditional 3-fund portfolio.

Next step I would like to add TIPS, but that is difficult because they are a new asset so data is limited.

What I can do is this: Current 20y TIPS yield is 0.96%. Since TIPS are the ultimate risk-free asset, we can assume the real return of a 20 year TIP held for 20 years will be exactly 0.96%. There is no term risk if held to maturity and there is no inflation risk because it is adjusted for inflation--unless you subscribe to the conspiracy theory that the government intentionally understates CPI so it can evade paying inflation-adjusted claims :D

So then I can do this: Suppose an investor today can choose between 20y TIPS at current rates, or they get a random 20 year stock return from the 125 overlapping sequences available from 1871-2015.

20 Real Returns, S&P 500 & 20y 0.96% TIPS

Code: Select all

  AA     Mean       SD    Worst
  0%    0.96%    0.00%    0.96%
 10%    1.66%    0.29%    1.04%
 20%    2.34%    0.57%    1.10%
 30%    2.98%    0.85%    1.14%
 40%    3.59%    1.14%    1.16%
 50%    4.17%    1.43%    1.15%
 60%    4.73%    1.71%    1.12%
 70%    5.25%    2.00%    1.07%
 80%    5.75%    2.30%    1.00%
 90%    6.21%    2.60%    0.90%
100%    6.65%    2.90%    0.77%
And here are the preferred stock % allocations for investors of different risk aversions and horizons. I call ra=2 low, ra=4 medium, and ra=8 high

Code: Select all

       ra=2   ra=4  ra=8
N=5    100%    70%   40%
N=10   100%    80%   40%
N=20   100%   100%   80%
If TIPS yields were a bit higher this would be entirely different. Suppose the 20y TIPS yield was back its juicy 3% from ten years ago? Then Mr. 8 would prefer only 40% equity for 20 year horizon and Mr. 4 would prefer 70%.

In summary it may not be fair to assume current TIPS yields but historical stock yields, with CAPE high and earnings growth low. So I think TIPS definitely do have a role in a portfolio. But the classic 3-fund portfolio that is just stocks and nominal bonds? May as well be a 2-fund portfolio for anyone with a horizon longer than a decade because those nominal bonds just have too much inflation risk for their returns. As a result of this analysis I don't think I will ever let my portfolio have more than more than 10 or 20% in nominal bonds, and they would be short to intermediate in duration. As I approach retirement, I will be selling equities for TIPS, not nominal bonds.

On the OTHER HAND, maybe the historical inflation outcomes, now that the Fed has "matured" and learned its lesson, are very unlikely to be repeated? Who knows! If so, then nominal bonds won't be such a bad idea after all. But they do have incredible left-tail risk is all it takes is one run of the printing press and your nominal bond returns disappear.

So in summary I think it is highly irresponsible for the 3-fund portfolio to not include TIPS. For an aggressive accumulator who is 80-100% equity it won't matter. But for retirees holding 30-60% allocations in nominal bonds it is a huge mistake. Even the Vanguard Target Retirement Income has a 16% holding of TIPS, although its nominal bond holdings are 53% which would scare me to death if I was a retiree. That's just asking to lose all your money to inflation. I would reverse the ratios entirely: 53% TIPS and 16% nominal bonds would be better. And if the yield is too small, increase equities, which you can now afford since you shed that undesirable inflation risk for more desirable equity risk.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by TradingPlaces »

Good thread, thanks.

I would be great to have an IR column: Mean / Sd.

You must have some error in your SD computation. There is no way a 100% equity portfolio has such a low SD.

The drastically different conclusions regarding asset allocation have to do with the fact that if you take more out of the mean, a more risky portfolio will be preferred.

Let's say we come up with a new metric: super-real, which means you take out inflation and then 1.5 extra percent. Under such condition, treasuries will be posting negative returns. Thus, you would prefer to have 0% in them.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

TradingPlaces wrote:Good thread, thanks.

I would be great to have an IR column: Mean / Sd.

You must have some error in your SD computation. There is no way a 100% equity portfolio has such a low SD.
Yes way. That is the standard deviation of 20y real returns. N-year returns will generally be 1/sqrt(N) times the annual standard deviation, maybe a little less if there's reversion to the mean (hint: there is.) That's why it's so small. Since the average was 6.65% and worst was 0.77%, the worst 20y return had a z-score of -2.03, which is a pretty reasonable min z-score for 125 overlapping samples. So I'm quite sure I calculated it right.

Here is a chart with Sharpe ratios with the hypothetical 0.96% TIPS asset.

Code: Select all

  AA     CAGR       SD   Sharpe    Worst
  0%    0.96%    0.00%      inf    0.96%
 10%    1.66%    0.29%    2.458    1.04%
 20%    2.33%    0.57%    2.408    1.10%
 30%    2.97%    0.85%    2.357    1.14%
 40%    3.58%    1.14%    2.304    1.16%
 50%    4.16%    1.43%    2.248    1.15%
 60%    4.71%    1.71%    2.191    1.12%
 70%    5.23%    2.00%    2.133    1.07%
 80%    5.72%    2.30%    2.073    1.00%
 90%    6.18%    2.60%    2.010    0.90%
100%    6.61%    2.90%    1.947    0.77%
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

Is there any benefit to holding a small slice of nominal bonds, say, for diversification benefit in a market crash flight to quality situation? How does one model the expected correlation moving forward? Do nominal bonds offer an "inflation premium" over TIPS for taking on inflation risk?
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siamond
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by siamond »

Yup, I ran somewhat similar math a while ago, but combining it with a couple of adaptive (variable) withdrawal methods, and found similar results.

The age in bonds or similar rules of thumb never made any sense to me, nor the assumption that bonds are low risk.
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Trevor
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by Trevor »

Does using data from the 1800s seem a bit ridiculous to anyone else? :confused
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

Trevor wrote:Does using data from the 1800s seem a bit ridiculous to anyone else? :confused
More data is better, right? Avoid recency bias.

Not that it matters. The old data actually favors bonds on average. The decade that killed nominal bonds was the hyperinflation of the 1970s.

20 year real returns, 1980-2015

Code: Select all

  AA     CAGR       SD   Sharpe    Worst
  0%    5.71%    1.45%    3.279    3.43%
 10%    6.12%    1.44%    3.578    3.97%
 20%    6.49%    1.46%    3.800    4.47%
 30%    6.83%    1.49%    3.935    4.91%
 40%    7.13%    1.55%    3.982    5.30%
 50%    7.40%    1.63%    3.948    5.64%
 60%    7.62%    1.73%    3.847    5.71%
 70%    7.82%    1.86%    3.693    5.69%
 80%    7.97%    2.00%    3.501    5.57%
 90%    8.08%    2.17%    3.284    5.32%
100%    8.15%    2.36%    3.052    5.02%
Even since 1980, when hyperinflation was under control, your worst 20 year returns were still maximized at 60/40. And this period isn't very representative.

20 year real returns, 1950-2015

Code: Select all

  AA     CAGR       SD   Sharpe    Worst
  0%    2.38%    3.18%    0.448   -3.56%
 10%    2.90%    3.11%    0.622   -3.02%
 20%    3.38%    3.06%    0.790   -2.51%
 30%    3.84%    3.03%    0.950   -2.02%
 40%    4.27%    3.01%    1.099   -1.55%
 50%    4.67%    3.00%    1.235   -1.11%
 60%    5.04%    3.02%    1.353   -0.69%
 70%    5.39%    3.05%    1.453   -0.29%
 80%    5.71%    3.10%    1.532    0.09%
 90%    6.00%    3.17%    1.589    0.44%
100%    6.26%    3.26%    1.624    0.77%
20 year real returns, 1900-2015

Code: Select all

  AA     CAGR       SD   Sharpe    Worst
  0%    1.69%    2.80%    0.262   -3.56%
 10%    2.34%    2.68%    0.517   -3.02%
 20%    2.96%    2.58%    0.775   -2.51%
 30%    3.53%    2.51%    1.025   -2.02%
 40%    4.08%    2.48%    1.255   -1.55%
 50%    4.58%    2.50%    1.451   -1.11%
 60%    5.05%    2.55%    1.603   -0.69%
 70%    5.49%    2.65%    1.706   -0.29%
 80%    5.89%    2.80%    1.762    0.09%
 90%    6.25%    2.98%    1.776    0.44%
100%    6.57%    3.20%    1.754    0.77%
20y real returns, 1871-2015

Code: Select all

  AA     CAGR       SD   Sharpe    Worst
  0%    2.19%    2.90%    0.423   -3.56%
 10%    2.77%    2.74%    0.661   -3.02%
 20%    3.33%    2.61%    0.907   -2.51%
 30%    3.85%    2.51%    1.151   -2.02%
 40%    4.34%    2.45%    1.383   -1.55%
 50%    4.80%    2.42%    1.587   -1.11%
 60%    5.23%    2.43%    1.754   -0.69%
 70%    5.62%    2.49%    1.873   -0.29%
 80%    5.98%    2.59%    1.942    0.09%
 90%    6.31%    2.73%    1.964    0.44%
100%    6.61%    2.90%    1.947    0.77%
lack_ey
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by lack_ey »

bh7 wrote:Is there any benefit to holding a small slice of nominal bonds, say, for diversification benefit in a market crash flight to quality situation? How does one model the expected correlation moving forward? Do nominal bonds offer an "inflation premium" over TIPS for taking on inflation risk?
I have heard handwaving explanations that the inflation risk (nominal Treasuries can be hit bad by unexpected inflation and so should yield more) is balanced by the liquidity premium (nominal Treasuries are more liquid and should yield less), and in net they about cancel out. Dunno.

About the correlations, it is a mystery to me.
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siamond
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by siamond »

bh7, may I suggest something? Take the UK returns since 1900 (equities + gilts, which are government bonds), run your math again, and share your results & analysis. I think this could be interesting.

Here is the (public) source where to find UK historical numbers. I'll send you by PM a link to a more conveniently formatted Excel spreadsheet.
http://lwmconsultants.com/wp-content/up ... dition.pdf
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by saltycaper »

bh7,

Thank you for running the numbers. Do you feel like posting similar tables for a few different time periods to present using 1 year and 5 year treasuries?
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raven15
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by raven15 »

That was a nice analysis, it showed that data in a new light. It has been my observation that the chief benefit of typical bonds for a buy and holder is "mental pacifier", unless being held for use within 5 years.
bh7 wrote:Is there any benefit to holding a small slice of nominal bonds, say, for diversification benefit in a market crash flight to quality situation? How does one model the expected correlation moving forward? Do nominal bonds offer an "inflation premium" over TIPS for taking on inflation risk?
There can be, you need to look at the longer duration bonds to find it, ie. 20 to 30 year nominal. I think the maximum benefit is around 10% bonds.

It looks to me like there is an inflation premium, which makes nominal bonds the better choice unless unexpected inflation occurs. I don't know how to model the future, but you could look into the Permanent Portfolio for a theory on correlations between stocks, long term bonds, and gold (and cash).
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backpacker
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by backpacker »

Super interesting thread. Years of low inflation have caused many investors to conclude, consciously or not, that inflation is not a real risk to their portfolio. But it is. Inflation was a tame, almost depressing 1% at the beginning of 1965. Five years later it was 6.2%. Ten years later is was 11.8%. These things sneak up on you.

It would be interesting to see what the results look like for seven year treasuries, since that's closer to the duration of the bonds most Bogleheads actually hold.

Here are two of my favorite charts from the 2011 Credit Suisse Yearbook. The first is maximum drawdowns for stocks and bonds in the US. The second is for bonds and stocks in the UK. Note that the bonds are twenty year government bonds, so quite a bit longer than the bonds most people hold. But, given the mountains of red, it's not surprising that portfolios with minimum drawdowns are light on nominal bonds.

Image
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

saltycaper wrote:bh7,

Thank you for running the numbers. Do you feel like posting similar tables for a few different time periods to present using 1 year and 5 year treasuries?
Unfortunately I only have Shiller's data on 10y treasuries.

If someone has data of other bond yields I can test them out, but I think that data would only go back to the 70s at the earliest.

However one should be able to simulate a 7y treasury, though not perfectly, by holding a mix of 10y bonds and cash.

Unfortunately cash is also destroyed by inflation. Nominal assets can only protect against expected inflation not unexpected inflation.

Short Term Treasuries lost 2% annualized from 1972-1980. They returned 0 from 1972-1983. So this might hedge the loss better than a long term bond, but it's still quite a loss. Maybe it's not as high as stocks. Again I would like to run the numbers for shorter term bonds but just don't have the data before 1972. If anyone is interested in just seeing the 1972-2015 numbers I can whip that up.

From just using Portfolio Visualizer:

Here are the nominal and real returns from 1972-1980
Cash/Money Market: 7.04% (-1.43%)
ST treasuries: 6.32% (-2.09%)
TIPS: 6.07% (-2.32%)
TBM: 5.27% (-3.06%)
10y treasuries: 2.80% (-5.33%)

And from 1972-2015 to better capture the broad average:
TBM: 7.56% (3.29%)
10y treasuries: 7.21% (2.95%)
TIPS: 6.96% (2.71%)
ST treasuries: 6.32% (2.10%)
Cash/MM: 5.04% (0.86%)

So it does appear one can hedge risk better by taking a shorter duration. Somehow cash and STT fared inflation better than TIPS in the inflationary 1970s. There also seems to be a positive relationship between risk and reward as the assets that did best in the 70s did worst over the longer run, so that at least helps rationalize efficient market theory. Except TBM, the only diversified fund, which was 4th worst in crisis and 1st best overall. Diversification helps.

So in conclusion I think 10y treasuries are a bad hold -- you're better off taking risk on the equity side. It's too bad we don't have better data on other kinds of bonds going back further than 1972.

Next step: I'm going to work with 1972+ data since it's richer. I will download returns for different kinds of bonds and try to work out the true min-risk portfolio. Obviously it's not going to have 10y treasuries. The contenders are TBM, TIPS, STT, and Cash.

In the old days cash was considered an integral part of a retiree's portfolio but these days most people just hold TBM. I wonder if that is actually good for a retiree since the duration on TBM is kind of long exposing them to inflation risk.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

Here are some preliminary results with asset returns in isolation

Worst 10y real returns (Ticker, Start Year, Real 10y CAGR)

Code: Select all

CMM  1972 -0.88%
STT  1972 -1.96%
TIPS 1973 -3.19%
TSM  1990 -3.09%
ITT  1972 -3.23%
TBM  1972 -3.42%
T10  1972 -5.49%
LTT  1972 -6.30%
In terms of safety, TBM ranked 5/7 among all assets, 4/6 among all bonds, and 3/5 among nominal bonds.

Fortunately there is diversification benefit between stocks and bonds, with their worst decades spaced 17 years apart. But not much between bonds, with all nominal bonds returning the worst in the same decade, and TIPS only offset by a single year.

Next step: Test combinations of assets. Which combination is truly the safest? Is TBM saved through its interaction with stocks? Or are shorter term bonds and/or TIPS necessary to reduce risk? My intuition is that cash and TIPS will play an important role.

Aside: I'll be damned if I end up converging on a psuedo Harry Browne portfolio with stocks, bonds, cash, and TIPS. I could have included gold as an asset class but I think that would infuriate some people here :D
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

First, which 2-fund portfolio is safest?

(Asset, Safest % Stocks, Worst Start Year, 10y real CAGR)

Code: Select all

CMM   20%   1972  -0.739%
STT   50%   1972  -1.540%
TIPS  60%   1973  -1.899%
ITT   70%   1972  -2.014%
TBM   70%   1972  -2.062%
T10   90%   1972  -2.318%
LTT   90%   1972  -2.417%
To my surprise, cash and short term treasuries beat TIPS. Long term bonds are very risky, so much so that the investor has to go almost all the way to 100% equity to hedge against inflation.

Testing 3-fund and 4-fund (or even an arbitrary 8-fund) portfolio is going to take some time to code. It will be interesting to see what the optimal combination is and whether it approaches the Permanent Portfolio or not.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by texaspapas »

This is a really interesting topic for me as I'm new to investing and optimal asset allocation is something that I struggle with a lot. But how is investing over a 144 year time frame relevant to me? Not trying to be argumentative, but just wondering I guess if this is just a philosophical discussion or relevant to actual investors. I'm hoping to start withdrawing in around 30 years.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

texaspapas wrote:This is a really interesting topic for me as I'm new to investing and optimal asset allocation is something that I struggle with a lot. But how is investing over a 144 year time frame relevant to me? Not trying to be argumentative, but just wondering I guess if this is just a philosophical discussion or relevant to actual investors. I'm hoping to start withdrawing in around 30 years.
There was no 144 year time frame in my results. So far I have only taken rolling 5-, 10-, and 20-year returns. The 144 years is the sample of potential rolling returns. Within 144 years there are 125 rolling 20y-year returns. That's what an investor with a 20-year horizon would be interested in, as an example.

UPDATES: It turns out there is no free lunch to bonds. With a 10 year horizon, starting from 24% equity / 76% cash, adding any amount of short, medium, long bonds or TIPS only adds risk. And if your horizon is 20 years, you may as well be 100% equity, although there are limited independent 20-year rolling returns from 1972-2015 so don't trust that conclusion entirely.

Next step I will be testing preferences other than infinite risk aversion, since most of us have some capacity for risk at the benefit of better returns.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by SimpleGift »

bh7 wrote:Next step: Test combinations of assets. Which combination is truly the safest? Is TBM saved through its interaction with stocks? Or are shorter term bonds and/or TIPS necessary to reduce risk? My intuition is that cash and TIPS will play an important role.
These are all very interesting analyses, bh7, but one needs to view the results with a certain amount of caution, I believe. The 20th century (from which we have nearly all of our data on the returns of stocks and bonds) was an unusual time in human history — with fast rising population and productivity growth rates — and it very likely will not at all resemble the 21st century (when we will be investing our money), since population growth rates are now declining and the trend growth in global productivity has also been falling. For more details, see this recent thread.

My point is simply that the overall relationships between inflation and asset returns may continue to hold true in the future, but it would be hubris to assign too much specificity and certainty to them, based on the 20th century data alone.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by Rx 4 investing »

Dear bh7:

Might you be able to do an analysis of Rx 4 CAPE-timing model vs...

1. Harry Browne, but modified for gold at only 5%. Remaining 20% (Browne recommended 25% gold ; I agree with you 25% is non- BH worthy). I would push the additional 20% to the Long Term Treasury bucket ? See Crawling Road assets used at link...

http://www.crawlingroad.com/blog/2008/1 ... l-returns/

2. 50% / 50% portfolio, i.e. 50% stocks, and 50% in long-term Treasuries. In the 2008 decline, this portfolio was down only -2%. In crashes like that , the value of long-term treasuries helped offset the equity risk.

Here's an article by an author who discussed Ray Dalio's "All Weather Portfolio" and Browne's "Permanent Portfolio."

http://seekingalpha.com/article/878251- ... -portfolio

Thanks in advance!
“Everyone is a disciplined, long-term investor until the market goes down.” – Steve Forbes
texaspapas
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by texaspapas »

bh7 wrote: There was no 144 year time frame in my results. So far I have only taken rolling 5-, 10-, and 20-year returns. The 144 years is the sample of potential rolling returns. Within 144 years there are 125 rolling 20y-year returns. That's what an investor with a 20-year horizon would be interested in, as an example.
Thanks for the explanation (obvious to me now), now I appreciate your point.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by garlandwhizzer »

Simplegift wrote:

These are all very interesting analyses, bh7, but one needs to view the results with a certain amount of caution, I believe. The 20th century (from which we have nearly all of our data on the returns of stocks and bonds) was an unusual time in human history — with fast rising population and productivity growth rates — and it very likely will not at all resemble the 21st century (when we will be investing our money), since population growth rates are now declining and the trend growth in global productivity has also been falling. For more details, see this recent thread.

My point is simply that the overall relationships between inflation and asset returns may continue to hold true in the future, but it would be hubris to assign too much specificity and certainty to them, based on the 20th century data alone.
1+

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backpacker
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by backpacker »

Simplegift wrote:
bh7 wrote:Next step: Test combinations of assets. Which combination is truly the safest? Is TBM saved through its interaction with stocks? Or are shorter term bonds and/or TIPS necessary to reduce risk? My intuition is that cash and TIPS will play an important role.
These are all very interesting analyses, bh7, but one needs to view the results with a certain amount of caution, I believe. The 20th century (from which we have nearly all of our data on the returns of stocks and bonds) was an unusual time in human history — with fast rising population and productivity growth rates — and it very likely will not at all resemble the 21st century (when we will be investing our money), since population growth rates are now declining and the trend growth in global productivity has also been falling. For more details, see this recent thread.

My point is simply that the overall relationships between inflation and asset returns may continue to hold true in the future, but it would be hubris to assign too much specificity and certainty to them, based on the 20th century data alone.
One thing to keep in mind is that while the 21st century will almost certainly be different than the 20th, we have no idea how it will be different. Inflation could be lower than the 20th century. It could be higher. No one knows. The global economic system is too complex and noisy to make predictions with much confidence.

Think of 20th century returns as giving us an expectation value for the risk of bonds and stocks. We know that we'll almost certainly get something other than the expectation value, but the expectation value is still the best estimate we have of future risk.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by backpacker »

bh7 wrote:Testing 3-fund and 4-fund (or even an arbitrary 8-fund) portfolio is going to take some time to code.
What do you use to generate your results? I've thought for awhile that I need to figure out how to do my own work on financial data.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by kolea »

A couple of comments on the set-up of the problem.

I believe you have modeled a static account that starts with a fixed amount of money and no cash flow in or out. That is not what the majority of us are doing. Some of us are accumulating at a constant annual rate, some of us a withdrawing, perhaps at a constant rate but just as likely at some variable rate. You should run your model for those two situations. My observation from when I have done similar back-testing is that the results change when you have cash flows.

The psychology of investing is that people tend to have comfort zones in the distribution of outcomes. I tend to invest to the most-likely scenario but a lot of people will invest to the scenario with the lowest chance of failing (your "best-worst"). You have sort-of captured that with mean/SD/worst, but the actual distribution is always interesting. For instance, is the best-worst an outlier or is it significant?

You might want to run 30 year sequences which are more typical for a period of accumulation.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by SimpleGift »

backpacker wrote:Think of 20th century returns as giving us an expectation value for the risk of bonds and stocks. We know that we'll almost certainly get something other than the expectation value, but the expectation value is still the best estimate we have of future risk.
Completely agree, this is a very reasonable approach to risk. My only concern was that, often when working with historical asset return data, a certain cognitive fallacy creeps into our thinking:
  • This was true in the past (1871-2015) — ergo — this will be true in the future (2015-2100).
We're all prone to this fallacy to some degree (myself included!), and it's just something to be especially aware of when designing a life-long portfolio allocation. The past can only tell us so much — and certainly not the whole truth about expected returns.
Last edited by SimpleGift on Wed Sep 09, 2015 2:12 pm, edited 1 time in total.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

Rx 4 investing wrote:Dear bh7:

Might you be able to do an analysis of Rx 4 CAPE-timing model vs...

1. Harry Browne, but modified for gold at only 5%. Remaining 20% (Browne recommended 25% gold ; I agree with you 25% is non- BH worthy). I would push the additional 20% to the Long Term Treasury bucket ? See Crawling Road assets used at link...

http://www.crawlingroad.com/blog/2008/1 ... l-returns/

2. 50% / 50% portfolio, i.e. 50% stocks, and 50% in long-term Treasuries. In the 2008 decline, this portfolio was down only -2%. In crashes like that , the value of long-term treasuries helped offset the equity risk.

Here's an article by an author who discussed Ray Dalio's "All Weather Portfolio" and Browne's "Permanent Portfolio."

http://seekingalpha.com/article/878251- ... -portfolio

Thanks in advance!
50/50 TSM/LTT did well in 2008 but not so well in 1972. 1972 was worse than 2008. So an investor with infinite risk aversion would have been best off with 24% cash / 76% stock if their horizon was 10 years, because the pain of holding LTT in 1972 outweighs the benefit they provided in 2008. My next step is to test finite risk aversions, which might give LTT an advantage because of their higher mean returns.
backpacker wrote:
bh7 wrote:Testing 3-fund and 4-fund (or even an arbitrary 8-fund) portfolio is going to take some time to code.
What do you use to generate your results? I've thought for awhile that I need to figure out how to do my own work on financial data.
Python. Load CSV data, get it into parallel arrays of real returns, then write loops to process results and print out aggregate statistics.
TwoByFour wrote:A couple of comments on the set-up of the problem.

I believe you have modeled a static account that starts with a fixed amount of money and no cash flow in or out. That is not what the majority of us are doing. Some of us are accumulating at a constant annual rate, some of us a withdrawing, perhaps at a constant rate but just as likely at some variable rate. You should run your model for those two situations. My observation from when I have done similar back-testing is that the results change when you have cash flows.

The psychology of investing is that people tend to have comfort zones in the distribution of outcomes. I tend to invest to the most-likely scenario but a lot of people will invest to the scenario with the lowest chance of failing (your "best-worst"). You have sort-of captured that with mean/SD/worst, but the actual distribution is always interesting. For instance, is the best-worst an outlier or is it significant?

You might want to run 30 year sequences which are more typical for a period of accumulation.

Excellent point. Adding variables for accumulation and withdrawals are my next next step. It's just harder to code since ou can no longer compute the CAGR from a simple sequence of returns but need to modify the equation. I will share this when I get to it!
Simplegift wrote:
backpacker wrote:Think of 20th century returns as giving us an expectation value for the risk of bonds and stocks. We know that we'll almost certainly get something other than the expectation value, but the expectation value is still the best estimate we have of future risk.
Completely agree, this is a very reasonable approach. My only concern was that, often when working with historical asset return data, a certain cognitive fallacy creeps into our thinking:
  • This was true in the past (1871-2015) — ergo — this will be true in the future (2015-2100).
We're all prone to this fallacy to some degree (myself included!), and it's just something to be especially aware of when designing a life-long portfolio allocation. The past can only tell us so much — and certainly not the whole truth about expected returns.

Absolutely true. However I think the past is a good benchmark. You have to base your future expectations on something. It's also illuminating to find out that, for example, cash hedged against 1970s hyperinflation better than TIPS. I assumed TIPS would win in all scenarios, but here is one where it didn't. So historical data makes me more cautious about ascribing ultimate superiority to any one asset. The past is screaming, "Diverisify, idiot!" which is consistent with basic common sense.

If I had to make a "coward's portfolio" with no data I would probably do equal parts stock, cash, bonds, and TIPS. A modification of the harry browne portfolio. But it will be interesting to see if the data says "no, when your horizon is X, you should actually hold Y" etc.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by backpacker »

Simplegift wrote:
backpacker wrote:Think of 20th century returns as giving us an expectation value for the risk of bonds and stocks. We know that we'll almost certainly get something other than the expectation value, but the expectation value is still the best estimate we have of future risk.
Completely agree, this is a very reasonable approach to risk. My only concern was that, often when working with historical asset return data, a certain cognitive fallacy creeps into our thinking:
  • This was true in the past (1871-2015) — ergo — this will be true in the future (2015-2100).
We're all prone to this fallacy to some degree (myself included!), and it's just something to be especially aware of when designing a life-long portfolio allocation. The past can only tell us so much — and certainly not the whole truth about expected returns.
Excellent. I think we're on the same page. :beer
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

backpacker wrote:
Simplegift wrote:
backpacker wrote:Think of 20th century returns as giving us an expectation value for the risk of bonds and stocks. We know that we'll almost certainly get something other than the expectation value, but the expectation value is still the best estimate we have of future risk.
Completely agree, this is a very reasonable approach to risk. My only concern was that, often when working with historical asset return data, a certain cognitive fallacy creeps into our thinking:
  • This was true in the past (1871-2015) — ergo — this will be true in the future (2015-2100).
We're all prone to this fallacy to some degree (myself included!), and it's just something to be especially aware of when designing a life-long portfolio allocation. The past can only tell us so much — and certainly not the whole truth about expected returns.
Excellent. I think we're on the same page. :beer

Also there is a confusion here between strategy and outcome. The optimal strategy will probably never have the best outcome. The best outcome can only be known ex-post. Hence, the best we can do is choose the best strategy that maximizes utility over the ex-ante probability distribution of outcomes. Assuming we get the best estimate of future returns from past returns, optimizing over past returns is the best we can do in the future. I think this is a good starting point. If you have a better approach to optimizing future ex-ante future returns, I would love to hear it.

I think one we can get robustness in strategies is by (1) holding a static allocation -- do not engage in market timing, since it is too easy to overfit a strategy that relies on dynamic asset allocation. (2) use many years in the data sample, and use rolling periods short enough that there are enough independent periods within the sample, i.e. don't use 30 year returns from a 45-year sample, maybe 5-10 years at best. (3) Other suggestions?
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by SimpleGift »

bh7 wrote:Other suggestions?
A few thoughts. Long-term, historical asset returns can help determine the parameters of expected risk, I believe — but since the valuations of both stocks and bonds today are at or near historical highs, this is probably one of the worst times to be using historical data for expected returns. I'd suggest testing your results against a few of the more accepted forecasting methods, including current yields for bonds, and the earnings yield or dividend growth model for stocks. Some threads with more details:
Secondly, it seems quite unlikely that, with declining growth rates for both global population (already baked in) and labor productivity (declining worldwide), one can expect the same pace of economic growth in the 21st century that was seen in the 20th century. Slower global economic growth generally indicates lower bond yields (an excess of savings over investment) and lower equity returns (due to slower aggregate earnings growth).

This has some implications for portfolio design and construction, in my view, including perhaps compensating for lower returns with a somewhat higher equity allocation (consistent with one's risk tolerance) and expecting a higher likelihood of persistent, mild deflation in the decades to come (ala Japan), rather than high inflation. Some threads with more background:
Finally, I'm not suggesting that one ignore historical asset returns entirely, but rather adjust and modify them with reasonable forecasts of future expected returns. Different investors will certainly have disparate views of future expectations (which is what makes the world go around, they say) — but each investor should at least make a reasoned judgement about the future, I believe, rather than just blindly expect the asset returns of the 21st century to be the same as those of the historical past.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

I've got some results. (I may need to make a new topic for this but I'll see what traffic I get here).

I managed to code a loop that would test permutations of a 4-fund portfolio. I only test to 5% discrete slices because of computational burden and because people like nice 5% slices. Unfortunately this causes some messy jumping in the optimal portfolio as the sample changes, but it's a good benchmark.

I decided to only test TSM, TBM, Cash, and TIPS. I did not test Short/Long/Intermediate/10y Treasuries because those are less popular. The decision between Short Treasuries and Cash was a toss-up, but I went with Cash because it has an even shorter duration so it would barbell with TBM better. I eliminated Long/Intermediate/10y Treasuries because TBM seems more popular and better diversified than those, with better risk-adjusted returns and more prevalence here.

The setup is as follows. An investor invests with a known horizon N. The investor takes a random draw of N consecutive years from the historical 1972-2015 returns. The investor rebalances annually. All returns are reported in real terms and the investor's own price index is accurately reflected in the CPI. The investor has preferences over the final balance at the end of the horizon, perhaps because he uses it to purchase a lump-sum annuity for his retirement. Who knows!

1. Risk minimization (or: Utility Maximization with infinite risk aversion.)

Code: Select all

                         Worst    Worst
  N  TSM Cash TIPS  TBM   Year   Return
  1   0% 100%   0%   0%   1974   -4.34%
  2   0% 100%   0%   0%   1973   -3.07%
  3   0% 100%   0%   0%   1973   -2.43%
  5   5%  75%   0%  20%   1973   -1.72%
  7   0% 100%   0%   0%   1973   -1.92%
 10  25%  75%   0%   0%   1972   -0.73%
 15  55%   0%   0%  45%   1973    2.64%
 20  90%   0%   0%  10%   1973    4.50%
 25 100%   0%   0%   0%   1972    6.17%
 30  90%   0%   0%  10%   1973    5.04%
2. Utility Maximization, Constant Relative Risk Aversion (CRRA).

ra=16 (Very High)

Code: Select all

  N  TSM Cash TIPS  TBM     CAGR       SD
  1   5%  45%  25%  25%    2.36%    4.03%
  2   5%  70%  15%  10%    1.81%    2.85%
  3   5%  70%  20%   5%    1.89%    2.56%
  5  15%  50%  15%  20%    3.02%    2.73%
  7  20%  70%  10%   0%    2.81%    2.30%
 10  30%  65%   5%   0%    3.59%    2.15%
 15  55%   0%   0%  45%    6.61%    2.34%
 20  90%   0%   0%  10%    7.97%    2.12%
 25 100%   0%   0%   0%    8.14%    1.52%
 30  90%   0%   0%  10%    7.36%    0.90%
ra=8 (High)

Code: Select all

  N  TSM Cash TIPS  TBM     CAGR       SD
  1  15%   0%  35%  50%    3.80%    6.44%
  2  10%  15%  35%  40%    3.28%    4.45%
  3  15%  20%  30%  35%    3.51%    3.92%
  5  30%   0%  35%  35%    4.81%    3.81%
  7  30%  20%  35%  15%    4.39%    3.01%
 10  40%  35%  10%  15%    4.72%    2.66%
 15  60%   0%   0%  40%    6.76%    2.45%
 20  95%   0%   0%   5%    8.09%    2.21%
 25 100%   0%   0%   0%    8.14%    1.52%
 30  95%   0%   0%   5%    7.45%    0.94%
ra=4 (Medium)

Code: Select all

  N  TSM Cash TIPS  TBM     CAGR       SD
  1  30%   0%  15%  55%    4.42%    8.20%
  2  30%   0%  20%  50%    4.39%    6.10%
  3  35%   0%  20%  45%    4.68%    5.27%
  5  50%   0%  25%  25%    5.45%    4.59%
  7  55%   0%  40%   5%    5.61%    3.87%
 10  55%   0%  15%  30%    6.07%    3.40%
 15  75%   0%   0%  25%    7.16%    2.80%
 20 100%   0%   0%   0%    8.20%    2.30%
 25 100%   0%   0%   0%    8.14%    1.52%
 30 100%   0%   0%   0%    7.53%    0.99%
ra=2 (Low)

Code: Select all

  N  TSM Cash TIPS  TBM     CAGR       SD
  1  65%   0%   0%  35%    5.47%   13.02%
  2  60%   0%   0%  40%    5.27%    8.98%
  3  65%   0%   0%  35%    5.47%    7.38%
  5  80%   0%   0%  20%    6.18%    6.36%
  7  90%   0%  10%   0%    6.36%    5.30%
 10  90%   0%   0%  10%    6.89%    4.55%
 15 100%   0%   0%   0%    7.67%    3.47%
 20 100%   0%   0%   0%    8.20%    2.30%
 25 100%   0%   0%   0%    8.14%    1.52%
 30 100%   0%   0%   0%    7.53%    0.99%
3. Utility Maximization, Constant Absolute Risk Aversion (CARA).

Code: Select all

  N  TSM Cash TIPS  TBM     CAGR       SD
  1 100%   0%   0%   0%    6.02%   18.42%
  2 100%   0%   0%   0%    5.87%   13.58%
  3 100%   0%   0%   0%    5.95%   10.46%
  5 100%   0%   0%   0%    6.47%    7.66%
  7 100%   0%   0%   0%    6.49%    5.80%
 10 100%   0%   0%   0%    7.05%    4.92%
 15 100%   0%   0%   0%    7.67%    3.47%
 20 100%   0%   0%   0%    8.20%    2.30%
 25 100%   0%   0%   0%    8.14%    1.52%
 30 100%   0%   0%   0%    7.53%    0.99%
These might be good starting points for investors trying to pin down a sensible mix of assets.

Next step: If there is demand to see how the other bonds perform, I could go deeper into a 5-fund or 6-fund portfolio, but adding each additional fund makes the program run exponentially slower so I've left it at 4 for now.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

The problem with the raw historical data is that the optimal portfolio jumps around based on the rolling window.

Here is one with allocations rounded to 2.5%, every year 1-30.

CRRA=8

Code: Select all

  N  TSM Cash TIPS  TBM     CAGR       SD
  1  15%   0%  32%  52%    3.81%    6.49%
  2  12%  15%  30%  42%    3.39%    4.58%
  3  15%  22%  30%  32%    3.45%    3.85%
  4  30%   0%  35%  35%    4.72%    4.16%
  5  30%   0%  35%  35%    4.81%    3.81%
  6  30%   2%  26%  42%    4.80%    3.56%
  7  32%  18%  35%  15%    4.54%    3.10%
  8  42%  15%  42%   0%    5.02%    3.09%
  9  35%  28%  38%   0%    4.59%    2.66%
 10  38%  35%  11%  16%    4.64%    2.59%
 11  42%   0%   0%  57%    5.88%    2.85%
 12  42%   0%   0%  57%    5.98%    2.62%
 13  42%   0%   0%  57%    6.05%    2.40%
 14  50%   0%   0%  50%    6.38%    2.37%
 15  57%   0%   0%  43%    6.69%    2.40%
 16  72%   0%   0%  28%    7.21%    2.55%
 17  85%   0%   0%  15%    7.66%    2.60%
 18  80%   0%   0%  20%    7.63%    2.29%
 19  85%   0%   0%  15%    7.79%    2.25%
 20  95%   0%   0%   5%    8.09%    2.21%
 21 100%   0%   0%   0%    8.17%    2.19%
 22  98%   0%   0%   3%    8.12%    2.08%
 23 100%   0%   0%   0%    8.17%    1.96%
 24 100%   0%   0%   0%    8.20%    1.68%
 25 100%   0%   0%   0%    8.14%    1.52%
 26 100%   0%   0%   0%    8.10%    1.20%
 27 100%   0%   0%   0%    7.99%    0.81%
 28 100%   0%   0%   0%    7.84%    0.72%
 29 100%   0%   0%   0%    7.67%    0.89%
 30  95%   0%   0%   5%    7.45%    0.94%
The non-monotonicity is disturbing. Suggestions for abating this? One thing I could do is infer a statistical distribution of returns, and then integrate it, which would give smoother results. The problem is that fitting statistical distribution may not be accurate. These are complicated processes. So perhaps the best one can do is use the chart as a rough benchmark and then eyeball an appropriate portfolio. The most volatile allocation is choosing between cash and bonds, or in other words, the effective duration of one's nominal bonds. It should monotonic in horizon, but it actually starts off with lots of bonds, then moves to cash, then back to bonds, until stocks take over. This doesn't make sense to me. . I would imagine it would start with cash then gradually convert from cash to bonds as the horizon lengthens. This must be because of sampling error.

One problem with the relative strength of nominal bonds to TIPS in this backtesting is that the 1980s had unrealized expected inflation. People were afraid of inflation, and only realized in retrospect that it was tamed. This led to nominal bonds outperforming. How to get around this problem? If the data has limited samples, any conclusions formed from it will be deeply flawed.
lack_ey
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by lack_ey »

Which "TIPS" data are you using for 1972-1997 or so (before they actually existed)? I know this paper has some simulated "what if" data:
http://www.cfapubs.org/doi/pdf/10.2469/faj.v60.n1.2592

Maybe you could extend it back further, if we're playing that game.

As noted by others, I really doubt the underlying historical distribution of returns is static and on average looks that much like the future underlying distribution, so I suppose cleaning up issues with precision of results and worrying about which window to use is a secondary concern.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

lack_ey wrote:Which "TIPS" data are you using for 1972-1997 or so (before they actually existed)? I know this paper has some simulated "what if" data:
http://www.cfapubs.org/doi/pdf/10.2469/faj.v60.n1.2592

Maybe you could extend it back further, if we're playing that game.

As noted by others, I really doubt the underlying historical distribution of returns is static and on average looks that much like the future underlying distribution, so I suppose cleaning up issues with precision of results and worrying about which window to use is a secondary concern.
I use synthetic TIPS data from Portfolio Visualizer for the 1972-2000 TIPS data.

So, your second paragraph doesn't answer my question.. what do I do?
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DonCamillo
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by DonCamillo »

backpacker wrote: It would be interesting to see what the results look like for seven year treasuries, since that's closer to the duration of the bonds most Bogleheads actually hold.
I have a theory question.

Assume that a Boglehead ladders 10 year bonds, replacing 10% of them each year. The average maturity would be about five years. However, ten year bonds pay more interest than five year bonds, and the portfolio only holds ten year bonds.

If you are going to analyze the returns on this laddered portfolio, would it be better to analyze based on five year maturities (the duration) or on ten year maturities (the actual bonds)?
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lack_ey
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by lack_ey »

bh7 wrote:
lack_ey wrote:Which "TIPS" data are you using for 1972-1997 or so (before they actually existed)? I know this paper has some simulated "what if" data:
http://www.cfapubs.org/doi/pdf/10.2469/faj.v60.n1.2592

Maybe you could extend it back further, if we're playing that game.

As noted by others, I really doubt the underlying historical distribution of returns is static and on average looks that much like the future underlying distribution, so I suppose cleaning up issues with precision of results and worrying about which window to use is a secondary concern.
I use synthetic TIPS data from Portfolio Visualizer for the 1972-2000 TIPS data.

So, your second paragraph doesn't answer my question.. what do I do?
For one, you might implement one of many "corrections" to the data.

One idea might be to interpret historical asset class returns as expected return + deviation. The expected return would be based on whichever model you want to use. See above posts by Simplegift, for example. The deviation captures the difference between the expected and realized returns. Then rerun all the calculations using today's expected return and rolling over historical sequences of deviations from the expected value (rather than the raw historical returns themselves).

That might work out reasonably if we think that the expected value changes over time but the shape of the distribution otherwise doesn't. And that our model to generate the expected value is sensible.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

lack_ey wrote:
bh7 wrote:
lack_ey wrote:Which "TIPS" data are you using for 1972-1997 or so (before they actually existed)? I know this paper has some simulated "what if" data:
http://www.cfapubs.org/doi/pdf/10.2469/faj.v60.n1.2592

Maybe you could extend it back further, if we're playing that game.

As noted by others, I really doubt the underlying historical distribution of returns is static and on average looks that much like the future underlying distribution, so I suppose cleaning up issues with precision of results and worrying about which window to use is a secondary concern.
I use synthetic TIPS data from Portfolio Visualizer for the 1972-2000 TIPS data.

So, your second paragraph doesn't answer my question.. what do I do?
For one, you might implement one of many "corrections" to the data.

One idea might be to interpret historical asset class returns as expected return + deviation. The expected return would be based on whichever model you want to use. See above posts by Simplegift, for example. The deviation captures the difference between the expected and realized returns. Then rerun all the calculations using today's expected return and rolling over historical sequences of deviations from the expected value (rather than the raw historical returns themselves).

That might work out reasonably if we think that the expected value changes over time but the shape of the distribution otherwise doesn't. And that our model to generate the expected value is sensible.
So essentially you define a parameterized CDF. You estimate the primitive parameters of the CDF from historical data. Then some of the parameters would be things like CAPE for stocks, current yields for bonds, and inflation expectations derived from the nominal-yield bond spread. I will give that a shot. Sounds promising!
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backpacker
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by backpacker »

DonCamillo wrote:
backpacker wrote: It would be interesting to see what the results look like for seven year treasuries, since that's closer to the duration of the bonds most Bogleheads actually hold.
I have a theory question.

Assume that a Boglehead ladders 10 year bonds, replacing 10% of them each year. The average maturity would be about five years. However, ten year bonds pay more interest than five year bonds, and the portfolio only holds ten year bonds.

If you are going to analyze the returns on this laddered portfolio, would it be better to analyze based on five year maturities (the duration) or on ten year maturities (the actual bonds)?
Five-year maturities, since that's closer to the duration of the ladder.
EnjoyIt
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by EnjoyIt »

Pardon my ignorance, but this is the way I see things:

Mathematically 100% equities will most likely give the best results. While holding a position in equities and cash protects you from the worst case scenario.

Unfortunately we do not live in a mathematical computation where we can expect the best or the worst or the average. What we do have is a portfolio that needs to grow and then not evaporate in retirement. Since we have no idea what the future may hold, all we can do is hope for some sort of average return, and hedge for something worse. Unfortunately what the worse situation during our investment lifetime is a complete unknown. It can be hyperinflation, deflation, stagnation, or whatever else that could occur in whatever length and combination the future will bring us.

A portfolio that hedges against the worst case scenario that occurred 45 years ago, may very well not be the optimal portfolio to hedge against some future calamity.

Therefor the only answer is to diversify and hope for the best. Am I missing something here?
A time to EVALUATE your jitters: | https://www.bogleheads.org/forum/viewtopic.php?f=10&t=79939&start=400#p5275418
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

EnjoyIt wrote: Mathematically 100% equities will most likely give the best results. While holding a position in equities and cash protects you from the worst case scenario.
How are you defining "results"? I define results as the expected utility form a strategy. 100% equity rarely gives the best results unless you have the right combination of a high risk tolerance and a long investment horizon.
A portfolio that hedges against the worst case scenario that occurred 45 years ago, may very well not be the optimal portfolio to hedge against some future calamity.
I am trying to hedge against the average of scenarios that occurred from 1972-2015. I would do 1871-2015 but data is limited on everything but two assets. If there was a better way to assess risk of future calamities I would adopt it.
Therefor the only answer is to diversify and hope for the best. Am I missing something here?
Yes that's what I think. The classical 3-fund portfolio seems horribly undiversified as the bonds have a fairly long duration that exposes itself to extreme inflation risk (which has fat tails). If a person is using a 3-fund portfolio with 75% or more equity it might be okay. But if they are doing 30-70% equity and convesely 30-70% bonds, they should probably diversify more into TIPS or shorter duration bonds to hedge against inflation risk.
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by pkcrafter »

bh, first off, nice work.
The problem is that fitting statistical distribution may not be accurate. These are complicated processes. So perhaps the best one can do is use the chart as a rough benchmark and then eyeball an appropriate portfolio.
Are you now beginning to understand RodC's comments?

Another thought -- You find the optimal portfolio for 30 years and this portfolio is quite different than the 15, 10 year and 5 year portfolios, so my question is can one really hold the 30 year portfolio for 30 years? Starting at 30 years, doesn't the investor actually have only 15 years to hold that portfolio? And, of course, if the 30 year portfolio is only held 15 years, the returns will have a much higher dispersion.

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.
Rodc
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by Rodc »

Hi bh,

Since you are new and you are using rolling periods, you might find this of interest:

http://home.comcast.net/~rodec/finance/ ... eriods.pdf

In short, while the use of rolling periods makes lot of datapoints, it does not increase information beyond what you get from looking at independent (non-overlapping) periods.

So for example if you have 144 years and are using 10-year periods you have the information content of about 14 data values. Given the early data are from a historical period with a very different stock market and bond market, and the data are at best estimates of what happened, not a measurements of what happened, it is likely you really only have less than something like 10 good independent datapoints. Also, one tends to get into trouble doing pure statistical analysis without understanding the context or causation (the "physics" if you will).

So considering context, for bonds you have things like periods of high inflation or deflation, or a rising or dropping interest rate. These tend to take decades to play out, for example the decades before 1982 and the decades after 1982. We only have a couple of datapoints each of long rising interest rates or declining interest rates. Only one Great Depression for example, or one Tech Bubble. This means in reality the correlation and lack of information I mention is above is likely worse than the overlapping data window calculation would suggest.

What happened happened. Understanding what happened is important. But we do not have enough data for a statistical analysis that one can base bold decisions on. These analysis certainly hint at important things, but one should take the lessons that appear to be in the data with a large grain of salt because they may well be an illusion, or they may be real, but not something that will repeat. Even worse, with so few datapoints it is entirely possible that there is distinctly different possibilities we have not seen (yet).

For these reasons one really should avoid the hubris of thinking they have any accuracy as far as understand what will or even can happen in the future. Which leads to the wisdom of our elders to diversify widely -this way you will certainly not win big, but hopefully at least you won't lose big either.

Best of luck.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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bh7
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by bh7 »

So a severe limitation of my approach is that I was only allowed tbm, cash, and short/int/long treasuries for fixed income.

Why not CDs?

I don't have a data set of historical CD returns, so I did a crude approximation. KevinM might appreciate this.

I took the returns of short treasuries, and added 75 basis points.
CRRA=16

Code: Select all

  N  TSM   TBM  CDs TIPS     CAGR       SD
  1    0%   0%  80%  20%    2.89%    4.48%
  2    0%   0%  80%  20%    2.93%    3.87%
  3    0%   0%  80%  20%    3.07%    3.47%
  4   20%   0%  80%   0%    4.03%    3.38%
  5   20%   0%  80%   0%    4.14%    3.13%
  6   10%   0%  90%   0%    3.75%    2.75%
  7   10%   0%  90%   0%    3.83%    2.60%
  8   30%   0%  70%   0%    4.77%    2.85%
  9   20%   0%  80%   0%    4.47%    2.39%
 10   20%   0%  80%   0%    4.57%    2.18%
 11   30%   0%  70%   0%    5.12%    2.18%
 12   30%   0%  70%   0%    5.20%    2.00%
 13   30%   0%  70%   0%    5.26%    1.84%
 14   50%  50%   0%   0%    6.38%    2.37%
 15   50%  40%  10%   0%    6.40%    2.21%
 16   70%   0%  30%   0%    6.98%    2.38%
 17   80%   0%  20%   0%    7.43%    2.43%
 18   60%   0%  40%   0%    6.80%    1.84%
 19   80%   0%  20%   0%    7.54%    2.12%
 20   90%  10%   0%   0%    7.97%    2.12%

CRRA=8

Code: Select all

  N  TSM   TBM  CDs TIPS     CAGR       SD
  1   10%   0%  70%  20%    3.35%    4.86%
  2   10%   0%  70%  20%    3.38%    4.04%
  3   20%   0%  80%   0%    3.86%    3.91%
  4   30%   0%  60%  10%    4.47%    3.68%
  5   30%   0%  60%  10%    4.59%    3.42%
  6   30%   0%  70%   0%    4.59%    3.19%
  7   30%   0%  70%   0%    4.65%    3.02%
  8   40%   0%  60%   0%    5.15%    3.12%
  9   30%   0%  70%   0%    4.89%    2.62%
 10   30%   0%  70%   0%    4.99%    2.41%
 11   30%   0%  70%   0%    5.12%    2.18%
 12   40%   0%  60%   0%    5.60%    2.26%
 13   40%  20%  40%   0%    5.77%    2.17%
 14   50%  50%   0%   0%    6.38%    2.37%
 15   60%  40%   0%   0%    6.76%    2.45%
 16   70%  30%   0%   0%    7.14%    2.50%
 17   90%  10%   0%   0%    7.78%    2.70%
 18   80%  20%   0%   0%    7.63%    2.29%
 19   80%  20%   0%   0%    7.65%    2.17%
 20   90%  10%   0%   0%    7.97%    2.12%

CRRA=4

Code: Select all

  N  TSM   TBM  CDs TIPS     CAGR       SD
  1   30%  30%  30%  10%    4.32%    7.68%
  2   30%  10%  50%  10%    4.22%    5.51%
  3   40%   0%  60%   0%    4.60%    5.03%
  4   50%   0%  40%  10%    5.18%    4.75%
  5   50%   0%  30%  20%    5.33%    4.36%
  6   50%   0%  30%  20%    5.36%    3.93%
  7   60%   0%  20%  20%    5.70%    4.00%
  8   60%   0%  10%  30%    5.88%    3.75%
  9   50%   0%  40%  10%    5.66%    3.21%
 10   50%   0%  50%   0%    5.74%    3.00%
 11   60%   0%  40%   0%    6.21%    3.09%
 12   60%  30%  10%   0%    6.46%    3.00%
 13   60%  40%   0%   0%    6.57%    2.81%
 14   70%  30%   0%   0%    6.93%    2.84%
 15   80%  20%   0%   0%    7.28%    2.92%
 16   90%  10%   0%   0%    7.64%    2.93%
 17  100%   0%   0%   0%    7.99%    2.92%
 18  100%   0%   0%   0%    8.10%    2.66%
 19  100%   0%   0%   0%    8.14%    2.54%
 20  100%   0%   0%   0%    8.20%    2.30%
So now TIPS and TBM have a very limited role in the optimal portfolio. CDs are sufficient to cover your bases for fixed income.

I don't know why but years 1 and 2 horizons seem to have wonky results. I think this has something to do with the fact that large losses are mitigated by short holding periods, so the investor's preferences approach risk neutral. A horizon of 3 years is potentially the riskiest because that's how long some of the biggest drawdowns are and thus the potential loss of capital is greater. Rebalancing annually throughout the downturn probably hurts also. Since no one really has a 1- or 2- year horizon, from now on I will omit these years as their results are noisy.

Notice now that TBM only enters the portfolio 12-14 years, depending on the risk aversion. In this case the longer duration can be mitigated. But I didn't model longer term brokered CDs so those might be useful at that horizon.
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siamond
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by siamond »

siamond wrote:bh7, may I suggest something? Take the UK returns since 1900 (equities + gilts, which are government bonds), run your math again, and share your results & analysis. I think this could be interesting.

Here is the (public) source where to find UK historical numbers. I'll send you by PM a link to a more conveniently formatted Excel spreadsheet.
http://lwmconsultants.com/wp-content/up ... dition.pdf
bh7, I don't know if you noticed this post I issued a few days ago, or saw the PM I sent you. At the point where you are with your (interesting) analysis, a test out of sample would seem of great interest. Using the UK returns, you should be able to do that if you are so inclined.
TorturedRegret
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Re: Money illusion: Why bonds? See S&P 500 & 10y T-bond returns, 1871-2015

Post by TorturedRegret »

In the long run, it makes sense to buy 200% equities
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