What determines how much diversification reduces risk?
Portfolio risk depends on each variance and their covariance, not merely asset count.
Follow the cause and effect
Define portfolio weights that sum to one.
Calculate total variance including covariance terms.
Compare ρ=1, 0, and negative correlation to read diversification gains.
The model you are using
Conditions for this model
Hypothetical assets, weights sum to one, no fees; mean–variance is a simplified model, not an investment recommendation.
The exam trap
Holding two assets does not guarantee lower risk when their returns move perfectly together.
Connect the reasoning to the graph
What changes
- A mean–standard-deviation plot shows feasible portfolios and the efficient frontier.
What stays fixed
Hypothetical assets, weights sum to one, no fees; mean–variance is a simplified model, not an investment recommendation.
Keep these conditions throughout the comparison; change only what the case above specifies.
What to inspect
Compare ρ=1, 0, and negative correlation to read diversification gains.
Compare before and after, and locate the conclusion on the graph.
5 MINUTES · TRANSFER THE IDEA
Can you explain it without the lesson?
Compare the variance of a half-and-half portfolio when ρ=1 versus ρ=−1.