Why is the long-run real bond yield anchored to trend real GDP growth?

Short answer: in equilibrium, the real return on safe (default-free) capital cannot be much different from the real return on productive capital in the economy. The marginal product of capital — which determines what borrowers can profitably pay — is tied to the trend growth rate. So when trend growth is high, the equilibrium real lending rate is also high. To forecast long-run nominal yields, add trend inflation and a small term premium.

Reading the symbols: $g_Y$ = trend real GDP growth; $\pi$ = trend inflation; $y$ = nominal default-free bond yield; $r^*$ = equilibrium real rate; $\text{TP}$ = term premium.

The mechanism

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The argument:

1. In a competitive economy, capital flows to its highest-return use. The marginal product of capital (MPK) is bid down through investment until investors are indifferent.
2. The trend growth rate $g_Y$ reflects what the economy can produce per unit of capital and labor input. Higher trend growth = higher MPK = higher equilibrium real rate.
3. Default-free bonds compete with productive capital. Their yields must approximate the equilibrium real rate or capital reallocates.

The simple equation

$$r^* \approx g_Y$$ $$y = r^* + \pi + \text{TP} \approx g_Y + \pi + \text{TP}$$

For a typical developed economy:

• $g_Y \approx 2\%$ trend real growth
• $\pi \approx 2\%$ trend inflation
• $\text{TP} \approx 0.5\% - 1\%$ term premium for the 10-year point
• Long-run nominal 10-year yield $\approx 4.5\% - 5\%$

Why this anchoring matters

Two reasons CFA candidates need this anchor:

1. Intertemporal consistency. Even your near-term yield forecast must imply a path back to the long-run anchor. Forecasting permanently low yields in a high-trend-growth economy is internally inconsistent.

2. Cross-asset consistency. The growth-accounting forecast for $g_Y$ is the SAME number you use to anchor equity returns AND bond yields. Using two different $g_Y$ figures across asset classes implies an arbitrage opportunity that should not exist.

A concrete example

Suppose your growth-accounting forecast gives US trend real growth of 2.4% and trend inflation of 2.1%. The implied long-run 10-year Treasury yield is:

$$y \approx 2.4\% + 2.1\% + 0.5\% = 5.0\%$$

If the current 10-year is at 3.8%, your model says yields should drift UP toward 5% over the long run. Bond returns over a long horizon are therefore likely to be poor (you take a capital loss as yields rise toward the anchor).

If current 10-year is at 6.5%, your model says yields should drift DOWN toward 5%, giving bondholders capital gains in addition to coupon.

The empirical caveats

The textbook is careful: the link is a LONG-RUN average relationship, not a tight short-run relationship. Real yields can deviate substantially for years:

• Demographic shifts (aging populations push real rates DOWN)
• Global savings glut (excess savings push real rates DOWN)
• Risk-off episodes (flight to quality temporarily compresses real yields)
• Quantitative easing (central bank purchases compress yields)

Each of these can keep the actual real yield away from $g_Y$ for an extended period. The framework still anchors LONG-RUN forecasts, but allows for finite-horizon deviations.

Exam-day usage

When a question gives you trend growth and inflation forecasts, you can:

1. Compute the long-run nominal yield anchor: $y_\text{anchor} = g_Y + \pi + \text{TP}$
2. Compare to current yield
3. Forecast direction of yield change over the long horizon
4. Compute expected bond return including capital gain/loss from yield movement

For the broader growth-anchoring framework, see our CME application article.