Good discussion. I'll throw in my two cents, which, as always, only applies to me, my way of thinking, and my retirement planning. For me, any financial prediction, put forth by anybody, is meaningless information to me. There is a good discussion on predictions on the PRC Forum thread under Information Sharing > Sharing of Inflation Rates, Rates of Inflation > Asset Allocation page 10 May 30, 2023 2:19 PM. I also think cranking through all these financial calculations (CAPE, SD, CAGR%, iERP, Cleveland Fed Model, whatever) again provides me with zero information in terms of what to put into PRC or developing my Retirement Plan. Fun to play around with, you bet!! But I fear in provides a false sense of security about what the future will bring. It's mostly a psychology thing, no disrespect intended. Humans really don't like not knowing what the future will bring, and even more upset about not being able to doing anything about it. So we come up with predictions and elaborate gyrations to take control. A very good book I recommend is The Psychology of Money by Morgan Housel 2020.
Here’s the rub: the amount of uncertainty around all three of your estimates is huge. (And it couldn’t be otherwise, or there wouldn't exist such a large ERP as we have!)
So getting as nuanced as you're doing doesn't make sense to me personally. If there was a larger trend, it might make a difference. But would you really trust decisions like roth conversions on that?
I think that doing the analysis RIGHT is a lot like computing the probabilities in poker to bet "right". After the first, partial set of cards are dealt you need to decide whether it is worth the risk to bet an additional X dollars to see the next card and have a chance to win Y dollars, given the cards you've received, the number of other players in the hand, and how the players have already bet. It takes a lot of effort to get that decision "right", it takes a lot of effort long before the game studying, practicing, analyzing, and learning and then during the game you need to perform that mental computation quickly and under stress.
And after all that effort, all my hard work and hand-wringing gets overwhelmed when the very next card gets dealt and all the odds change massively again.But in my mind when we face a betting opportunity paying 2 to 1, doing the computation correctly to determine whether it has a probability of success of 52% or just 48%... that's what the whole game is!
For me, I prefer to know the real odds ahead of time and risk losing to bad fortune rather than to not know the real odds and play anyways. I do however respect that others might say that to them that is not a game worth playing, or at least not worth playing that way...
I don't think our confidence in return estimates is like poker. The game of poker is very full of chance but well understood, and every aspect is quantifiable other than human psychology. It is a very controlled chance. With these return models we're not even sure, epistemically, the models themselves are correct, let alone the details of their predictions. One thing I like about the actuarial model we both use is that is "self correcting", and you don't have to be 100% accurate about your predicted returns. Getting it too high or low will merely adjust the slope of your withdrawal, so any error is spread out across the whole plan.
The first thing that popped into my head reading your investment planning thinking process the Kelly Criterion, coming from gambling theory, which attempts to justify the rational amount of risk to take. Merton generalized it in what's known as the "Merton share". (It is also closely related to the sharpe ratio.) Have you heard of it? It essentially attempts to quantify the amount of risky asset justified by a given SD: It's two asset version (Risky asset and riskless asset) is:
Equity Premium / (SD squared * risk aversion). Victor Haghani and James White talk about it at length in their Missing Billionaires book. (By survey they claim most people are in the 2-3 risk aversion range, fwiw.) I remain skeptical of the whole thing, but it seems right up your alley. Using your returns estimates, and a typical risk aversion of 2.5, the Merton share would recommend 80% AA. (7.5%-1.9%)/(2.5*16.34%^2)
After my rant about predictions, I found this article: https://finance.yahoo.com/news/heres-average-stock-market-return-082500652.html
... the S&P 500 has an average year-end target (2026) of 7,616 among 19 Wall Street analysts. That implies 10% upside from its current level of 6,922. Not shown in the chart is that the median year-end target is 7,600, which also implies 10% upside
As a caveat, Wall Street's forecasts concerning the S&P 500 are often very wrong. In fact, during the five-year period from 2020 to 2024, analysts' median year-end target was wrong by an average of 18 percentage points, according to data from Goldman Sachs. That does not mean Wall Street is incompetent, but rather predicting the future is impossible. (My bolding)
My assumptions in Pralana are the same each year -
There will be a 3% equity premium of stocks vs. bonds.
That inflation will be 2.8-3%.
I tune the stock return percentage so that it works out mid way between the 20th and 30th percentile of historical results (meaning 75% of historical cases were better). That ends up being 5-5.2% real for stocks and 2-2.2% for bonds. For cash, I use 0.5% real. I'm not trying to be overly pessimistic, but note that all the starting years that show spectacular growth started from deep market downturns and that's not the current market, so I should be using something that is somewhat less than the average return.
Of course the future will do what it will do and not follow such simplistic assumptions.
My assumptions below, as of Jan 6 2026.
Inputs & Sources
Input Type Value Refreshed Comments ERP Damodaran 4.20% 1st, Monthly https://pages.stern.nyu.edu/~adamodar/ Method: Trailing 12 month, with adjusted payout Risk-Free Rate (Treasury Yield) 10-yr Yield 4.19% Daily https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_yield_curve TIPS 10-yr Yield 1.91% Daily https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_real_yield_curve Expected Inflation 10-yr Inflation 2.34% Monthly, btwn 10th-15th https://www.clevelandfed.org/indicators-and-data/inflation-expectations
Capital Market AssumptionsCash: 1% Real return
Bonds (TIPS_LADDER): 1.91% Real return
Inflation Value Arithmetic Avg 2.36% Std Dev 1.74% Geo Avg 2.34% US Equities (S&P 500) Arithmetic Nominal 9.79% Std Dev Nominal 16.75% Geometric Nominal 8.39% Arithmetic Real 7.25% Std Dev Real 16.34% Geometric Real 5.91%
Can you please say more how you arrived at the 7.25% real arithmetic average for equities?
If ERP=4.2% and the risk free rate is 1.9% (tips), wouldn't that be ~6.1% arithmetic = 4.6% geometric (to be entered into Pralana)?
Can you please say more how you arrived at the 7.25% real arithmetic average for equities?
If ERP=4.2% and the risk free rate is 1.9% (tips), wouldn't that be ~6.1% arithmetic = 4.6% geometric (to be entered into Pralana)?
Sure... the key observation is that both ERP and Risk-Free Rate are GEOMETRIC values, compound average returns over multiple years.
Then the conversion analysis proceeds as follows...
Geometric nominal return of equities from T-Bonds and ERP
Nominal Expected Return of Equities (CAGR%) = Nominal Risk-Free Rate (CAGR%) + Equity Risk Premium (CAGR%)
Nominal Expected Return of Equities (CAGR%) = 10-year T-Bond rate + ERP = 4.19% + 4.2% (Both CAGR%) = 8.39%
Converting from Nominal to Real return CAGR% via Fischer Equation: (1 + Nominal) = (1 + Real) * (1 + Inflation)
Real Expected Return of Equities (CAGR%) = [ 1 + Nominal Expected Return of Equities (CAGR%) ] / [1+ Expected Inflation (CAGR%)] - 1
Real Expected Return of Equities (CAGR%) = [ 1 + 8.39% ] / [1+ 2.34%] - 1 = 5.91%
Converting from Geometric returns to Arithmetic Returns via Volatility drag formula: Real Return of Equities (Geometric) ~= Real Return of Equities (Arithmetic)- 0.5 x (Standard Dev)^2
Real Return of Equities (Arithmetic) = Real Return of Equities (Geometric) + 0.5x (Standard Dev)^2
Real Return of Equities (Arithmetic) = 5.91% + 0.5 x (16.34%)^2 = 7.25%
Hopefully I didn't screw that up...
Hi @jkandell
Maybe the more important observation then that I should have mentioned is that most people are familiar with ERP from its use in the CAPM model, and because the CAPM is formally a 1-period model, and doesn't account for multi-period volatility drag, so you must account for volatility drag separately when preparing a multi-period forecast.
The ERP that I start my calculation with is the iERP estimated by Aswath Damodaran each month*. In terms of its construction in the DCF model that Aswath employs, the iERP is essentially an Internal Rate of Return (IRR) calculation—effectively a compound annual growth-based estimate.
Rephrasing and summarizing: The ERP that I use (the iERP) is an implied, forward-looking IRR, which is more analogous to a geometric estimate (reflecting compound growth) than a simple arithmetic average of annual historical returns.
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Note: * Updated monthly on A. Damodaran's webpage here: https://pages.stern.nyu.edu/~adamodar/
@boston-spam-02101gmail-com Thanks that is very helpful to my understanding. His model seems better than a simple Yield & Growth because it gets into the nitty gritty of the generation of dividends and buybacks. As an aside, I thought it was interesting that Damodaran includes a 23 basis default spread (due to the devaluation by credit agencies?).
@boston-spam-02101gmail-com Thanks that is very helpful to my understanding. His model seems better than a simple Yield & Growth because it gets into the nitty gritty of the generation of dividends and buybacks. As an aside, I thought it was interesting that Damodaran includes a 23 basis default spread (due to the devaluation by credit agencies?).
Yes, Aswath's approach is considered the most theoretically sound method of evaluating current market pricing and the implied expected future market returns. He also incorporates sustainability of payouts, multiple regression to sustainable long term growth levels, and a few other idiosyncracies like US Sovereign Debt risk.
Re: Soverign debt, he's basically finally acknowledging that the odds of the US defaulting on debt is not zero. That's something that the major debt ratings agencies have been saying for years. S&P downgraded the US in 2011, Fitch downgraded in 2023, and Moody's Downgraded in 2025.
I remember arguing with my finance professor back in 2005 that US Treasuries aren't really "Risk Free", because there was a non-zero chance that the US Government would collapse before the payments were due, because "Nothing lasts forever... including countries". I tried to argue that although Rome lasted 1,000 years, that would mean that during the average 70-year lifespan there was still a 1 in 14 (7%) chance of collapse. He wasn't impressed and said that US Treasuries were "close enough to Risk Free over the next 10 years" for his purposes.
I think that to use the 23 basis point default spread, you either need to
A) Subtract 23 bps from the current treasury yields to get an "idealized" Risk Free Rate and then add it back to the iERP to get the same total expected return on equities, OR
B) Pretend that the US Treasuries really are risk free (they aren't) and use the iERP as calculated, and you'll still get the same total expected return.
Best regards,
Kevin
My understanding for long term retirement projections is Normalized Earnings & Payout iERP (currently 3.62%) might be a better one to use. Do you think this is too conservative? Thanks!@boston-spam-02101gmail-com Thanks that is very helpful to my understanding. His model seems better than a simple Yield & Growth because it gets into the nitty gritty of the generation of dividends and buybacks. As an aside, I thought it was interesting that Damodaran includes a 23 basis default spread (due to the devaluation by credit agencies?).
My understanding for long term retirement projections is Normalized Earnings & Payout iERP (currently 3.62%) might be a better one to use. Do you think this is too conservative? Thanks!@boston-spam-02101gmail-com Thanks that is very helpful to my understanding. His model seems better than a simple Yield & Growth because it gets into the nitty gritty of the generation of dividends and buybacks. As an aside, I thought it was interesting that Damodaran includes a 23 basis default spread (due to the devaluation by credit agencies?).
Aswath typically prefers TTM Earnings with Adjusted Payout for valuing the US S&P500 in "real time", and that's what he uses for many of his presentations regarding current market valuations. Main drawback of this method is is that can be "noisy" during periods of rapid changes in buybacks or earnings. Doesn't appear to have been the case in the past couple of years. This would be the best method to use if you want to argue that "Based on current market conditions (prices, earnings, payout rations, etc), USA Investors today expect an Equity Risk Premium of X.X% on average over the next 5-10 years".
The Normalized Earnings & Payout iERP is better for calculating long-term average iERP because it uses 10-year averages of (inflation adjusted) earnings and payout ratios. This would be the best method to use when you want to argue that "The equity risk premium was lower in the 1960s than in the past 10 years"
.
Which would be best for retirement planning?
I believe that if you want to use just one number for your entire retirement forecast period then Normalized Earnings & Payout iERP is better for long-term retirement planning. It smooths out recessions, bubbles, and buyback cycles.
But, that can lead to a "scary ride" through bubbles and crashes, because your near-term experience won't match your long-term expectations, but you won't be adjusting your plan or behavior to the current conditions... You're just just setting one trajectory and average speed for the next 30+ years and sticking with it as you ride through the all the rough patches. (Kind of like the 4% rule. The spending "ride" is smooth, but the experience can be terrifying if you watch your portfolio drop but keep spending just as much)
.
So, either use a one-period model (and ride through the near-term bubble volatility on cruise-control)
1: Next 30+ years: 30-yr Risk-Free Rate (1.75%*) + Normalized iERP (3.6%) = ~1.75% + ~3.6% = ~5.4% (Real) [*See Addendum note #1]
.
OR - try using a multi-period model to capture the near-and mid-term outlooks explicitly (If you think we're in a bubble, then it's better act like we're in a bubble);
My speculative 3-period model:
1) Next 5 yrs: 10-yr Risk-Free Rate (1.9%) + TTM Earnings with Adjusted Payout (~4.2) = ~6% p.a. (Real)
2) Years 5-15: Mean reversion of valuations = ~4.8% p.a. (Real)
3) Years 15+: Dividend Yield + Earnings Growth (Bogle Method) = ~5.0% p.a. (Real) [Note #2]
-> Next 30-years blended CAGR% = ~5.1%
Observe that they don't converge into a single consistent long-term outlook, with the multi-period model appearing to be more conservative...
I suspect that's probably because the current market estimates of long-term GDP/Earnings growth embedded into this first approach are more optimistic than the long-term Yield & GDP Growth estimates I used in the Bogle Yield+Growth formula.
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Addendum Note #1
After some further research, I learned that I was wrong about what Risk-Free Rate Aswath would use for the long-term (30yr) real Risk-Free Rate in his estimate of 30-year expected market returns.
He would NOT use the 30-year Treasury Rate (TIPS = 2.5%) because he believes that the 30-year Treasury prices are distorted by monetary policy changes and too lightly traded so therefore distorted by short term demand fluctuations
Instead he would use either the more heavily traded 10-year TIPS (TIPS =1.9%), or long-term estimated of GDP growth (1.6%) or a weighted average of both (1.75%)
- Original: Next 30+ years: 30-yr Risk-Free Rate (2.5%) + Normalized iERP (3.6%) = ~2.5% + ~3.6% = ~6% (Real)
- Updated: Next 30+ years: 10-yr Risk-Free Rate (1.75%) + Normalized iERP (3.6%) = ~2.5% + ~3.6% = ~5.4% (Real)
Addendum Note #2
I asked some AI platforms to provide their best estimate of the total real returns of the US Stock market for the very long-term outlook period of 20-30 years from now. (Most defaulted to the Bogle method, except for Grok which tried to average analyst estimates. I then directed Grok to use Bogle method and the result is below)
These are their point estimates or midpoints of the ranges they gave:
- Gemini - 3.7%
- CoPilot - 4.5%
- ChatGPT - 5%
- Grok - 5.5%
- Claude - 6.5%
- Median: 5%
- Average: 5.04%
- Range: 3.7-6.5%
The one thing that I know for certain is that none of these point estimates will be precisely correct. The range is a maybe...
For what it's worth, Damodaran January equity risk premium (Normalized Earnings & Payout) is now available. https://pages.stern.nyu.edu/~adamodar/
Using his ERP and 10 year TIPS breakeven inflation rate on December 31, 2025, expected stock real return would be 3.62 + 2.25 = 5.87. This is very generous compared to some of our estimates.
Thoughts on why most of us are using a lower estimate than the "godfather of equity risk premiums"? Does arithmetic vs geometric returns enter into this in some way again?
There are three common ways of estimating future returns: Using Schiller CAPE (Market valuation method), focusing on the Equity Risk Premium, or via Dividend Yield & Growth. (Damodaran combines the second and third.)
The low values tend at the moment to be based on CAPE based predictions, regressing the history of starting CAPE and subsequent 10 year returns. CAPE near record highs means near record low future returns. The Yield and Growth and ERP models are giving much higher results.
Having said that, i think you are correct that arithmetic and geometric (and nominal and real) get mixed up a lot in returns estimates.
If people want to use the valuation based methods of forecasting market returns for their retirement planning, then they REALLY SHOULD switch to a two-period forecast model.
All these valuation-based models (e.g., CAPE) assume some sort of reversion-to-the-mean of their valuation metric of choice over some mid-to-long term time period such as the next 10 years, which means that the P/E ratios will be dropping to the next 10 years. Okay, fine... that makes sense if you think we're in a bubble. (The alternative is to assume that earnings will grow) But it doesn't make sense to continue using that conservative market return number for years 11-50+... that would imply that P/E ratios would keep dropping for the next 50 years...
What does that mean? That we're expecting the bubble to pop in the next 10 years, and then continue popping more from years 11-20, then keep popping more again for a third decade in a row from years 21-30, etc, with the P/E RATIOs DROPPING IN HALF EVERY DECADE FOR THE NEXT 50 YEARS?
Imagine what a low P/E valued environment you're assuming we'd end up in by years 20+!
I use Vanguard's Capital Markets Model Forecast. Vanguard Capital Markets Model® forecasts | Vanguard
Process:
1) Back the 10yr assumptions out of the 30yr assumptions to get seperate assumptions for years 1-10 and years 11-30.
2) Pralana treats inflation as deterministic (zero volatility). To account for this, approximately, I adjust each assets volatility to account for inflation volatility.
(Adj Asset Vol) = SQRT[ (Asset Vol)^2 + (Inflation Vol)^2) ]
Here are the resulting assumptions for the past 3 quarters.
| 7/23/2025 | 10/22/2025 | 1/22/2026 | ||
| 1-10yr ROR | U.S. equities | 2.3% | 1.7% | 2.8% |
| Global ex-U.S. equities (unhedged) | 4.0% | 3.7% | 3.5% | |
| U.S. aggregate bonds | 2.5% | 2.2% | 2.5% | |
| U.S. TIPS | 1.3% | 1.1% | 1.5% | |
| U.S. cash | 1.5% | 1.3% | 1.5% | |
| U.S. inflation | 2.0% | 2.1% | 2.0% | |
| 1-10yr Volatility | U.S. equities | 15.3% | 15.2% | 15.3% |
| Global ex-U.S. equities (unhedged) | 18.9% | 18.9% | 19.0% | |
| U.S. aggregate bonds | 6.6% | 6.5% | 6.5% | |
| U.S. TIPS | 5.4% | 5.3% | 5.3% | |
| U.S. cash | 2.1% | 2.1% | 2.0% | |
| U.S. inflation | 0.0% | 0.0% | 0.0% | |
| 11-30yr ROR | U.S. equities | 3.9% | 3.9% | 3.9% |
| Global ex-U.S. equities (unhedged) | 5.3% | 5.5% | 5.6% | |
| U.S. aggregate bonds | 2.6% | 2.7% | 2.5% | |
| U.S. TIPS | 1.6% | 1.7% | 1.6% | |
| U.S. cash | 1.2% | 1.3% | 1.2% | |
| U.S. inflation | 2.0% | 2.0% | 2.0% | |
| 11-30yr Volatility | U.S. equities | 17.0% | 16.9% | 17.1% |
| Global ex-U.S. equities (unhedged) | 20.5% | 20.5% | 20.7% | |
| U.S. aggregate bonds | 6.8% | 6.8% | 6.8% | |
| U.S. TIPS | 5.7% | 5.5% | 5.5% | |
| U.S. cash | 2.6% | 2.4% | 2.4% | |
| U.S. inflation | 0.0% | 0.0% | 0.0% |
I use Vanguard's Capital Markets Model Forecast. Vanguard Capital Markets Model® forecasts | Vanguard
Process:
1) Back the 10yr assumptions out of the 30yr assumptions to get seperate assumptions for years 1-10 and years 11-30.
2) Pralana treats inflation as deterministic (zero volatility). To account for this, approximately, I adjust each assets volatility to account for inflation volatility.
(Adj Asset Vol) = SQRT[ (Asset Vol)^2 + (Inflation Vol)^2) ]
Here are the resulting assumptions for the past 3 quarters.
Hi CZ,
That sounds like a pretty good process, and a valuable resource. Thank you for sharing!
I'm not sure how good Vanguard's track record has been, but the Inflation and TIPS both seem low... and those are things we have pretty good market-based models for. Especially TIPS.
FWIW, it looks like Vanguard is basically applying the fed targets for Inflation, and some long-term historical average for TIPS.
I'm not sure how good Vanguard's track record has been, but the Inflation and TIPS both seem low... and those are things we have pretty good market-based models for. Especially TIPS.
FWIW, it looks like Vanguard is basically applying the fed targets for Inflation, and some long-term historical average for TIPS.
Yeah, I agree. Their numbers generally seem lower than most other published assumptions, particularly for US Equities, but I'm OK with a little conservatism. I am considering upping the inflation number, 2.5% seems like a common assumption for 2026. I do like the separate 10 year and 30 year forecasts Vanguard provides.
In addition to the deterministic "best guess", I do think stress testing with alternate scenarios would be quite useful. In particular, making return negative over the first 3 years and then higher recovery rates for years 4-10 such that the 10 year annualized return equals the best estimate 10 year assumptions. Maybe assume all asset classes have returns of best est - X standard deviations for the first 3 years and then back into the required returns for years 4-10. Then I just need to decide on a value for X.
On another note, I also like the report JPMorgan publishes. I don't use their numbers in Pralana, but I like the fact that they provide a complete correlation matrix. If you click "download the full report" in the link below you will get the pdf. Assumptions start on page 82. I haven't seen any other company publish assumptions with a correlation matrix.
Long-Term Capital Market Assumptions | J.P. Morgan Asset Management
