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.