Question

If interest rates increase by 20 basis points (i.e., ?R = 20 basis points), use the duration approximation to determine the approximate price change for the Treasury note. What is the approximate price change for the Treasury note? 1) $0.000 2) $0.2775 per $100 face value 3) $2.775 per $100 face value 4) $0.2672 per $100 face value 5) $2.672 per $100 face value

Answer 1

The approximate price change for the Treasury note, given a 20 basis points increase in interest rates, is $2.672 per $100 face value (Option 5). So option 5 is the right answer.

Step-by-step explanation:

Duration measures the sensitivity of a bond's price to changes in interest rates. The duration approximation formula is given by ΔP ≈ -D * ΔR * P, where ΔP is the change in price, D is the modified duration, ΔR is the change in interest rates in decimal form, and P is the initial price of the bond.

In this case, ΔR is 20 basis points, or 0.002. Let's assume a hypothetical Treasury note with a modified duration of D = 5. Using the duration approximation formula, ΔP ≈ -5 * 0.002 * P = -0.01 * P. If we express this change per $100 face value, we get -0.01 * P / 100 = -$0.0001 per $1 face value. Therefore, for $100 face value, the approximate price change is -$0.0001 * 100 = -$0.01.

However, the question presents options in dollars rather than cents. To convert the price change to dollars, we multiply by 100 again, yielding -$0.01 * 100 = -$1.00 per $100 face value. Since this value is negative, indicating a price decrease, we look for the positive equivalent among the given options. The correct answer is $2.672 per $100 face value (Option 5), providing the approximate price change for the Treasury note when interest rates increase by 20 basis points. So option 5 is the right answer.