Immunization Notes
IEOR 221 - Spring 2014
Immunization Notes
February 13, 2014
1
Assumptions
The risk-free interest rate is 9%. The following bonds (with face value $100 and same
YTMs are also available on the market:
Bond 1
Bond 2
Bond 3
2
Coupon Rate
6%
11%
9%
Maturity
30 years
10 years
20 years
Price
Yield Duration
$69.18 9%
11.8809
$112.84 9%
6.745
$100.00 9%
9.9501
Setting
Groupon has an obligation to pay $1 million in 10 years. The president of Groupon sets aside $1million = $422, 410.801, and asks you to put in the bank, which is earning 9% per
1.0910
year. His argument is that by year 10, this will grow to $1 million, allowing the company to pay off the debt.
1. Is this a sound approach? What would go wrong?
2. Everything is fine if the interest rate stays at 9% throughtout the 10-year period.
Otherwise, we will either have more than 1 million in year 10 (which is the favorable scenario, everyone will be happy), or less than 1 million in year 10.
3. As an example, suppose interest rate stays at 9% for the first 3 years, but changes to
8% in the 4th year, and stays the same thereafter. The value of the investment in year
10 is going to be
422, 410.81 × 1.093 × 1.087 = 937, 520.57 < 1million
4. Suppose we want stability. That is, we want to be able to pay off the $ 1million obligation in 10 years, no matter how th einterest rate (yields) changes (assuming if they do change, yields for each bond will change by the same percentage amount). Is it possible? If so, how can we do this?
3
Investing in One Bond
We may try to invest all of 422,410.81 in one bond, say bond 1. You can quickly convince yourself that this does not help solve our problem either. For example, with that money, we could have purchased 422,410.81 = 6105.9672 shares of bond 1.
69.18
1. Consider a situation where the yield for bond 1 is 9% for the first 3 years, but is changed to 10% in year 4, and stays the same thereafter. In this
Immunization Notes
February 13, 2014
1
Assumptions
The risk-free interest rate is 9%. The following bonds (with face value $100 and same
YTMs are also available on the market:
Bond 1
Bond 2
Bond 3
2
Coupon Rate
6%
11%
9%
Maturity
30 years
10 years
20 years
Price
Yield Duration
$69.18 9%
11.8809
$112.84 9%
6.745
$100.00 9%
9.9501
Setting
Groupon has an obligation to pay $1 million in 10 years. The president of Groupon sets aside $1million = $422, 410.801, and asks you to put in the bank, which is earning 9% per
1.0910
year. His argument is that by year 10, this will grow to $1 million, allowing the company to pay off the debt.
1. Is this a sound approach? What would go wrong?
2. Everything is fine if the interest rate stays at 9% throughtout the 10-year period.
Otherwise, we will either have more than 1 million in year 10 (which is the favorable scenario, everyone will be happy), or less than 1 million in year 10.
3. As an example, suppose interest rate stays at 9% for the first 3 years, but changes to
8% in the 4th year, and stays the same thereafter. The value of the investment in year
10 is going to be
422, 410.81 × 1.093 × 1.087 = 937, 520.57 < 1million
4. Suppose we want stability. That is, we want to be able to pay off the $ 1million obligation in 10 years, no matter how th einterest rate (yields) changes (assuming if they do change, yields for each bond will change by the same percentage amount). Is it possible? If so, how can we do this?
3
Investing in One Bond
We may try to invest all of 422,410.81 in one bond, say bond 1. You can quickly convince yourself that this does not help solve our problem either. For example, with that money, we could have purchased 422,410.81 = 6105.9672 shares of bond 1.
69.18
1. Consider a situation where the yield for bond 1 is 9% for the first 3 years, but is changed to 10% in year 4, and stays the same thereafter. In this