The repo agreement described essentially has a duration of zero.
Duration of bond positions = (52/193) × 8.2 + (61/193) × 6.8 + (80/193) × 5 = 6.43
The duration of the equity invested can be found as:
DE = (DiI - DBB)/E
where:
DE = duration of equity
Di = duration of invested assets
DB = duration of borrowed funds
I = amount of invested funds
B = amount of borrowed funds
E = amount of equity invested
Using the information provided in the question:
DE = [(6.43)(193,000 - (0)(40,000)] / 153,000 = (1,240,990 - 0) / 153,000 = 8.11
