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