A biotech stock has extremely high daily price volatility because its value depends on clinical trial outcomes uncorrelated with the economic cycle. What would you expect its beta to be?
AVery high (beta > 2) because the stock is very risky
BClose to zero, because low correlation to the market produces low beta regardless of total volatility
CEqual to 1, because all stocks must track the market over time
DNegative, because the stock falls when the market rises
Beta = Cov(rᵢ, rₘ) / Var(rₘ). If the stock's returns are uncorrelated with the market, Cov(rᵢ, rₘ) ≈ 0, so beta ≈ 0 — despite extremely high total volatility. This is the critical distinction between systematic and idiosyncratic risk. The biotech stock is risky in total, but its risk is firm-specific and diversifiable. A diversified portfolio holder can neutralize this risk, so the market offers no additional return for bearing it.
Question 2 Multiple Choice
Why might a high-volatility stock earn a lower expected return than a lower-volatility stock in an efficient market?
ABecause high-volatility stocks are more liquid and thus command lower premiums
BBecause the market misprices high-volatility stocks, creating arbitrage opportunities
CBecause the high-volatility stock's risk may be mostly idiosyncratic and diversifiable, leaving little systematic risk to be rewarded
DBecause investors prefer volatile stocks for upside potential and bid up their prices
If a stock's volatility comes from firm-specific events uncorrelated with the market, that volatility is idiosyncratic and can be eliminated by holding the stock in a diversified portfolio. Since investors can costlessly diversify it away, the market offers no additional return for bearing it. A stock with lower total volatility but higher beta commands a higher required return because its systematic risk cannot be diversified away. Required return is determined by beta, not raw volatility.
Question 3 True / False
A highly volatile stock with low correlation to the market can have low beta.
TTrue
FFalse
Answer: True
True — this is one of the most important distinctions in finance. Beta = Cov(rᵢ, rₘ) / Var(rₘ), which depends on correlation with the market, not on total volatility. A stock whose price swings wildly due to firm-specific events (drug trials, patent disputes) can have near-zero beta if those swings are uncorrelated with market movements. High idiosyncratic volatility does not imply high systematic risk.
Question 4 True / False
A stock with beta = 1.5 is expected to rise about 15% when the overall market rises 10%.
TTrue
FFalse
Answer: True
True. Beta measures sensitivity to market movements: a beta of 1.5 means the stock's returns are expected to move 1.5 times the market's returns. A 10% market gain corresponds to approximately a 15% expected gain; a 10% market decline corresponds to approximately a 15% expected decline. This amplification is why high-beta stocks are considered more exposed to market risk — they swing further in both directions.
Question 5 Short Answer
Explain why only systematic risk should command a risk premium in an efficient market, while idiosyncratic risk earns no additional expected return.
Think about your answer, then reveal below.
Model answer: Idiosyncratic risk is firm-specific and uncorrelated across stocks. By holding a diversified portfolio, investors eliminate this risk at virtually no cost — losses in one stock are offset by gains in others. Because investors can freely eliminate idiosyncratic risk, competition bids away any excess return it might offer. Systematic risk affects all stocks simultaneously and cannot be diversified away, so investors must bear it to participate in markets at all — they rationally demand compensation proportional to beta.
The logic: what you can eliminate at no cost, you won't be compensated for; what you cannot eliminate, you must be compensated for. Diversification renders idiosyncratic risk irrelevant for pricing, leaving beta — the undiversifiable component — as the sole driver of expected returns in the CAPM framework. This is why beta, not total volatility (standard deviation), is the relevant risk measure for a diversified investor.