Question

1. Provide an example of how:

   1. The duration of short-term certificates of deposit can be 0.4 years

   2. The duration of long-term certificates of deposit can be 2.5 years

   3. The duration of liquid securities can be 0.5 years

   4. The duration of investments can be 3.5 years

   5. The duration of fixed rate loans can be 2 years

Answer 1

1.  A short-term CD refers to one with a term from three to 12 months. Hence, if we have two short-term CDs of 4 and 5-month maturities and their amounts are in the ratio such that their average duration comes out to be 4.8 months or 0.4 years. The average duration is calculated as = (Duration1 x FaceValue1 + Duration2 x FaceValue2)/(FaceValue1 + FaceValue2).

2. CD terms tend to range from three months to five years, although there are shorter and longer terms on either side of that span. Hence, we can have two CDs of maturities 2 and 3 years in equal proportion for the total duration to be 2.5 years by the formula written in 1.

3. Liquid Security means a Traded Security which can be bought or sold any time. Hence, there are many money-market securities available with maturities less than 1 year. For this example, we can have securities with a duration of half a year to have a duration of 0.5 years (basically a zero-coupon security which pays back the principal in half a year).

4. This can be done by having 2 bonds of durations 3 and 4 years in equal amounts (face values) to make the duration to be 3.5 years.

5. If there are no coupons (intermediate payments to be made in the loan), and the principal has to be paid back in 2 years, the duration comes out to be 2 years.