hard · FRM Part 2 Risk & Investment Management
Under a two-factor APT model with R_f = 4%, two well-diversified portfolios are observed: Portfolio X has factor betas (b_1, b_2) = (1.0, 0.5) and E(R_X) = 12%; Portfolio Y has betas (0.5, 1.0) and E(R_Y) = 11%. A third portfolio, Z, has betas (1.5, 1.5) but E(R_Z) = 17%.
Which arbitrage strategy is correctly constructed and priced to exploit Z's mispricing?
- Short Z, go long X and long Y each at full notional, financed by borrowing an equal amount at R_f; this zero-net-investment portfolio matches Z's betas exactly and nets about 2% riskless profit.
- Go long Z, short X and short Y each at full notional, investing the proceeds at R_f; this zero-net-investment portfolio matches Z's betas exactly and nets about 2% riskless profit.
- Short Z, go long an equal-weighted 50/50 blend of X and Y; this replicates Z's betas of (1.5, 1.5) exactly and captures the full 6% pricing gap risk-free.
- Short Z, go long X and long Y each at full notional financed by borrowing at R_f; the factor prices imply Z is actually fairly priced, so this trade merely swaps one fair-value risk profile for another with zero expected profit.
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