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The Math of Long Horizons

Setting Realistic Return Expectations

Pomegra Learn

Setting Realistic Return Expectations

Many investors assume the future will look like the past. If the S&P 500 has returned 10% annually since 1926, they expect 10% going forward. But markets are not time machines. Expected returns are fundamentally shaped by current valuations, yields, interest rates, and economic growth assumptions—not by what happened decades ago.

A straightforward truth: When valuations are high, expected returns are lower. When valuations are low, expected returns are higher. This is the equity risk premium in action. Projecting forward returns requires adjusting historical averages for the current starting point.

Quick definition: Forward-looking expected returns are estimates of future returns based on current valuations, dividend yields, earnings growth expectations, and interest rates—not on historical averages. They're always time-dependent and context-dependent.

Key Takeaways

  1. Historical average returns (10% for S&P 500) should not be your planning assumption
  2. Starting valuation matters enormously: High Shiller P/E ratios predict lower forward returns
  3. Current yields provide a floor: Dividend yields plus reasonable growth suggest a return range
  4. Interest rates drive expected returns: Rising rates lower equity return expectations
  5. Sector and asset class differences exist: Bond expected returns are easier to estimate (current yield). Equity returns require valuation judgment
  6. Conservative assumptions beat over-optimism for retirement planning; better to plan for 6-7% and be pleasantly surprised than plan for 10% and fail

The Problem with Extrapolating Historical Returns

The S&P 500's average return from 1926-2023 is 9.6% annually (nominal). But this average masks massive variation across time periods:

PeriodAnnualized Return
1926-19508.1%
1950-197512.2%
1975-200017.3%
2000-2010 ("Lost Decade")-0.5%
2010-202014.7%
2020-20239.5%

One period (1975-2000) averaged 17%+, while another (2000-2010) was negative. None of these subperiods predicted the next. Yet an investor planning their retirement based on "the 100-year average of 10%" is relying on an abstraction that never actually occurred.

Why the Variation?

Variation comes from starting valuations. When the S&P 500 traded at low Shiller P/E ratios in 1975 (P/E of 6), expected returns were high (earnings yields were 16%+). Between 1975 and 2000, the market didn't just earn dividends and earnings growth; valuations expanded dramatically (P/E rose from 6 to 44). This valuation expansion, on top of earnings growth, created the 17%+ returns.

By contrast, in 2000, the Shiller P/E peaked at 44. Earnings growth from 2000-2010 was minimal, and valuations compressed back to 24. The return was negative despite earnings growth, because valuation expansion (which had driven 1975-2000 returns) reversed.

Historical 10% average returns included substantial valuation expansion. Future returns cannot assume further expansion at valuations that are already elevated.

Building Expected Returns from Components

Rather than assuming "10% because history," build expected returns from observable components:

1. Dividend Yield + Earnings Growth

Current S&P 500 dividend yield (2024): 1.5% Expected earnings growth (consensus forecast): 6-7% Estimated total return: 7.5-8.5%

This is a simple model: shareholders receive dividends (1.5%) plus earnings growth (6-7%). This assumes P/E multiples stay constant (no valuation expansion or compression).

2. Shiller P/E Cyclically-Adjusted Estimate

The Shiller Cyclically-Adjusted P/E (CAPE) ratio compares market price to average earnings over the past 10 years, smoothing business-cycle effects.

CAPE-based expected return = (Earnings Yield) + (Earnings Growth Rate) – (Change in P/E Ratio)

If CAPE is 30:

  • Earnings Yield = 1/30 = 3.3%
  • Expected earnings growth = 6%
  • Expected P/E compression (valuation mean reversion): -1% annually
  • Expected return = 3.3% + 6% – 1% = 8.3%

This model explicitly assumes mean reversion (CAPE eventually returns to its 27 historical average).

3. Fed Model (Interest Rate Adjusted)

The Fed Model compares the earnings yield of stocks to the yield of Treasury bonds:

If Treasury yield > Earnings yield, stocks are overvalued If Treasury yield < Earnings yield, stocks are undervalued

In early 2024:

  • S&P 500 Earnings Yield: 4.8% (inverse of forward P/E of ~21)
  • 10-Year Treasury Yield: 4.5%
  • Stocks appear roughly fairly valued

Expected return = Expected earnings yield (4.8%) + earnings growth (6%) – inflation adjustment = roughly 8-9% nominal or 6-7% real.

Asset Class Specific Expectations

Stocks

Large-Cap U.S. Stocks (S&P 500):

  • Current valuation: Moderate-to-high (CAPE ~27, forward P/E ~21)
  • Expected return: 6-8% nominal, 3-5% real
  • Justification: Dividend yield (1.5%) + earnings growth (6%) – valuation compression (-1% if CAPE means-reverts)

Small-Cap Stocks:

  • Current valuation: Cheaper than large-cap on many metrics
  • Expected return: 7-9% nominal
  • Justification: Higher earnings growth potential partially offsets valuation risk

International Developed Stocks:

  • Current valuation: Cheaper than U.S. (lower P/E multiples)
  • Expected return: 7-8% nominal
  • Justification: Valuation discount plus similar earnings growth

Emerging Markets:

  • Current valuation: Mixed (some cheap, some expensive)
  • Expected return: 8-10% nominal
  • Justification: Higher growth but higher risk

Bonds

U.S. Treasury Bonds (10-Year):

  • Current yield: ~4.5% (2024)
  • Expected return: 4.5% nominal, 2% real (assuming inflation at 2.5%)
  • Justification: Yield is predictable (barring inflation surprises)

Corporate Bonds (Investment Grade):

  • Current yield: ~5.2%
  • Expected return: 5% nominal (accounting for credit losses and inflation)
  • Justification: Higher yield compensates for credit risk

Real Assets

Real Estate (REITs or direct):

  • Current yield: 3.5-4%
  • Expected return: 5-6% nominal, 2-3% real
  • Justification: Yield plus moderate cap rate growth minus inflation

Commodities and Inflation-Protected Securities:

  • Current return: Varies by commodity; complex to forecast
  • Expected return: 2-3% real (inflation hedge, not return generator)

The Impact of Current Conditions

Expected returns are fundamentally state-dependent. They change as the world changes:

Market ConditionImplied S&P 500 Return
1980 (High Yields, High Rates)12%+
2000 (Peak Valuation)2-3%
2009 (Post-Crisis, Low Valuation)10%+
2020 (Rising Valuations, Low Rates)7-8%
2024 (Moderate Valuation, Rising Rates)6-8%

Notice: After massive crashes (2009), expected returns are high. After massive rallies (2000), expected returns are low. This is mean reversion; high expected returns lure capital in, compressing valuations and future returns. Low expected returns discourage investors, pushing valuations down and future returns up.

Adjusting Expectations for Time Horizon

Long-term expected returns stabilize around the "secular" rate: the average return you expect over a full market cycle (typically 20-30 years).

Short-term returns (next 1-3 years) can deviate significantly from secular expectations due to valuation changes. For example:

  • 1-Year Expected Return: Depends heavily on valuation change. If P/E multiples expand from 21 to 23, you gain from multiple expansion even if earnings are flat. Prediction difficulty: Very High.

  • 5-Year Expected Return: Blends earnings growth with modest valuation assumptions. Historical volatility is still high. Prediction difficulty: High.

  • 10-Year Expected Return: Largely driven by earnings growth and dividend yield. Valuation assumptions matter less (reversion has time to occur). Prediction difficulty: Medium.

  • 30-Year Expected Return: Dominated by earnings growth, economic growth, and sector rotation. Short-term valuations are noise. Prediction difficulty: Low.

Valuation Metrics and Their Signals

Metric2024 LevelInterpretation
Shiller P/E~27Slightly above 27 historical mean; valuations moderate-to-high
Forward P/E~21Close to historical average; markets fairly valued on current earnings
Price-to-Book~3.5Historically high; suggests low expected returns relative to cost of capital
Dividend Yield1.5%Low; typical of late-cycle markets
Equity Risk Premium4-5%Historical average; suggests fair valuation

Interpretation: With P/E ratios at 21x and dividend yield at 1.5%, forward returns of 6-8% are reasonable. If P/E multiples were 15x, forward returns might be 8-10%. If P/E multiples were 25x, forward returns might be 4-6%.

Building Your Planning Assumptions

For a 30-year investor planning retirement:

  1. Base case assumption (50% probability): 6-7% real (post-inflation) returns

    • S&P 500 dividend yield (1.5%) + earnings growth (6%) – valuation compression (-1%) = 6.5% nominal
    • Minus inflation (2.5%) = 4% real
    • (More conservative estimate: 6% real using 7% nominal returns)
  2. Upside case (25% probability): 8-9% real returns

    • Scenario: Earnings growth accelerates to 7%, inflation moderates to 1%
    • 1.5% dividend + 7% growth – 1% = 7.5% nominal → 6.5% real
  3. Downside case (25% probability): 2-3% real returns

    • Scenario: Recession, earnings decline, valuations compress, inflation stays elevated
    • 1.5% dividend – 2% earnings contraction – 2% valuation = -2.5% nominal → -5% real

Running Monte Carlo with these assumptions (rather than historical 10%) produces more realistic retirement outcomes.

Forward Expected Returns by Asset Class (2024)

Asset ClassExpected Nominal ReturnExpected Real ReturnConfidence
U.S. Large-Cap Stocks6-8%3-5%Medium
U.S. Small-Cap Stocks7-9%4-6%Medium
International Developed6-8%3-5%Medium
Emerging Markets8-10%5-7%Low
10-Year Treasuries4.5%2%High
Investment-Grade Bonds5%2.5%High
Real Estate (REITs)5-6%2-3%Medium
Diversified 60/40 Portfolio5.5-6.5%3-4%Medium

Common Mistakes

  1. Using 10% as a planning assumption in a high-valuation environment: If forward returns are 6%, planning for 10% leads to shortfall. Underestimating future returns beats over-estimating when stakes are retirement security.

  2. Ignoring valuation metrics: Assuming "history repeats" at any valuation level is naive. At CAPE 30, historical returns predict 5-6% ahead; at CAPE 18, they predict 9-10% ahead.

  3. Confusing arithmetic and geometric means: If returns are +20%, -10%, +20%, the geometric mean is 9.4%, not 10%. Over decades, geometric means matter; average returns overstate outcomes.

  4. Not adjusting for inflation: A nominal 7% return in a 3% inflation environment is a real 4% return. Planning requires real returns.

  5. Extrapolating from a single period: The 2010-2020 period returned 14%+ due to falling rates and multiple expansion. This was exceptional, not normal.

  6. Ignoring fees and taxes: If you expect 7% returns but pay 1% in fees and 1% in taxes, net return is 5%. Account for friction.

FAQ

Q: What return should I assume for retirement planning? A: 5-6% real (post-inflation) for a diversified portfolio. This is lower than historical averages but reflects current valuations and is more realistic. Run Monte Carlo with this assumption.

Q: How often should I revise my expected return assumptions? A: Annually. If valuations change significantly, update expectations. If the Fed changes rates, update expectations. But avoid over-reacting to monthly noise. Quarterly or annual reviews are appropriate.

Q: Should I adjust for my time horizon? A: Yes. For 5-year planning, expected returns might be 5-6%. For 30-year planning, 6-8%. Longer horizons have higher expected returns because you can ride out valuation cycles.

Q: Is there a simple formula I can use? A: Yes, the most basic: Expected Return = Current Dividend Yield + Consensus Earnings Growth Rate – Expected Inflation Rate. For 2024: 1.5% + 6% – 2.5% = 5% real return. This is simplistic but captures the essentials.

Q: What if experts disagree on forward returns? A: Use a range. If expected returns estimate range from 5% to 8%, plan conservatively (5-6%) and hope for 7-8%. Better to surprise yourself to the upside than plan optimistically and fall short.

Q: Should I use nominal or real returns for planning? A: Real returns. You care about purchasing power, not dollar amounts. But input your inflation assumption explicitly (typically 2-2.5%).

  1. Valuation Metrics (CAPE, P/E, Dividend Yield): Inputs to expected return estimation
  2. Interest Rates and Equity Returns: The relationship between yields and expected returns
  3. Earnings Growth and GDP Growth: Long-term return drivers
  4. Inflation Expectations: Critical to real vs. nominal return distinction
  5. Risk Premium: The additional return demanded for bearing stock risk vs. bonds
  6. Monte Carlo Planning: Uses expected returns as inputs to simulate outcomes

Summary

Forward-looking expected returns—based on current valuations, yields, and growth expectations—are far more relevant for planning than historical averages. A high-valuation environment (CAPE 30) predicts lower forward returns (5-6%). A low-valuation environment (CAPE 18) predicts higher returns (8-10%).

For 2024, reasonable planning assumptions are:

  • U.S. stocks: 6-8% nominal, 3-5% real
  • Bonds: 4-5% nominal, 1.5-2.5% real
  • Diversified 60/40: 5.5-6.5% nominal, 3-4% real

Conservative planning—assuming 5-6% real returns despite historical averages of 7%—protects you against valuation-compressed futures. If valuations remain elevated or fall, you've planned conservatively. If valuations fall and returns exceed expectations, you benefit.

The final lesson: Expectations should change with conditions. In 1980 (high yields, high rates, low valuations), conservative planners assumed 10%+ returns. In 2000 (low yields, high rates, high valuations), conservative planners assumed 3-4% returns. Both were closer to reality than assuming "always 10%."

Next

Having built a foundation of the mathematical principles underlying long-term investing—from dividends and reinvestment risk, through cost of capital and exponential growth, to Monte Carlo modeling and realistic expectations—we now transition to Chapter 4, where we examine the behavioral and psychological obstacles that make "doing nothing" the hardest part of investing: The Psychology of Holding.