The following information is about current spot rates for Second Duration Savings' assets (loans) and liabilities (CDs). All interest rates are fixed and paid annually.
-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

Question

The following information is about current spot rates for Second Duration Savings' assets (loans) and liabilities (CDs). All interest rates are fixed and paid annually. 
-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

Quizplus · Accepted Answer

To approximate the change in market value, we need to use the modified duration formula:

Modified Duration = - (1/Price)*(dPrice/dy)

Here, the two-year loan can be assumed to have a duration equal to its maturity. Let's assume the market value of the loan is $100, so the modified duration would be:

Modified Duration = - (1/100)*(dPrice/dy)

Using the duration model, we can approximate that the change in price for a 100 basis point increase in interest rates is:

Change in Price = - Modified Duration * Δy * Price

Δy = 100 basis points = 1%

Using the above equation, we get:

Change in Price = -(1/100)*(1%)*$100 = -$1.00

Therefore, the market value would decrease by $1 per $100 face value. The answer closest to this value is option B, -$1.775.

The Following Information Is About Current Spot Rates for Second