11.1 Portfolio Return, Risk, and Diversification
Key Takeaways
- Portfolio expected return is the weighted average of component expected returns.
- Portfolio risk depends on asset volatilities, weights, and correlations, not just average individual risk.
- Diversification can reduce unsystematic risk, but systematic risk remains tied to broad market exposure.
- Correlation is the key Level I link between asset selection and portfolio risk reduction.
Return, risk, and the diversification engine
A portfolio is more than a list of securities. It is a set of weighted exposures that interact. The expected return of a portfolio is straightforward: multiply each asset's expected return by its portfolio weight and add the results. If 60% is invested at an expected return of 8% and 40% at 4%, the portfolio expected return is 6.4%.
Risk is more subtle. A security's standard deviation measures stand-alone uncertainty. A portfolio's standard deviation also depends on how the securities move together. That joint movement is measured by covariance and correlation. Correlation standardizes covariance into a value from -1 to +1.
When correlation is less than +1, the combined portfolio can have less risk than a weighted average of asset risks. This is the core diversification benefit. The benefit is strongest when assets have low or negative correlation and meaningful weights. A small holding in a diversifying asset may help, but it cannot transform the whole portfolio by itself.
| Concept | Level I use | Candidate trap |
|---|---|---|
| Expected return | Weighted average of expected returns. | Averaging returns without weights. |
| Variance | Squared measure of total risk. | Forgetting covariance terms. |
| Standard deviation | Square root of variance. | Treating it like expected loss. |
| Correlation | Strength and direction of co-movement. | Assuming lower correlation always means lower return. |
The two-asset risk rule
For two risky assets, portfolio variance includes weighted asset variances plus a covariance term. The intuition matters more than the algebra. If two assets move together perfectly, diversification does little. If they move together imperfectly, one asset may offset some of the other's bad outcomes.
Correlation does not erase risk. It changes how risk combines. A stock and a bond may have low correlation during many periods, but both can lose value when inflation expectations rise sharply. Portfolio managers still need to identify the economic forces behind the numbers.
Systematic and unsystematic risk
Unsystematic risk is specific to a company, industry, security, or narrow exposure. Examples include a product failure, management problem, lawsuit, or plant closure. Holding many different securities can reduce this risk because the events are not perfectly related across holdings.
Systematic risk comes from broad factors such as interest rates, recession risk, inflation, credit conditions, and market-wide risk aversion. Diversification within risky assets cannot remove systematic risk. Investors are generally compensated for bearing systematic risk, not for taking avoidable concentration risk.
Efficient diversification
Diversification is not the same as buying many securities randomly. Efficient diversification combines assets so the portfolio offers the highest expected return for a given level of risk, or the lowest risk for a given expected return. At Level I, this idea supports the efficient frontier, where dominated portfolios are left behind.
A portfolio is dominated if another available portfolio has the same expected return with lower risk, or higher expected return with the same risk. Rational investors prefer efficient portfolios, but the best efficient portfolio depends on investor objectives, constraints, and risk tolerance.
Exam reasoning checklist
| Step | Ask |
|---|---|
| 1 | Are returns being weighted correctly? |
| 2 | Is the question asking for stand-alone risk or portfolio risk? |
| 3 | What is the correlation or covariance effect? |
| 4 | Is the risk diversifiable or systematic? |
| 5 | Is one portfolio dominated by another? |
On exam day, slow down when a question gives two standard deviations and a correlation. The likely test is not vocabulary. It is whether you know that portfolio risk uses co-movement. The most common wrong answer treats portfolio risk as a simple weighted average of standard deviations.
A portfolio contains two risky assets with correlation below +1. Compared with a weighted average of the two stand-alone standard deviations, portfolio standard deviation is most likely:
Which risk is most directly reduced by broad diversification across many issuers?
A portfolio is best described as dominated when another available portfolio offers: