Diversification and portfolios
Combining investments can reduce risk without sacrificing expected return. Diversification is often called the only free lunch in finance.
Portfolio return
A portfolio's expected return is the weighted average of its assets' expected returns. If 60% is invested in a stock fund expecting 9% and 40% in a bond fund expecting 4%, the portfolio expects 0.6 x 9 + 0.4 x 4 = 7%.
Portfolio risk and correlation
Portfolio risk is not a simple average. It depends on how assets move together, measured by correlation, ranging from -1 (perfectly opposite) to +1 (perfectly together). When assets are less than perfectly correlated, gains in some offset losses in others, so portfolio volatility is lower than the weighted average of individual volatilities.
Diversification
Holding many different investments reduces risk specific to individual companies. Studies show that much of the benefit comes from holding a few dozen stocks across industries, and broad index funds hold hundreds or thousands. Harry Markowitz formalised these ideas in modern portfolio theory in 1952, later sharing the 1990 Nobel Prize in economics.
Systematic and unsystematic risk
Unsystematic (specific or diversifiable) risk affects individual companies or industries, such as a product failure or lawsuit, and can be diversified away. Systematic (market) risk affects nearly all assets, such as recessions, interest rate changes, and pandemics, and cannot be eliminated by diversification.
The efficient frontier
The efficient frontier is the set of portfolios offering the highest expected return for each level of risk. Rational investors choose a portfolio on the frontier according to their risk tolerance. Adding a risk-free asset creates the capital market line, combining the risk-free asset with an optimal risky portfolio.
Asset allocation
Asset allocation, the mix of stocks, bonds, cash, and other assets, is the main driver of a portfolio's long-run risk and return. Younger investors with long horizons often hold more stocks; those nearing goals often shift toward bonds. Target-date funds automatically adjust allocation over time.
International and other diversification
Investing across countries can reduce risk, because economies do not move perfectly together, though correlations tend to rise during global crises. Other assets, such as real estate and commodities, can add diversification. Rebalancing periodically restores the intended allocation as markets move.
Worked example
Two stocks each have an expected return of 10% and standard deviation of 30%. If they are perfectly correlated, a 50-50 portfolio still has 30% risk. If their correlation is 0, portfolio standard deviation falls to about 21%; if correlation is -1, it falls to 0. Lower correlation means more diversification benefit, with the same expected return.
Key takeaways
Portfolio expected return is the weighted average of asset returns. Portfolio risk depends on correlations; imperfect correlation reduces risk. Diversification removes unsystematic (company-specific) risk but not systematic (market) risk. Markowitz's modern portfolio theory defines the efficient frontier of best risk-return combinations. Asset allocation drives long-run results; target-date funds adjust over time. International diversification and rebalancing help manage risk.
Flashcard
Weighted average of asset returns
Check your understanding
Which type of risk can diversification eliminate?