Question

Company A has the following balance sheet in market values with duration in brackets Liabilities and Equity Assets Short-term debt 10 (2) 90 (15) Corporate Loans 20 (5) 100 (14) Long-term debt Mortgages Equity 20 and company B has the following balance sheet in market values also with duration in brackets Liabilities and Equity Assets Short-term debt 40 (0) Government Bonds 80 (20) Cash (2) Longer-term debt 70 (25) 10 Equity 40 a. What is duration of equity of company A? b. What is duration of equity of company B? I c. You're the manager of company A. You decide to sell corporate loans and acquire equity of company B. How much equity should you acquire to make the equity of company A immune to interest rate shocks?

Answer 1

Duration of the equity is calculated as Duration Gap.

Part 1:

Weighted Duration of Assets = (20*5 + 100*14)/(20 + 100) = 1500/120 = 12.5
Weighted Duration of Liabilities = (10*2 + 90*15)/(10 + 90) = 13.7

Duration Gap = Duration Asset - (L/A)*Duration Liability
= 12.5 - (100/120)*13.7
= 12.5 - 11.42
= 1.08

Part 2:

Weighted Duration of Assets = (40*0 + 80*20)/(40 + 80) = 1600/120 = 13.33
Weighted Duration of Liabilities = (10*2 + 70*25)/(10 + 70) = 22.125

Duration Gap = Duration Asset - (L/A)*Duration Liability
= 13.33 - (80/120)*22.125
= 13.33 - 14.75
= -1.41667

Part 3:

To make company immune to interest rate shocks, is to make company's Duration Gap or Duration of Equity = 0.

Say X amount of corporate loans are sold to buy equity of company B. So, balance sheet will look like this -

Asset -
Corporate Loans = 20-x (5)
Mortgages = 100(14)
B's Equity = x (-1.41667)

Liabilities will remain same.

Now, Duration Asset = [(20-x)*5 + 100*14 + x*(-1.41667)]/120
= (1500 - 6.41667x)/120
  
Duration Liability = 13.7

Duration Gap = (1500 - 6.41667x)/120 - (100/120)*13.7 = 0
1500 - 6.41667x = 100*13.7
6.41667x = 1500 - 1370
x = 130/6.41667 = 20.25

So A should acquire equity worth 20.25 in company B.

[It is higher than corporate loans which means additional liability of 0.25 on corporate loans]