Question

The durations of the assets and liabilities are 1.397 years and 0.5535 years, respectively. The debt/equity ratio is 10. What is the leveraged adjusted duration gap (LADG)? If the equity is $20 million, what will the new equity value be if the relative change in interest rates is a decrease of 0.5%? What variables are available for immunization?

Answer 1

Solution) Debt/Equity = 10

Thus, Debt (D) = 10* Equity (E)

D = 10*E

Assets (A) = Debt (D) + Equity (E)

A = 10E + E = 11E

Thus, Debt/Assets = 10E/11E = 10/11

Leveraged adjusted duration gap (LADG) = Da - K*Dl

where Da = Duration of assets =1.397 years

Dl = Duration of liabilities = 0.5535 years

K = Debt/Assets = 10/11

Thus, LADG = 1.397 - 10/11*0.5535

LADG = 1.397 - 0.503182

LADG = 0.893818 years

If Equity (E) = $20 million, then,

Assets = 11*E = 11*20 million = 220 million

Relative change in interest rate = (Change in R)/(1 + R) = -0.5%

where, R is the interest rate

Change in equity value = -LADG*Assets Value*Rlative change in interest rate

Thus, change in equity = -0.893818*220*(-0.5%)

= 0.893818*220*0.005

= 0.9831998 million

Hence, new equity = 20 + 0.9831998 = 20.9831998 million

= 20.98 million

For immunization, the LADG be 0.

Thus, (DA-DL*K) = 0

DA = Dl*K

DA = 0.5535*10/11 = 0.50318 years

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