Choosing Stock and Bond Allocations to Maximize Expected CAGR

Summary

This document examines how the stock allocation that maximizes expected compound annual growth changes with stock–bond correlation and relative expected returns. It assumes a fully invested two-asset portfolio of global equities and bonds, normally distributed returns, and a linear relationship between assets. Expected geometric growth is approximated as arithmetic expected return minus half the portfolio variance, and the author searches across equity weights to find the maximum.

The analysis varies correlation and the assets’ assumed Sharpe ratios, then compares the growth rates of several allocations under selected scenarios. It illustrates that bonds can improve expected CAGR despite a lower expected arithmetic return, while the preferred allocation is sensitive to relative return assumptions and correlation. The worked assumptions include specified return and volatility estimates, with real return expectations based partly on external estimates and an inflation assumption. This is a model-based illustration rather than a forecast: Gaussian returns, fixed inputs, the CAGR approximation, and full-Kelly allocation may not capture real-world risks or changing market conditions.

Key ideas

• Approximate expected CAGR as expected arithmetic return minus half the portfolio variance.
• Optimize the equity share of a fully invested stock and bond portfolio under different correlation assumptions.
• The optimal allocation depends on both stock–bond correlation and the relative expected Sharpe ratios.
• Lower-return bonds may still improve expected compound growth by reducing portfolio variance.
• The results depend on fixed return and volatility assumptions and a Gaussian-return approximation.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.