Assumptions about Stock/Bond?Intnl returns

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merddynemrys
Posts: 2
Joined: Sat Jun 07, 2008 9:14 am

Assumptions about Stock/Bond?Intnl returns

Post by merddynemrys »

Jim,
(me again, still playing with FRP)
I started looking at the investments styles and I'm intrigued about what assumptions are being made about the contributions to returns of each of the allocations.
My initial assumption was that (excepting the S&P500 only choice) that the stocks for each of the scenarios have the same percentage return, ditto bond and intn'l (i.e. if stocks return 10% in one scenario then they will return the same 10% in all scenarios, with the exception noted, so that the total contribution to of stocks to the portfolio will be the percentage of stocks in the portfolio multiplied by the stock return - seem reasonable?).
HOWEVER this is not what I'm finding.
Here are the equations I used to solve for the partial returns of each component):
1. Risk Averse: 0.17S+0.77B+0.05I=0.065
2. Below Average Risk: 0.3S+0.6B+0.1I=0.075
3. Moderate Risk: 0.41S+0.45B+0.14I=0.085
4. Above Average Risk: 0.62S+0.17B+0.21I=0.1
4. Aggressive: 0.7S+0.07B+0.23I=0.105
(S=Stock return, B=Bond return, I=Intn'l return)

If I solve these as sets of three simultaneous equations I get six sets of results for S,B,I
which are VERY incomsistent:
B has an outlier of about +4%, but the other 5 results range from +5.1% to +5.5% (so not too bad)
S ranges from -8.9% to +42.7%
I ranges from -77.4% to +69.6%
(see what I mean about consistency?)

Am I doing something wrong?

The only conclusion that I can reach is that the same MIX of Stocks/Bonds/Intn'l are not being used for each of the scenarios. (For example going from Averse to Aggressive maybe stocks are going from stodgy, reliable "old" world (Averse) all the way up to highly speculative (Aggressive).

Would you care to shed some light on this (and in particular where did the numbers for the original mix and returns come from).

Thanks,

dave (smith)

jimr
Posts: 596
Joined: Thu Feb 28, 2008 6:48 pm

Re: Assumptions about Stock/Bond?Intnl returns

Post by jimr »

Dave,

The fact that you've noticed some inconsistencies in the canned return/std data doesn't surprise me.

The truth is, I added them as an after-thought in the FRP GUI to make it more user friendly. They were an amalgam of a few historical index portfolio data sources with attempts to adjust for investment expenses.

I found it surprisingly difficult to find good sources for this info that include stocks, bonds, and international returns that are also adjusted for expenses. Data for just stocks vs bonds is easy to come by, but I felt that including at least three asset classes would be more realistic. The main problem is that historical data on international returns is all over the map depending on exactly what's included and how the data was acquired.

Anyhow, to the extent that the data are flawed, I think they're too conservative, but honestly I don't feel great about what's there now. If you know of any good sources that I could use to replace these, I'd be eager to check them out.

Jim

Keith Sharp

Re: Assumptions about Stock/Bond?Intnl returns

Post by Keith Sharp »

This retirement calculator does an excellent job in many ways. But the results are only as good as the assumptions. In 2010, with the stock market having given approximately zero return over the last 10 years, assuming 5% above inflation looks mighty optimistic. My opinion is that the market TIPS yield, currently about 1.5% real, is a hard data point that deserves a lot of respect and prominence.

jimr
Posts: 596
Joined: Thu Feb 28, 2008 6:48 pm

Re: Assumptions about Stock/Bond?Intnl returns

Post by jimr »

Keith Sharp wrote:This retirement calculator does an excellent job in many ways. But the results are only as good as the assumptions. In 2010, with the stock market having given approximately zero return over the last 10 years, assuming 5% above inflation looks mighty optimistic. My opinion is that the market TIPS yield, currently about 1.5% real, is a hard data point that deserves a lot of respect and prominence.
Choosing an expected rate of return in retirement planning is certainly a tough problem and IMO there isn't a single right answer. Personally, I like to try multiple runs with different return/std dev values to see how sensitive my plan is to market performance. For plans with a long accumulation phase in front of them, it might make sense to use the additional inputs and model different rates of returns over different phases of the plan (more aggressive during accumulation, more conservative during withdrawal).

It is important to keep in mind that tools like the Flexible Retirement Planner don't make predictions. They only compute results based on the inputs that the user provides. This is why I'm a strong proponent of stress-testing the plan by varying the inputs to see the impact on the results.

Also, while it's true that after the last ten years, 5% real return looks optimistic, historically, the best results have come after periods of poor results and vice-versa. The long-term real compound annual growth rate for the S&P500 is over 6% real.

Here are historical returns in real CAGR for the SP500:
2000-2009 -3.42%
1990-2000 12.17
1980-1990 9.88
1970-1980 0.18
1960-1970 4.47
1950-1960 15.13
1940-1950 5.43
1930-1940 .85
1920-1930 12.97
1910-1920 -3.19
1900-1910 7.11
1900-2009 6.28
(source moneychimp.com CAGR calculator)
Finally, if you'd like to play it completely safe and use a real return around 1.5%, you probably don't need to use Monte Carlo simulation at all, since the variance (std dev) of a portfolio returning 1.5% real is probably quite small.

Jim

Willie
Posts: 5
Joined: Thu Dec 26, 2013 12:54 pm

Re: Assumptions about Stock/Bond?Intnl returns

Post by Willie »

Hello. I've always been skeptical of published returns out there on the various investment mixes. I could never figure out how these numbers were calculated or where they came from, and they always seemed high to me. So I went looking for historical data and found Robert Shiller's historical returns going back to 1871. I downloaded his spreadsheet and did my own number crunching on the raw data.

I also researched how to mix stocks, bonds and cash together for different overall returns and standard deviations. And I learned how to calculate risk (std dev) for different time horizons. Moneychimp.com talks about the effects of increasing time horizons on risk and how it's reduced with longer horizons. In other words, if you have to live year to year off your stock investments in retirement, you will be forced to sell your stocks each year to live (1 yr time horz) and your risk will be 17.9% (rather high since you will be required to sell in bad years also). But if you maintain a 4 year cash fund to live off of and fund it only in good years then your risk drops in half to 8.9%.

The numbers that I'm using in FRP are for 50% stk, 25% bonds and 25% cash:

Return = 7.5% with SD = 9.0% (7.1% geometric mean)
Inflation = 2.25% with SD = 6.0%

If you can increase your time horizon to 4 years:

Return = 6.9% with SD = 4.6% (6.8% geo mean)

I use 4 years because that number has the most bang for the buck. Beyond 4 yrs, the drop in risk is less dramatic.

My actual historical numbers that I calculated are:

S&P (with dividends) 10.3% mean x 17.9% SD
10yr bonds 4.64% mean x 2.25% SD
Cash (1 yr interest rates) 4.72% x 2.79% SD
Inflation (CPI) 2.25% x 6.04 SD

If you take these S&P returns for each year and graph it out on a log graph, and fit a line to it from 1871 to 1944 and a line from 1944 to present, it shows the S&P has doubled every 10 years like clockwork from 1944 with a 96% fit. I choose 1944 because the two fitted lines meet here nicely. If you extrapolate back, the early line interestingly intersects the x axis in 1792 at a value of 1, which was when the NYSE was formalized. Extrapolating forward, it has the S&P at 2048 in 2015 and 4096 in 2025 and 8192 in 2035.

If you superimpose a cyclical waveform (sinusiodal) on top of the fitted line from 1944 on, it fits the data even better. I used the excel solver to fit the cyclical line. This line passes up through the linear line in 1950, down through in 1970 (just before the 73-74 crash), back up through in 1990 for that bull run, and back down through in 2010. The bottom of this upcoming trough will be in 2019. This cycle is 39.3 years. I though this all was kind of interesting so I thought I'd share.

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