Answer: 248 bps.

## Explanation The G-spread is the difference between the yield to maturity (YTM) of a corporate bond and the YTM of a government bond with the same maturity. We need to calculate the YTM for both bonds and then find the difference. **Step 1: Calculate YTM for the Canadian government benchmark bond** Bond details: - Coupon rate: 3.0% - Price: 101 (per 100 face value) - Years to maturity: 2 - Annual compounding Using the bond pricing formula: \[ P = \frac{C}{(1+r)} + \frac{C}{(1+r)^2} + \frac{F}{(1+r)^2} \] Where: - P = Price = 101 - C = Coupon payment = 3 - F = Face value = 100 - r = YTM (unknown) \[ 101 = \frac{3}{(1+r)} + \frac{3}{(1+r)^2} + \frac{100}{(1+r)^2} \] \[ 101 = \frac{3}{(1+r)} + \frac{103}{(1+r)^2} \] Solving for r: Let's test r = 2.5% (0.025): \[ \frac{3}{1.025} + \frac{103}{(1.025)^2} = 2.9268 + 98.0489 = 100.9757 \] (too low) Test r = 2.0% (0.02): \[ \frac{3}{1.02} + \frac{103}{(1.02)^2} = 2.9412 + 99.0196 = 101.9608 \] (too high) Test r = 2.2% (0.022): \[ \frac{3}{1.022} + \frac{103}{(1.022)^2} = 2.9354 + 98.6357 = 101.5711 \] (too high) Test r = 2.4% (0.024): \[ \frac{3}{1.024} + \frac{103}{(1.024)^2} = 2.9297 + 98.2583 = 101.1880 \] (close) Test r = 2.45% (0.0245): \[ \frac{3}{1.0245} + \frac{103}{(1.0245)^2} = 2.9283 + 98.0695 = 100.9978 \] (very close) So government bond YTM ≈ 2.45% **Step 2: Calculate YTM for the Canadian corporate bond** Bond details: - Coupon rate: 5.0% - Price: 102 - Years to maturity: 2 - Annual compounding \[ 102 = \frac{5}{(1+r)} + \frac{5}{(1+r)^2} + \frac{100}{(1+r)^2} \] \[ 102 = \frac{5}{(1+r)} + \frac{105}{(1+r)^2} \] Solving for r: Test r = 4.0% (0.04): \[ \frac{5}{1.04} + \frac{105}{(1.04)^2} = 4.8077 + 97.0874 = 101.8951 \] (too low) Test r = 3.8% (0.038): \[ \frac{5}{1.038} + \frac{105}{(1.038)^2} = 4.8170 + 97.4908 = 102.3078 \] (too high) Test r = 3.9% (0.039): \[ \frac{5}{1.039} + \frac{105}{(1.039)^2} = 4.8123 + 97.2887 = 102.1010 \] (close) Test r = 3.93% (0.0393): \[ \frac{5}{1.0393} + \frac{105}{(1.0393)^2} = 4.8109 + 97.1891 = 102.0000 \] (exact) So corporate bond YTM ≈ 3.93% **Step 3: Calculate G-spread** G-spread = Corporate bond YTM - Government bond YTM = 3.93% - 2.45% = 1.48% = 148 basis points **Step 4: Compare with options** - 146 bps (1.46%) is closest to our calculated 148 bps - 200 bps (2.00%) is too high - 248 bps (2.48%) is too high However, let's check more precisely: Using exact calculations: Government bond YTM: Solving 101 = 3/(1+r) + 103/(1+r)² gives r ≈ 2.455% Corporate bond YTM: Solving 102 = 5/(1+r) + 105/(1+r)² gives r ≈ 3.926% G-spread = 3.926% - 2.455% = 1.471% = 147.1 bps This is closest to 146 bps among the given options. **Therefore, the correct answer is C (248 bps is incorrect, 146 bps is the closest).** Wait, I need to re-examine. The options are: A. 146 bps B. 200 bps C. 248 bps My calculation gives approximately 147 bps, which is closest to 146 bps (A). However, let me double-check the calculation more carefully. **More precise calculation:** For government bond: 101 = 3/(1+r) + 103/(1+r)² Let x = 1/(1+r) 101 = 3x + 103x² 103x² + 3x - 101 = 0 x = [-3 ± √(9 + 4×103×101)]/(2×103) = [-3 ± √(9 + 41612)]/206 = [-3 ± √41621]/206 x = [-3 ± 204.01]/206 Positive solution: x = 201.01/206 = 0.9758 So 1+r = 1/x = 1.0248 r = 0.0248 = 2.48% For corporate bond: 102 = 5/(1+r) + 105/(1+r)² Let x = 1/(1+r) 102 = 5x + 105x² 105x² + 5x - 102 = 0 x = [-5 ± √(25 + 4×105×102)]/(2×105) = [-5 ± √(25 + 42840)]/210 = [-5 ± √42865]/210 x = [-5 ± 207.04]/210 Positive solution: x = 202.04/210 = 0.9621 So 1+r = 1/x = 1.0394 r = 0.0394 = 3.94% G-spread = 3.94% - 2.48% = 1.46% = 146 bps **So the correct answer is A. 146 bps.**