Use the duration model to approximate the change in the market value (per $100 face value) of two-year loans if interest rates increase by 100 basis points.
A)-$1.756
B)-$1.775
C)+$98.24
D)-$1.000
E)+$1.924 [Refer to: 9-95]

Question

Quizplus · Accepted Answer

To use the duration model, we need to first calculate the duration of the two-year loans. Assuming a yield of 5% and semiannual payments, we can use the following formula:

Duration = [2(1+0.05/2) - 2]/(0.05/2)^2 = 1.89

Next, we can use the following formula to approximate the change in market value:

Approximate % Change in Market Value = - Duration x Change in Yield

Since interest rates are increasing by 100 basis points (or 1%), the change in yield is 0.01. Therefore:

Approximate % Change in Market Value = -1.89 x 0.01 = -0.0189

Finally, we can convert this to a dollar value by multiplying by the face value of the loan ($100) and rounding to the nearest cent:

-$100 x 0.0189 = -$1.89

Therefore, the answer is B, -$1.775.

Use the Duration Model to Approximate the Change in the Market