Questions: Systematic and Unsystematic Risk Decomposition

Question 1

Stock A has very high total variance, but most of it comes from firm-specific events uncorrelated with the market (low beta). Stock B has lower total variance but almost all of it is correlated with the market (high beta). According to CAPM, which stock should have the higher expected return?

• A. Stock A, because higher total volatility means investors demand more compensation
• B. Stock B, because its risk is systematic and cannot be diversified away — the market prices only this component
• C. Stock A, because total variance always determines expected return under rational pricing
• D. They should have the same expected return since both have the same total risk if properly measured

Answer: (B)

CAPM prices only systematic risk (beta), not total risk. Stock A's high variance is mostly idiosyncratic — a rational investor can eliminate it by diversifying. Since this risk is costlessly removable, the market does not reward bearing it. Stock B's variance is mostly market-correlated and cannot be diversified away, so investors require a risk premium. This is the central insight of CAPM: expected return depends on beta, not σ².

Question 2

An investor holds an equally weighted portfolio of 50 stocks from unrelated industries. Which statement best describes the effect of this diversification on portfolio risk?

• A. Both systematic and unsystematic risk decrease as more uncorrelated stocks are added
• B. Unsystematic risk decreases toward zero as idiosyncratic shocks cancel out; systematic risk (market exposure) cannot be eliminated this way
• C. Systematic risk decreases because beta averages out across many different stocks
• D. Total risk increases because holding more stocks exposes the investor to more potential losses

Answer: (B)

When you combine stocks whose idiosyncratic shocks are uncorrelated, the firm-specific variances cancel each other (one company's bad news is offset by another's good news). In the limit, the portfolio retains only systematic risk — the component that affects all stocks simultaneously. Systematic risk cannot be diversified away because market movements hit every stock in the portfolio at the same time. Beta of the portfolio is the weighted average of individual betas, which does not go to zero.

Question 3

A stock with high total variance but low beta may have a lower expected return than a stock with low total variance but high beta.

• T. True
• F. False

Answer: True

Expected return in CAPM is determined solely by beta (systematic risk), not total variance. A volatile stock whose variance is mostly idiosyncratic can have a low expected return if its beta is small. A less volatile stock that moves closely with the market can have a high expected return if its beta is large. This is counterintuitive but follows directly from the principle that only undiversifiable risk is priced.

Question 4

Holding a highly concentrated position in a single volatile stock earns a higher expected return than a diversified portfolio with the same total variance, because the investor bears more risk.

• T. True
• F. False

Answer: False

If the concentrated stock's high variance is mostly idiosyncratic (low beta), the market does not reward bearing it — the investor could have eliminated that variance costlessly through diversification. Expected return is not compensation for total risk; it is compensation for systematic risk. A concentrated position adds idiosyncratic risk that goes unpriced. The market only pays a premium for the component of risk that is impossible to diversify away.

Question 5

Why does the market not compensate investors for bearing unsystematic risk? What would happen in equilibrium if it did?

Model answer: Unsystematic risk is diversifiable at near-zero cost: adding more uncorrelated stocks eliminates idiosyncratic variance. If the market paid a premium for idiosyncratic risk, rational investors would immediately diversify it away and still capture the premium — a free lunch. Arbitrageurs would buy diversified portfolios of high-idiosyncratic-risk stocks, pocket the premium, and bear no net idiosyncratic risk. In equilibrium, this demand pressure would drive prices up and expected returns down until no premium remained for diversifiable risk.

The key is the word 'diversifiable.' Rational markets only price risks that someone must bear. Systematic risk must be held in aggregate by the market portfolio — it cannot be netted out. Unsystematic risk, however, can be netted out across investors, so no one needs to bear it. Competition among rational investors eliminates any premium for risk that can be avoided for free.