Answer: Yes and S2 = S1

**Explanation for each option:** **Option A: No (no longer efficient), and S2 < S1** This is **incorrect**. The Capital Market Line (CML) *is* the efficient frontier once a risk-free asset is available. Any portfolio that is a combination of the market portfolio (M) and the risk-free asset (including borrowing at Rf) lies directly on the CML. Therefore the leveraged position (130 % in M) remains fully efficient. Additionally, the Sharpe ratio does **not** fall; it stays exactly equal to S1 (see calculation below). Both parts of A are wrong. **Option B: No, but S2 = S1** This is **incorrect**. While the statement about the Sharpe ratio being unchanged is true, the first part is false. The investor **is** still on the efficient frontier (the CML). The two-fund separation theorem tells us that all investors, regardless of risk aversion, hold only combinations of M and the risk-free asset; leveraging simply moves the investor further out along the same CML. Hence the portfolio cannot become inefficient. **Option C: Yes (still efficient), but S2 < S1** This is **incorrect**. The first part is correct (the portfolio remains on the CML), but the second part is wrong. Leverage does **not** reduce the Sharpe ratio. Because both the excess return and the volatility are scaled by exactly the same factor (1.3 in this case), the ratio stays identical. **Option D: Yes and S2 = S1** This is **correct**. **Rigorous proof (FRM Part I level):** Let: - \( w = 1.3 \) (weight in M) - \( 1 - w = -0.3 \) (borrowing) Portfolio return: \[ R_p = 1.3 \times R_m + (-0.3) \times R_f = 1.3 R_m - 0.3 R_f \] Excess return: \[ R_p - R_f = 1.3 R_m - 0.3 R_f - R_f = 1.3 (R_m - R_f) \] Portfolio volatility (Rf has zero volatility and zero correlation with M): \[ \sigma_p = 1.3 \times \sigma_m \] Sharpe ratio of the leveraged portfolio: \[ S_2 = \frac{R_p - R_f}{\sigma_p} = \frac{1.3 (R_m - R_f)}{1.3 \sigma_m} = \frac{R_m - R_f}{\sigma_m} = S_1 \] The 1.3 factors cancel out → Sharpe ratio is invariant to leverage along the CML. This is a direct implication of the CML being a straight line from (0, Rf) through (σ_m, R_m) and beyond; the slope of the CML is exactly the market Sharpe ratio S1 and is constant everywhere on the line. **Key FRM takeaways** - When a risk-free asset exists, the efficient frontier becomes the Capital Market Line (CML). - All portfolios on the CML have the **same maximum Sharpe ratio** (equal to that of the market portfolio). - Borrowing at Rf to buy more of M simply moves you **along** the CML (higher risk, higher expected return, unchanged Sharpe ratio). - This result underpins the two-fund separation theorem and is frequently tested in FRM Part I (Quantitative Analysis and Portfolio Management sections). **Reference Answer: D**