First Duration, a securities dealer, has a leverage-adjusted duration gap of 1.21 years, $60 million in assets, 7 percent equity to assets ratio, and market rates are 8 percent. What is the impact on the dealer's market value of equity per $100 of assets if the change in all interest rates is an increase of 0.5 percent [i.e., ΔR = 0.5 percent]

Question

Quizplus · Accepted Answer

The impact of the change in interest rates on the market value of equity per $100 of assets (MMVE) can be calculated as:

MMVE = -(LADR × ΔR × V / E)

Where:
LADR = Leverage-Adjusted Duration Gap
ΔR = Change in interest rates
V = Total assets
E = Equity

Substituting the given values:

LADR = 1.21 years
ΔR = 0.5%
V = $60 million
E = 7% × $60 million = $4.2 million

MMVE = -(1.21 × 0.5% × $60 million / $4.2 million) = -$336,111

Therefore, the market value of equity per $100 of assets would decrease by 0.3361 or $33.61 per $10,000 of assets. The answer is (C).

First Duration, a Securities Dealer, Has a Leverage-Adjusted Duration Gap