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Hong KongModern portfolio theory, and what correlation actually buys
Portfolios are evaluated by expected return and risk together rather than security by security. Combining assets with correlation below one reduces portfolio standard deviation, producing an efficient frontier of best-available portfolios.
One insight, and it is worth stating plainly because the maths obscures it.
A portfolio's risk is not the average of its holdings' risks. It is less, provided the holdings do not move together.
Correlation is the engine
| Correlation | Diversification benefit |
|---|---|
| +1.0 | None - the assets move identically |
| +0.5 | Some |
| 0 | Substantial |
| -0.5 | Large |
| -1.0 | Theoretically, risk can be eliminated entirely |
Anything below one produces a benefit. You do not need negative correlation, which is the point candidates most often miss. Below one is enough.
Adding an asset with higher standard deviation than the existing portfolio can lower total portfolio risk, if its correlation is low enough. That is the single most examined idea in this topic, and it is the reason emerging markets or commodities appear in an allocation.
The efficient frontier
Plot every possible portfolio by expected return and standard deviation. The upper-left boundary is the efficient frontier: for each level of risk, the portfolio with the highest expected return. The boundary is the frontier.
Anything below it is inefficient - the same risk is available with more return, or the same return with less risk. A question describing a portfolio below the frontier is asking you to say that.
Adding a risk-free asset
Combining the risk-free asset with the optimal risky portfolio produces the capital market line, which dominates the frontier. It dominates.
The practical translation: choose the same risky portfolio regardless of risk tolerance, and vary how much cash sits alongside it. That is the theoretical justification for a simple two-fund approach.
Indifference curves
A client's willingness to trade risk for return. The optimal portfolio for that client is where their indifference curve is tangent to the frontier.
Steeper curves mean more risk-averse. Questions occasionally present two clients and ask which portfolio suits each, and the shape is the whole answer.
The assumptions
- Investors are rational and risk averse.
- Returns are normally distributed.
- Correlations are stable.
- Investors can borrow and lend at the risk-free rate.
- No taxes or transaction costs.
Every one is questionable, and the second and third fail worst when it matters. Correlations rise in a crisis, which is exactly when diversification is being relied upon.
The exam expects you to know the theory and to know that. Behavioral finance, now its own domain, exists largely because the first assumption does not hold.
Dollar limits and rate thresholds here are indexed annually. Confirm the current figure before relying on it, and expect the exam to test the rule rather than the number.
Common questions
What is modern portfolio theory?
The idea that portfolios should be evaluated by expected return and risk together rather than security by security, and that combining assets with correlation below one reduces total portfolio risk.
Do you need negatively correlated assets?
No. Any correlation below one produces a diversification benefit. Negative correlation increases it, but it is not the threshold.
Can adding a riskier asset reduce portfolio risk?
Yes, if its correlation with the existing portfolio is low enough. It is the most examined idea in this topic and the reason emerging markets or commodities appear in allocations.
What is the efficient frontier?
The set of portfolios offering the highest expected return for each level of risk. Anything below it is inefficient, because the same risk is available with more return.
What are the weaknesses of the theory?
It assumes rational investors, normally distributed returns and stable correlations. Correlations rise in a crisis, which is exactly when diversification is being relied on.