| Parameter | Value | Source |
|---|---|---|
| Inputs | ||
| Real Risk-Free Rate (TIPS 10Y) | 1.88% | FRED: DFII10 (3-month avg) |
| Expected Inflation (10Y Breakeven) | 2.32% | FRED: T10YIE (3-month avg) |
| Nominal 10Y Treasury Yield | 4.20% | FRED: DGS10 (3-month avg) |
| Cash Rate / Risk-Free (3M T-Bill) | 3.69% | FRED: DGS3MO (3-month avg) |
| Shiller CAPE | 38.1x | Shiller ie_data.xls (3-month avg) |
| Implied Earnings Yield (1/CAPE) | 2.63% | Calculated: 1 / CAPE |
| Equity | ||
| Implied Equity Risk Premium | 0.75% | Calculated: Earnings Yield - Real Rf |
| Expected Real Return — Stocks | 2.63% | Calculated: Real Rf + ERP |
| Expected Nominal Return — Stocks | 4.94% | Calculated: Real Return + Breakeven |
| Std Dev — Stocks | 14.01% | Shiller ie_data.xls — full history 1871-present |
| Bonds | ||
| Expected Real Return — Bonds | 1.88% | Calculated: Nominal Yield - Breakeven |
| Expected Nominal Return — Bonds | 4.20% | FRED: DGS10 - YTM as return forecast |
| Std Dev — Bonds | 6.04% | Shiller ie_data.xls — since 1990 (modern regime) |
| Portfolio Parameters | ||
| Stock-Bond Correlation (base case) | +0.20 (forward estimate) | Judgment: regime-weighted forward estimate |
| Stock-Bond Correlation (pre-2022) | -0.588 (2019-2021) | Calculated: FRED SP500 vs DGS10 returns |
| Stock-Bond Correlation (post-2022) | 0.345 (2022-present) | Calculated: FRED SP500 vs DGS10 returns |
The Weight of the Future
Capital Market Assumptions & Optimal Portfolio Construction
Part I: Capital Market Assumptions
Methodology
The capital market assumptions (CMAs) presented in this memorandum were constructed using a building block approach, in which each component of expected return is anchored to a current, observable market price rather than derived from a long-run historical average. As Siegel (1992) documents, the real return on U.S. equities has averaged approximately 6.2% per year since 1802, a figure that is frequently cited in practice as a forward-looking return estimate. However, that figure does not account for the valuation at which an investor enters the market. A growing body of evidence, most prominently associated with Campbell and Shiller (1988) and subsequently formalized by Damodaran (2023), demonstrates that the cyclically adjusted price-to-earnings ratio (CAPE) is a statistically meaningful predictor of subsequent 10-year real equity returns. At current valuations, a forward-looking model produces different and more defensible estimates than the historical record.
All market data were sourced from the Federal Reserve Economic Data (FRED) database maintained by the Federal Reserve Bank of St. Louis, using three-month averages ending April 2026 to reduce sensitivity to single-month noise. The Shiller CAPE ratio was sourced directly from Robert Shiller’s dataset (Shiller, 2000), the primary source from which all secondary CAPE data providers derive their figures.
The Building Blocks
Real Risk-Free Rate. The foundation of the model is the real risk-free rate, estimated from the 10-year Treasury Inflation-Protected Securities (TIPS) yield (FRED series DFII10). Unlike the nominal Treasury yield, the TIPS yield reflects the market’s required real return on a riskless asset, net of inflation. The three-month average as of April 2026 stands at 1.88%. This figure sits within the historical range of 1–2% that Siegel (1992) identifies as characteristic of non-distorted fixed income markets.
Expected Inflation. Inflation expectations are estimated from the 10-year breakeven inflation rate (FRED series T10YIE), defined as the spread between the nominal 10-year Treasury yield and the 10-year TIPS yield. This market-implied measure reflects the collective forward-looking inflation expectations of bond market participants and is preferred over survey-based alternatives for its real-time responsiveness to new information. The current breakeven stands at 2.32%. As a cross-check, the Fisher equation requires that the nominal 10-year Treasury yield equal the sum of the real rate and expected inflation: 1.88% + 2.32% = 4.20%, which matches the observed 10-year Treasury yield (FRED series DGS10) exactly.
Expected Bond Return. For investment-grade bonds held to maturity, the current YTM is the theoretically appropriate forecast of future nominal return (Ilmanen, 2011). The 10-year Treasury yield of 4.20% therefore serves directly as the expected nominal bond return. The implied real bond return, computed as the nominal yield less the inflation breakeven, is 1.88%, equal to the TIPS yield by construction.
Expected Equity Return. The expected equity return is derived from the implied earnings yield of the S&P 500, following the Gordon Growth Model framework as used by Damodaran (2023). The Shiller CAPE stands at 38.1x as of April 2026, representing more than double its long-run historical average of approximately 16–17x (Shiller, 2000). The inverse of this ratio, the cyclically adjusted earnings yield, is 2.63%, which represents the real return the market is currently priced to deliver per dollar invested. The implied equity risk premium (ERP), defined as the earnings yield less the real risk-free rate, is therefore 0.75%. Adding expected inflation of 2.32% yields an expected nominal equity return of 4.94%.
The Siegel (1992) historical arithmetic mean nominal return on equities since 1926 is approximately 11.9%; the geometric equivalent is 9.8%. The forward-looking estimate of 4.94% is materially lower. This gap is the direct consequence of a CAPE ratio that is much higher than its historical mean. An investor paying 38x smoothed earnings is paying a premium that, all else equal, compresses future returns.
Volatility Assumptions. Equity volatility is assumed at 14.01%, derived from Shiller’s full price history (1871–present). Bond volatility is assumed at 6.04%, derived from Shiller’s data since 1990, reflecting the modern floating rate regime.
Stock-Bond Correlation. The correlation between stock and bond returns is the most regime-dependent assumption in the model and warrants careful treatment. Monthly return series for stocks (FRED series SP500) and bonds (approximated from 10-year Treasury yield changes using a modified duration of 8) were constructed from January 2019 through April 2026. The realized correlation over the full sample is effectively zero (+0.003), but this figure is the product of two sharply distinct regimes rather than a stable underlying relationship. Prior to 2022, the correlation was -0.588, reflecting the well-documented flight-to-quality dynamic in which falling equity markets coincided with rising bond prices. Following the 2022 inflation shock, the correlation shifted to +0.345, as the Federal Reserve’s aggressive tightening cycle drove simultaneous losses in both asset classes. The rolling 12-month correlation, displayed in Figure 1, illustrates this structural break clearly.
Given this evidence, a base case correlation of +0.20 is adopted as a forward-looking estimate. This reflects a judgment that the post-2022 positive correlation regime is more representative of the current inflation-aware environment than the pre-2022 deflationary regime, while acknowledging that the full magnitude of the post-2022 correlation (+0.345) may overstate the persistence of the shock. The sensitivity of portfolio recommendations to this assumption is discussed in Part III.
Summary of Assumptions
Table 1 presents the complete set of capital market assumptions used in the portfolio construction that follows.
Stock-Bond Correlation Regime Analysis
Figure 1 plots the 12-month rolling correlation between U.S. equity and Treasury bond returns from January 2020 through April 2026. The structural break in 2022 is clearly visible: the correlation transitions from persistently negative, consistent with the post-2008 quantitative easing regime in which bonds served as a reliable equity hedge, to persistently positive following the onset of the inflation shock. This shift has direct implications for portfolio construction. A positive stock-bond correlation reduces the diversification benefit of combining the two assets, compressing the efficient frontier and making the risk-free asset relatively more attractive across all levels of risk aversion.
Part II: Portfolio Construction
The Optimal Risky Portfolio
Using the capital market assumptions derived in Part I, a set of feasible two-asset portfolios was constructed by varying the allocation to equities from 0% to 100% in increments of 0.1%, with the residual allocated to bonds. For each combination, the expected return, standard deviation, and Sharpe ratio were computed using the standard two-asset portfolio formulas:
\[E[R_p] = w_s \cdot E[R_s] + w_b \cdot E[R_b]\]
\[\sigma_p = \sqrt{w_s^2 \sigma_s^2 + w_b^2 \sigma_b^2 + 2 w_s w_b \sigma_s \sigma_b \rho_{sb}}\]
\[S_p = \frac{E[R_p] - R_f}{\sigma_p}\]
where \(w_s\) and \(w_b\) denote the weights in stocks and bonds respectively, \(\sigma_s\) and \(\sigma_b\) their standard deviations, \(\rho_{sb}\) the stock-bond correlation, and \(R_f\) the risk-free rate.
The optimal risky portfolio, defined as the combination of stocks and bonds that maximizes the Sharpe ratio, was identified by searching across the full feasible set. The results are presented below.
| Parameter | Value |
|---|---|
| Stock Weight | 32.3% |
| Bond Weight | 67.7% |
| Expected Return | 4.44% |
| Standard Deviation | 6.68% |
| Sharpe Ratio | 0.1115 |
The optimal risky portfolio tilts heavily toward bonds, allocating approximately 67.7%. At a Shiller CAPE of 38.1x, the implied equity risk premium is only 0.75%, meaning equities offer barely three-quarters of a percentage point of additional expected return per unit of real risk relative to the risk-free rate. With bonds offering a nominal return of 4.20% at a standard deviation of 6.04%, and equities offering only 4.94% at a standard deviation of 14.01%, the optimizer correctly identifies that the marginal return-per-unit-of-risk of increasing equity exposure is modest. The resulting Sharpe ratio of 0.1115 is strikingly low by historical standards, Siegel (1992) documents an implied equity Sharpe ratio of approximately 0.40 over the post-1926 period and reflects the degree to which current valuations have compressed the attractiveness of the risky portfolio relative to cash.
The Optimal Complete Portfolios
Given the optimal risky portfolio, the optimal complete portfolio for each client was determined by allocating between the risky portfolio and the risk-free asset according to the standard mean-variance utility maximization formula:
\[y^* = \frac{E[R_p] - R_f}{A \cdot \sigma_p^2}\]
where \(y^*\) is the fraction of total wealth allocated to the optimal risky portfolio, \(A\) is the client’s coefficient of risk aversion, and \(\sigma_p^2\) is the variance of the optimal risky portfolio. The fraction \((1 - y^*)\) is allocated to the risk-free asset (3-month Treasury bills at 3.69%). The final allocations to stocks, bonds, and the risk-free asset are then:
\[w_{\text{stocks}} = y^* \cdot w_s^* \qquad w_{\text{bonds}} = y^* \cdot w_b^* \qquad w_{\text{rf}} = 1 - y^*\]
Table 3 presents the resulting allocations for each client.
| Client | Risk Aversion | Allocation to Stocks | Allocation to Bonds | Allocation to Risk-Free | Expected Return | Std Dev | Sharpe Ratio |
|---|---|---|---|---|---|---|---|
| Ruiz Family | 2.5 | 21.6% | 45.2% | 33.2% | 4.19% | 4.46% | 0.1115 |
| Angela Brooks | 4.5 | 12.0% | 25.1% | 62.9% | 3.97% | 2.48% | 0.1115 |
| Thomas Whitaker | 8.0 | 6.7% | 14.1% | 79.1% | 3.85% | 1.39% | 0.1115 |
The Efficient Frontier and Capital Allocation Line
Figure 2 plots the efficient frontier, the Capital Allocation Line (CAL), and the three client complete portfolios. The CAL originates at the risk-free rate of 3.69% on the vertical axis and passes through the optimal risky portfolio, extending along the line of maximum Sharpe ratio. Each client’s complete portfolio lies on the CAL between the risk-free asset and the optimal risky portfolio, at a position determined by their risk aversion coefficient.
A Note on the Role of the Risk-Free Rate
A recurring theme across all three client allocations is the outsized role of the risk-free asset. In a lower-rate environment the opportunity cost of holding cash was negligible and investors were effectively pushed into risky assets to earn any meaningful return. Clients can earn a real return of approximately 1.37% (3.69% nominal less 2.32% inflation) on riskless assets, which meaningfully raises the hurdle that the risky portfolio must clear to justify inclusion. The return of a “risk-free alternative” is one of the most consequential shifts in the investment landscape since 2022 and shapes every allocation recommendation in this analysis.
Part III: Reflection
Capital Market Assumption
Our CMAs are market-implied and not historically extrapolated. Rather than using Siegel’s 11.9% historical equity average, we built a model which derives the expected returns from current, observable prices. The real risk-free rate comes from the live TIPS yield, inflation expectations from the breakeven rate, the bond return directly from the 10-year Treasury yield, and the equity return from the inverse of the Shiller CAPE.
Secondly, our CMAs are internally consistent. The Fisher equation cross-check is exact: real rate + breakeven inflation = the nominal 10-year yield. This validates that the three inputs are drawn from the same pricing system rather than stitched together from various sources.
Lastly, the correlation assumption reflects the current regime. The full-sample correlation of 0.0003 is the result of two opposite regimes canceling out. We adopt a value of 0.20 which is informed by the post-2022 regime while discounting some of its persistence.
Fragility of CMAs
The CAPE-based equity return is mechanically sensitive to mean reversion. The model treats the CAPE earnings yield of 2.63% as a static return forecast with no reversion to the historical mean of 16-17x. If the CAPE reverts to its long-run average realized equity returns would differ dramatically from 4.94%.
The positive correlation assumption is a judgement call with enormous sensitivity to portfolio construction. This variable determines the diversification benefit bonds provide. If inflation decreases and the Fed returns to an easing bias, a negative correlation period could come about again. The result: the efficient frontier shifts outward and changes the optimal risky portfolio composition.
The bond return assumes a buy-and-hold investor. The model uses YTM as the expected bond return, which is only appropriate for investors who hold bonds to maturity and reinvest coupons at the same yield. For clients with shorter horizons or who might need to liquidate, the realized bond return could be different from 4.20%.
Client Who Is Most Exposed to Errors in Our Assumptions
The Ruiz family (A = 2.5), as the least risk-averse client they allocate the highest fraction of wealth to the risky portfolio (3.2x larger than Thomas Whitaker’s). Any error in the expected return on equities, the correlation assumption, or the volatility estimate is amplified in their portfolio.
By contrast, Thomas Whitaker is so heavily allocated to the risk-free asset that errors in risky asset assumptions matter relatively little to his actual portfolio. He effectively opted out of most of the uncertainty.
Sensitivity of Recommendations
Our recommendations are highly sensitive, because the model is currently operating with thin return margins. The equity expected return (4.94%) is only 0.74 percentage points above the bond expected return (4.20%). The Sharpe ratio of the optimal risky portfolio is just 0.0865 which is far below the historical norm of ~0.40. This means the optimizer is working with very small signal relative to noise.
If equity returns rise to ~7–8% (consistent with a CAPE reverting toward 25x, or with stronger-than-expected earnings growth), the ERP widens substantially. The optimal risky portfolio would shift toward a much higher equity weight, and the Sharpe ratio would improve. All three clients would be recommended to hold meaningfully more equity, and the risk-free asset becomes less attractive.
If equity returns fall to ~3–4% (consistent with CAPE remaining elevated or expanding further), the ERP nearly vanishes or turns negative in real terms. In that case the optimizer would push the optimal risky portfolio almost entirely into bonds pushing more wealth into T-bills.
References
Campbell, J. Y., & Shiller, R. J. (1988). Stock prices, earnings, and expected dividends. Journal of Finance, 43(3), 661–676. https://doi.org/10.1111/j.1540-6261.1988.tb04598.x
Damodaran, A. (2023). Equity risk premiums (ERP): Determinants, estimation and implications — The 2023 edition. Stern School of Business, New York University. https://pages.stern.nyu.edu/~adamodar/
Federal Reserve Bank of St. Louis. (2026). FRED economic data. https://fred.stlouisfed.org
Ilmanen, A. (2011). Expected returns: An investor’s guide to harvesting market rewards. Wiley.
Shiller, R. J. (2000). Irrational exuberance. Princeton University Press.
Siegel, J. J. (1992). The equity premium: Stock and bond returns since 1802. Financial Analysts Journal, 48(1), 28–38. https://doi.org/10.2469/faj.v48.n1.28