Asset A has an expected return of 8% and a standard deviation of 12%. Asset B has an expected return of 8% and a standard deviation of 18%. A risk-averse investor with no other holdings should prefer...
AAsset B, because higher volatility signals more upside opportunity
BAsset A, because it delivers the same expected return with less risk
CAsset B, because higher standard deviation leads to higher long-run compound returns
DNeither — identical expected returns make them equivalent for all rational investors
Risk-averse investors prefer less variance for a given expected return — that is precisely what risk aversion means. Option C confuses volatility with expected return; higher variance actually *reduces* long-run compound (geometric) returns through variance drag (geometric mean ≈ arithmetic mean − ½·variance). Option D is wrong because risk preferences distinguish otherwise identical expected returns. Option A misidentifies volatility as a signal of opportunity rather than a cost.
Question 2 True / False
Holding a fully diversified portfolio eliminates most investment risk.
TTrue
FFalse
Answer: False
Diversification eliminates idiosyncratic (firm-specific) risk — factors affecting individual companies. But systematic risk, the component of returns correlated with the overall market (recessions, interest rate shifts, inflation surprises), cannot be diversified away because all assets move together during such events. In competitive markets, only systematic risk earns a risk premium, because idiosyncratic risk can be costlessly diversified away.
Question 3 Short Answer
Why must risky assets offer expected returns above the risk-free rate in equilibrium?
Think about your answer, then reveal below.
Model answer: Risk-averse investors will not voluntarily hold a risky asset if its expected return equals a safe alternative. They require a risk premium — extra expected return above the risk-free rate — as compensation for bearing uncertainty. If no premium existed, rational investors would shift to the risk-free asset, reducing demand for risky assets, pushing their prices down and their expected returns up until the premium is restored.
This equilibrium logic underlies every asset pricing model. The size of the required premium depends on both the quantity of risk (variance, or beta in the CAPM) and the market price of risk (aggregate investor risk aversion). Assets with more systematic risk must offer larger premiums to attract holders.