Happy New Year! 🥂 Time for annual updating of Pralana Online. Part of this process includes updating assumptions for inflation, asset class returns, etc. Here are my assumptions. Looking forward to seeing what others are using. These assumptions have a large influence on Pralana projections, so I think it is valuable to put some thought into this and to see what others are doing.
Inflation- 2.25% (10 year Breakeven Inflation Rate at FRED); https://fred.stlouisfed.org/series/T10YIE
Cash real return- 1.42% (3 mo t-bill nominal yield of 3.67% at Treasury.gov minus inflation assumption of 2.25%); https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_yield_curve&field_tdr_date_value=202512
Bonds real return- 1.93% (10 year TIPS yield at Treasury.gov); https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_real_yield_curve&field_tdr_date_value=202512
Stocks real return- 5.1% (default expected return at TPAW); https://tpawplanner.com/
I will add Aswath Damodaran expected return for stocks for January 2026 when it becomes available (Implied Equity Risk Premium Normalized Earnings & Payout plus 10 year TIPS real yield of 1.93%) as a separate scenario; https://pages.stern.nyu.edu/~adamodar/
Thanks! 😀
Very interesting links, cool stuff! Not sure I understand the 10 year Breakeven Inflation Rate at FRED. Can you explain what it is saying and why you are using it and how long you think the 2.25% can be used into the future?
@pizzaman - Breakeven inflation rate is the difference between 10 year nominal Treasury and 10 year TIPS and is used by some as an estimate of average inflation for the next 10 years.
"The breakeven inflation rate represents a measure of expected inflation derived from 10-Year Treasury Constant Maturity Securities (DGS10) and 10-Year Treasury Inflation-Indexed Constant Maturity Securities (DFII10). The latest value implies what market participants expect inflation to be in the next 10 years, on average." from https://fred.stlouisfed.org/series/T10YIE
I assume 3% inflation and then have three scenarios (all real rates): 1) conservative baseline (cash 0.5, bonds 1.5, stocks 4.0); 2) doomsday (all 0.0); and 3) historical average (cash 0.5, bonds 1.5, stocks 7.7). I'm not trying to be accurate, I'm trying to evaluate decisions under a broad range of possible futures.
@plaut - Thanks for your response. Sounds like a good process. Do current valuations enter into your assumptions? Do you account for international vs domestic equities?
@plaut - Thanks for your response. Sounds like a good process. Do current valuations enter into your assumptions? Do you account for international vs domestic equities?
Only insofar as they inform how conservative I make my "base" case, which I make slightly more pessimistic than my actual best estimates (which I know are really just guesses). Our US/ex-US equity split is about 75/25 but all that matters from the point of view of modeling in Pralana is the overall rate of return of the combination (whatever that may be).
Stocks real return- 5.1% (default expected return at TPAW); https://tpawplanner.com/
TPAW uses an arithmetic average in its stock returns. So 5.1% arithmetic for Pralana entry is about 3.5% geometric average.
Thank you for your response. Even though I enjoy using Pralana, I do not have an engineering/statistics background. 😟
Do you mean if I want to use an approximate TPAW equivalent assumption in Pralana, 3.5% real return for stocks would be about right? If so, Final Effective Savings decreases by about 30%. 😧 This is a good example of how dramatic the effects of these assumptions are!
Would you be able to expand on what you said or suggest a resource for a non-statistics background individual to learn more?
I wonder if you might share how you arrive at assumptions for expected returns, inflation, etc? Your posts are always insightful and I have learned a lot from them.
Thanks again!
Very interesting links, cool stuff! Not sure I understand the 10 year Breakeven Inflation Rate at FRED. Can you explain what it is saying and why you are using it and how long you think the 2.25% can be used into the future?
@Pizzaman, A few thoughts on inflation:
As @lancaster22 shared, the fastest way to calculate the estimated average inflation CAGR% over any particulat outlook period is to subtract the TIPS yield for that time period from the nominal yield for the same period.
This calculation is shown in the table below on the row labeled "Difference".
If you're looking at next-5 year only (2026-2030), the difference method implies an expected inflation CAGR% of 2.26%.
If you're looking at next-10 years (2026-2035), it's slightly lower at 2.25%.
Or if you're interested in the next 20 years (2026-2045), its higher still at 2.40%.
So, inflation is expected to change over time...
| Treasury Yield Curve | ||||||||
| As of 12/31/2025 | ||||||||
| https://home.treasury.gov/resource-center/data-chart-center/interest-rates/ | ||||||||
| Term | ||||||||
| 5 Yr | 7 Yr | 10 Yr | 20 Yr | 30 Yr | Comment | |||
| Daily Treasury Par Yield (T-Bond) | 3.73% | 3.94% | 4.18% | 4.79% | 4.84% | Nominal Yield CAGR% | ||
| Daily Treasure Pay Real Yield (TIPS) | 1.47% | 1.69% | 1.93% | 2.39% | 2.62% | Real Yield CAGR% | ||
| Difference | 2.26% | 2.25% | 2.25% | 2.40% | 2.22% | ~Inflation CAGR% | ||
| Inflation | 2.23% | 2.21% | 2.21% | 2.34% | 2.16% |
| ||
Methods of Calculating Expected Inflation from %Yields of T-Bonds and TIPS
This "difference" approach described above is definitely the most practical calculation method for daily use, but is just an approximation.
Inflation CAGR% = Nominal_Yield% - Real_Yield%
The more complex "division" method is only slightly more accurate
Inflation CAGR% = (1+Nominal_Yield%)/(1+Real_Yield%)-1
For the period of the next 10 years, the difference method predicts average inflation CAGR% of 2.25%, whereas the division method predicts average inflation CAGR% of 2.21%. That 0.04% difference is very close, and the difference of both methods from the actual REALIZED inflation over the next 10 years will certainly be much higher.
Logic for this more precise division method is as follows:
The realized payout yield for T-Bonds will be: (1+ Nominal_Yield%)
and the realized payout yield for TIPS will be: (1+ Real_Yield%) x (1+Inflation%)
In an efficient market, arbitrage ensures that two assets with identical risks and cash flows must have the same price. If investors expect inflation to be higher than this "gap," they would sell T-Bonds and buy TIPS to lock in a better deal. This buying pressure forces prices to adjust until the yields reflect the market's collective inflation forecast—the point where no "free lunch" (arbitrage) remains between the two.
Therefore investors buy and sell until prices reach equilibrium and
T-Bond payout = TIPS Payout = TIPS Yield + Inflation
(1+ Nominal_Yield%) = (1+ Real_Yield%) x (1+Inflation%)
and solving for inflation,
Inflation% = (1+Nominal Yield%)/(1+Real Yield%)-1
Observe that there's always some "noise" in these calculations... more on that below in the next section.
CAGR% versus v Inflation term structure
Both the difference and divisions methods above can calculate the expected effective average inflation over the term period (today until maturity).
To determine the expected inflation during any PARTICULAR future period (e.g., next year only or the period from years 11-30 specifically), then you need to divide out the effect of the earlier period from the inflation effect of the full term period from today until maturity.
That is, the expected 7-year inflation CAGR% is equal to the expected 5-year inflation CAGR% multiplied by the expected inflation CAGR% for years 6-7.
There is also a small amount of noise in the market estimates due in part to volatility in daily prices, differences in post-tax cashflows from TIPS v. T-Bonds, a risk premium demanded by T-Bond buyers in return for their willingness to take on inflation risk, and other factors.
Luckily, the FED does this calculation for us every month, smooths out the noise, and makes corrective adjustments where they think they know how and posts the resulting inflation forecast to this website: https://www.clevelandfed.org/indicators-and-data/inflation-expectations
And the current inflation term structure looks like the attached image, starting high today and decreasing for the next 10 years, then increasing again in the out-years.
Note that the long-term inflation estimate is < 2.5%, meaning that the bond market believes that the FED will generally be successful at keeping inflation under control.
So, how do we use this influx of information. Condensing all this down, since present US inflation is 2.7%, (the period of the next 10 years, the difference method predicts average inflation CAGR% of 2.25%), we should get 10 year TIPS vs regular US treasuries???
@lancaster22, The arithmetic average is just the simple mean return. You take each year's return and average them. The geometric average return is the growth average or compounding average: the even amount of growth that if it takes place year after year would result in your final dollar amount. (It involves dividing the growth by a root of the number of years.) Apy and cagr are examples of geometric average returns.
Pralana manual says the return entries are meant to be geometric averages (cagrs). My understanding is that for its Monte Carlo pralana behind the scenes takes the user’s (geometric) growth entries and converts them to arithmetic averages.
The formula for converting one to the other is arithmetic avg=geo + 1/2 variance. (Another way of thinking about it is that the geometric average has volatility “built in” whereas the arithmetic average doesn’t.)
So, yes, to get to the 5.1% that tpaw uses, you’d use 3.5% in Pralana (since the sd is 18). Then pralana will bring it back up to 5.1 for the Monte Carlo. Or put another way, a 5.1% average return stock will have a CAGR of about 3.5% in a monte carlo or real life due to volatility drag.
Tpaw bases it predictions on the cape, and record high valuations correlates with record low returns going forward. But who knows, right?
So, how do we use this influx of information. Condensing all this down, since present US inflation is 2.7%, (the period of the next 10 years, the difference method predicts average inflation CAGR% of 2.25%), we should get 10 year TIPS vs regular US treasuries???
The present inflation is not relevant. In theory if the treasury adjusted for breakeven yields higher then the tip you should get that. (1 + tip yield) * (1+ inflation prediction) -1 is what the market feels your TIP is worth as a treasury. In theory, assuming the inflation predictions are accurate.
@jkandell, Thank you for the great explanation. After further reading, I think I understand the difference between the two (1.6%) is volatility drag?
When using 3.5% as stock real ror (along with 1.42% for cash, 1.93% for bonds, and 2.25% for general inflation), my portfolio underperforms the worst three historical start years (1955, 1956, and 1965) under Historical Sequence Analysis. In your opinion, does this seem too conservative/pessimistic for baseline assumption?
Thanks again!
Current market prices for T-Bonds and TIPS mean that they will have identical yields if average over the next 10 years is equal to ~2.25% (CAGR%, difference method)
Stated differently, that means that the current market pricing means that the market expects the average inflation over the next 10 years to be ~2.25% (CAGR%).
How to use that information:
1) If you believe that average inflation over the next 10 years will be LOWER THAN 2.25% (CAGR%), then BUY T-BONDS because they will provide a higher yield.
2) If you believe that average inflation over the next 10 years will be EQUAL TO 2.25% (CAGR%), then IT DOESN'T MATTER whether you buy T-BONDS or TIPS because they will provide the same yield.
3) If you believe that average inflation over the next 10 years will be HIGHER THAN 2.25% (CAGR%), then BUY TIPS because they will provide a higher yield.
4) If you have no idea what inflation will be over the next 10 years, then BUY TIPS because they will protect you from the uncertain inflation risk.
About Taxes:
The reasoning / analysis above is true if you hold your T-BONDS or TIPS in a tax deferred or tax free account.
If you hold TIPS in taxable accounts, then you will face the complication of needing to pay tax on "phantom income" every year because the principal is market up based on that year's inflation and is taxable as interest income even though you don't receive actual cash interest payments in that year. (Instead you will receive the higher, marked up principal in the bond's maturity year).
This taxing scheme is designed to make T-BONDS and TIPS equivalent overall if realized inflation is actually equal to 2.25% (CAGR%) over the next 10 years.
