Questions: Risk Correlation and Portfolio Construction

Question 1

An investor holds shares in 15 different US technology companies, believing this provides strong diversification. During a tech sector downturn, all 15 stocks fall sharply. What explains this outcome?

• A. The investor was simply unlucky — with 15 stocks, diversification should have protected them.
• B. The stocks have high correlation with each other because they share the same sector and respond similarly to the same economic drivers.
• C. Diversification only works with more than 20 stocks.
• D. Correlation doesn't matter — what matters is the total number of holdings.

Answer: (B)

Diversification reduces risk only when assets move independently (low or negative correlation). Stocks within the same sector share common risk factors — revenue growth tied to tech spending, interest rate sensitivity, regulatory exposure — so they tend to move together. Spreading across 15 technology companies reduces company-specific risk (one firm's CEO scandal, for example) but leaves sector-wide risk intact. True diversification requires assets with low correlation, not just many assets in the same category.

Question 2

In 2008, an investor held a 'diversified' portfolio of US stocks, corporate bonds, real estate investment trusts, and commodities. All four fell significantly. What does this most directly illustrate?

• A. Diversification is fundamentally flawed as a strategy.
• B. Correlations between risky assets tend to increase during financial crises, reducing diversification exactly when it is most needed.
• C. The investor needed more asset classes to be truly diversified.
• D. The investor's expected return was too high, which inevitably meant higher risk.

Answer: (B)

This is 'correlation breakdown': in normal times, asset classes like stocks and corporate bonds may have low or moderate correlation. But during systemic crises, investors sell whatever they can — correlations across risky assets spike toward +1. The assets that held value in 2008 (government bonds, gold, cash) were not just 'different' risky assets — they were assets with fundamentally different risk profiles. The lesson: diversification protects against normal-market variance, not against systemic crisis risk.

Question 3

Two assets with a correlation of exactly -1 can theoretically be combined in the right proportions to eliminate all portfolio volatility.

• T. True
• F. False

Answer: True

With perfect negative correlation, every price increase in one asset is exactly offset by a price decrease in the other. By weighting them appropriately (weight each asset proportionally to the other's volatility), the combined portfolio's standard deviation falls to zero. In practice, true -1 correlations are essentially nonexistent, but negative correlations — like stocks and government bonds in many environments — still provide substantial risk reduction.

Question 4

Adding more assets to a portfolio generally reduces its overall risk, regardless of the correlations between those assets.

• T. True
• F. False

Answer: False

Risk reduction from adding assets depends entirely on correlation. If the new asset has correlation +1 with existing holdings, adding it provides zero diversification benefit — the portfolio's volatility is unchanged (only the scale changes). Assets must move at least partially independently to reduce portfolio risk. Adding highly correlated assets may reduce concentration in any single name (lowering idiosyncratic risk) but does nothing to reduce the common-factor risk that dominates most portfolios.

Question 5

Why does the diversification benefit of holding both stocks and corporate bonds tend to disappear during financial crises, even though they normally reduce each other's risk?

Model answer: In normal markets, stocks and corporate bonds have low or negative correlation because they respond differently to economic conditions. During crises, however, investors sell both to raise cash or reduce risk — 'flight to quality' pushes investors out of all risky assets simultaneously. Corporate bonds, like stocks, are exposed to default risk, which spikes in a crisis. The correlation between them rises toward +1 precisely when the portfolio needs diversification most. Only truly safe-haven assets (government bonds from stable countries, gold, cash) retain their protective properties, because their risk profiles are fundamentally different, not just statistically different during calm periods.

This is the core limitation of correlation as a risk measure: it is a calm-weather statistic. Stress-testing portfolios against crisis scenarios — asking 'what if all my risky assets fall 40% together?' — reveals hidden concentration risk that standard correlation analysis misses.