2 part question. Assuming the interest rates are currently 10%, what is expected

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2 part question. Assuming the interest rates are currently 10%, what is expected to happen to guyton's net worth if rates increase by 100 basis points?

Generally, for a financial institution with a positive duration gap that wishes to hedge its net worth position with futures contracts, the more sensitive that the underlying future's asset is to changes in interest rates, the more futures contracts that must be held to effectively hedge the position. true b. false Guyton's balance sheet is given below (in millions): Assets $200 Liabilities $150 Asset Duration (DA): 7.0 Equity $ 50 Total $200 Liabs Duration (Di): 4.5 Total $200 Assuming that interest rates are currently 10%, what is expected to happen to Guyton's net worth if rates increase by 100 basis points (give me the expected change expressed in S)? Assume that Guyton wishes to hedge its net worth position with T-bond futures (20-year maturity, 8% coupon) and that the current price of the underlying T-bond is $82,841 on face of $100,000. The annualized market yield is therefore 10.00%, and the duration for these bonds is 9.3854. How many contracts are necessary to fully hedge Guyton assuming that yield changes in the spot and futures markets are equivalent?

Explanation / Answer

Part 1.

Assume 100 basis points = 1%

Change of percentage = - duration×(change in rate ÷ (1+previous rate))

Change in assets = - 7×(1%÷(1+10%)) = -6.36%

Assets decreases by = 200×6.36% = 12.73

Change in liabilities= - 4.5×(1%÷(1+10%)) = -4.09%

Assets decreases by = 150×4.09% = 6.12

Change in net worth = - 12.73 - (-6.12) = -$6.59 million

Part 2.

Number of contracts = (Da -(L÷A)×Dl )×A ÷(Db×Pb)

Number of contracts = ( 7 - (150÷200)×4.5)×200×106 ÷ (9.3854×82841)

= 932.4808 or 932 contracts

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