If an investor can construct an investment portfolio that will yield a positive return in good states of the world and negative return in bad states of the world, …[Fill in the blank]

Question

BlackTom AI · Accepted Answer

Under the CAPM framework, a portfolio that pays off positively in “good” states and negatively in “bad” states is positively correlated with aggregate market outcomes and therefore has high systematic (market) risk.

1) Key concepts
- Systematic vs idiosyncratic risk: systematic risk is the component that covaries with the market and cannot be diversified away; idiosyncratic risk can be diversified away and does not command a risk premium.
- Beta and expected return (CAPM): beta = Cov(R_p, R_m) / Var(R_m). Expected excess return is E[R_p] − R_f = beta * (E[R_m] − R_f). Ex‑ante return = expected return before outcomes are realized; ex‑post return = realized return after outcomes occur.

2) Step‑by‑step reasoning
- If the portfolio gives positive returns when the economy/market is good and negative returns when the economy/market is bad, then Cov(R_p, R_m) > 0. That implies beta > 0 and likely a relatively large beta (high systematic risk) compared with an asset that pays well in bad states.
- By CAPM, a higher beta leads to a higher expected (ex‑ante) excess return: E[R_p] − R_f = beta_p × (E[R_m] − R_f). Thus investors require a higher expected return up front.

3) Intermediate expressions
- E[R_p] = p_good × R_p,good + p_bad × R_p,bad (definition of expectation).
- beta_p = Cov(R_p, R_m)/Var(R_m) and since Cov(R_p, R_m) > 0, beta_p > 0.
- E[R_p] − R_f = beta_p × (E[R_m] − R_f) (CAPM relation).

4) Why the correct answer is correct
- The described payoff pattern is exactly the signature of positive covariance with the market (high systematic risk). Market equilibrium requires compensation for systematic risk, so the portfolio should earn a high ex‑ante (expected) return.

5) Why other options are incorrect
- (a) Claims low systematic risk and low ex‑post return: wrong because the payoff pattern implies positive covariance with market (not low systematic risk). Also it mixes ex‑post and ex‑ante concepts.
- (b) Claims high systematic risk and high ex‑post return: incorrect because ex‑post (realized) returns can be high or low depending on which state occurs; equilibrium prediction is about expected (ex‑ante) return, not guaranteed realized return.
- (d) Incorrect because a correct equilibrium implication exists and is option (c).

6) Conclusion
- Therefore the portfolio appears to have high systematic risk and should earn a high ex‑ante return, matching option c.

If an investor can construct an investment portfolio that will yield a positive return in good states of the world and negative return in bad states of the world, …[Fill in the blank]Single choice

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