Questions: Portfolio Diversification

Question 1

An investor holds 50 technology stocks and believes the portfolio is well-diversified. What is the fundamental flaw in this reasoning?

• A. 50 stocks is too few — true diversification requires at least 200 stocks
• B. Technology stocks are highly correlated with each other, so sector-specific risk remains even with many holdings
• C. Diversification only reduces risk when combining stocks with bonds, not stocks with stocks
• D. The portfolio is over-diversified, which reduces expected returns below the market rate

Answer: (B)

Diversification reduces risk by combining assets whose returns are not perfectly correlated. Fifty tech stocks may move together during sector downturns, leaving substantial correlated (sector-specific) risk. True diversification requires low correlation across holdings, not merely a large number of them. This is the correlation insight: what matters is how assets move relative to each other, not how many you hold.

Question 2

Adding a highly volatile asset to a portfolio typically increases the portfolio's overall risk.

• T. True
• F. False

Answer: False

Portfolio risk (variance) depends not just on each asset's individual variance but on the covariances among all holdings. If a volatile asset has a low or negative correlation with existing holdings, its addition can reduce the portfolio's overall variance — the losses on existing assets tend to occur when this asset gains, and vice versa. Standalone volatility is not the right metric; what matters is the correlation structure.

Question 3

What is the distinction between idiosyncratic risk and systematic risk, and why does rational market pricing only compensate investors for one of them?

Model answer: Idiosyncratic risk is firm-specific (e.g., a product recall, a management scandal) and can be eliminated by holding many uncorrelated assets. Systematic risk is market-wide (e.g., recessions, interest rate changes) and affects all assets simultaneously, so it cannot be diversified away. Rational markets only compensate for systematic risk because investors can cheaply eliminate idiosyncratic risk through diversification — there is no reward for bearing risk you could have eliminated for free.

This distinction is the conceptual foundation of the CAPM model you will study next. If markets are rational and diversification is cheap, the only risk that should earn a risk premium is the risk that cannot be diversified — systematic risk, measured by beta. An undiversified investor bearing idiosyncratic risk is not compensated for it; they are simply taking unnecessary risk.