Question

Company T with total assets of $370 million and equity of $35 million has a leverage adjusted duration gap of +0.20 years. One-year maturity notes are currently priced at par and are paying 4.5 percent annually. Two-year maturity notes are currently priced at par and are paying 6 percent annually. The terms of a swap of $100 million notional value of liabilities' payments are 4.95 percent annual fixed payments in exchange for floating rate payments tied to the annual discount yield. Discuss your results.

a. What is the forward one-year discount yield expected next year?

b. What are the expected end-of-year profits or losses if the bank hedges its interest rate risk exposure using the swap?  

Answer 1

a.  

Both the notes are trading at par, hence yield on the notes is same the coupon rate

Yield on one year maturity note, S1 = 4.5%

Yield on two year maturity note, S2 = 6%

One year discount yield expected next year = (1+ S2)^2/ (1+S1)^1 -1

= (1+6%)^2 / (1+4.5%)^1 -1

One year discount yield expected next year = 7.52%

If bank hedges its interest rate risk exposure with swaps, one year interest rates are expected to increase from 4.5% to 4.95%

% Change in net worth = - Duration Gap * (Change in interest rate / (1+original interest rates)

= - 0.2 * (4.95%-4.5%) / (1+4.5%)

= -0.086%

Expected change in Net worth (loss at the end of year) = 35 * -0.086%

= -$0.03 million