CFAI Qbank - Portfolio Mgmt for Institutional Investors - Equity Duration Calc

[kkalantarli]

Hi, please help me to understand CFAI’s model answer to this Qbank question:

Meura Bancorp, a US bank, has an equity capital ratio for financial assets of 12%. Meura’s strategic plans include the incorporation of additional debt in order to leverage earnings since the current capital structure is relatively conservative. The bank plans to restructure the balance sheet so that the equity capitalization ratio drops to 10% and the modified duration of liabilities is 1.90. The bank also plans to rebalance its investment portfolio to achieve a modified duration of assets of 2.10. Given small changes in interest rates, the yield on liabilities is expected to move by 65 bps for every 100 bps of yield change in the asset portfolio.

The modified duration of the bank’s equity capital after restructuring is 9.89 years:
Dur(E) = (A/E) * Dur(A) − [(A/E)−1] * Dur(L) * (Δi/Δy) =
= [ 1/ 0.10 ]× 2.10 − [ 1/0.1 − 1 ] × 1.90 × 0.65 = 9.89 years

I did not get the treatment of expected yield curve movement… Screenshot is attached.

Thanks in advance!

[goodwill-hunting]

Here’s how I wrap my head around this:

As yield on liabilities is only moving 65bps for every 100bps of yield change in asset portfolio → liability is less sensitive than asset and we need to reduce its effect on the bank’s equity capital mod dur → we need to reduce the value of second portion of the formula after the substract sign → therefore we multiply it by 0.65