Expected returns and their limits: CAPE, bond yields and your own capital-market assumptions

What you will learn

• How the cyclically adjusted price–earnings ratio (CAPE) turns a valuation into a return estimate
• Why the starting yield is the best simple forecast for a bond allocation
• How to build a one-page set of capital-market assumptions (CMAs) for a portfolio
• Where these estimates fail and how wide the error bands really are

Explanation

Capital-market assumptions (CMAs) are the expected return, volatility and correlation figures you feed into an allocation decision. Large asset managers publish their own each year; a private investor can build a simpler, transparent version. The simple price–earnings ratio and its traps were covered in the course Stocks & Fundamental Analysis. The CAPE (cyclically adjusted price–earnings ratio, also called the Shiller P/E) divides the current index price by the average of the last ten years of inflation-adjusted earnings. Averaging ten years removes most of the business-cycle swing in profits.

The CAPE earnings yield is 1 ÷ CAPE. A common and defensible use is: expected real (after-inflation) equity return over roughly ten years ≈ CAPE earnings yield, assuming valuations neither rise nor fall. If you believe the CAPE will move towards a long-run average, add a valuation-change term: annual drag or boost = (target CAPE ÷ current CAPE)^(1/years) − 1. Add expected inflation to convert real into nominal.

For bonds the logic is simpler. If you hold a bond to maturity you earn roughly its yield to maturity (covered in the course Bonds & Fixed Income in Depth). For a bond fund with a constant duration, the historical observation is that the starting yield explains most of the return over a horizon close to twice the duration, because falling prices after a rate rise are offset by reinvesting coupons at higher rates. So: expected nominal bond return ≈ current yield to maturity of the fund, minus costs and expected credit losses.

Three limits must be written next to every estimate. First, CAPE is a weak guide over one to three years; historically it has mattered for ten-year averages, with error bands of several percentage points per year. Second, accounting rules and the sector mix of an index change over decades, so "the long-run average CAPE" is not a fixed number. Third, inflation expectations are themselves uncertain, so the nominal figure carries two errors. Use CMAs to compare allocations with each other, not to predict your wealth.

Worked example

Hypothetical example: assume a global equity index with a CAPE of 30, expected inflation of 2% per year, a euro government bond fund with a yield to maturity of 2.5%, and total product costs of 0.2% per year on the portfolio. These are round assumptions chosen for the calculation, not current market data.

Step 1 – equity, no valuation change. Earnings yield = 1 ÷ 30 = 3.33% real. Nominal ≈ 3.33% + 2% = 5.33%.

Step 2 – equity, valuation reverts. If the CAPE falls from 30 to 25 over ten years: (25 ÷ 30)^(1/10) − 1 = 0.8333^0.1 − 1 ≈ −1.81% per year. Nominal ≈ 5.33% − 1.81% = 3.52%.

Step 3 – bonds. Expected nominal return ≈ 2.5% (yield to maturity), assuming no defaults in government bonds.

Step 4 – 60/40 portfolio. Base case: 0.6 × 5.33% + 0.4 × 2.5% = 4.20%; after 0.2% costs ≈ 4.0% nominal, about 2.0% real. Reversion case: 0.6 × 3.52% + 0.4 × 2.5% = 3.11%; after costs ≈ 2.9% nominal, about 0.9% real.

The €15,000 gap between the two rows comes from one assumption about valuation. That is the size of uncertainty you should expect from any CMA. Taxes are excluded; German Abgeltungsteuer would reduce the nominal results further.

Common mistake

Practice activity

Build CMAs on paper for a 70/30 portfolio. Assumptions: CAPE 22, expected inflation 2.5%, bond fund yield to maturity 3.2%, costs 0.25% per year. Calculate the expected nominal portfolio return (a) with unchanged valuation and (b) if the CAPE rises from 22 to 25 over ten years. State the real return in each case.

Key takeaways

• Expected real equity return ≈ 1 ÷ CAPE, adjusted for any assumed change in valuation; add inflation for the nominal figure.
• Expected bond return ≈ starting yield to maturity, minus costs and credit losses.
• Always show a base case and a reversion case; the gap is your honest error band.
• Use CMAs to rank allocations against each other, never as a promise of wealth.

Next step

With volatilities, correlations and expected returns in hand, the portfolio will still drift away from its targets; the next lesson designs rebalancing bands that control drift at an acceptable cost.