The spot rate (zero coupon yield) curve is downward sloping (inverted). Assuming no arbitrage opportunities, the yield on a  coupon bond  with a maturity of 30 years is:

A 100 million dollar mortgage pool of 15-year mortgages has a contract rate of 6%. The CPR equals 10%. Compute the first principal prepayment to the entire pool in millions of dollars to four decimal places. Do not include the scheduled principal payment. 

The one-,  two-, and three-year zero-coupon rates are 8.00, 9.50, and 10.00 percent respectively. What is the fixed rate (in percent) on a three-year interest rate swap that makes three annual end of year payments? The floating rate is the one-year LIBOR.  Assume zero default risk.  

A floating rate bond and an inverse floating rate bond are backed by $100 million portfolio of 10-year bonds. The coupon rate on the inverse floater equals: 12% – 2r. The market value of the portfolio of 10-year bonds rises to $110 million. Assume the credit quality of the portfolio does not change. At the reset date, the value of the inverse floating tranche will:

The price of one-year zero coupon bond is 92.593. The price of a two-year bond with a coupon rate of 7.0 percent is 101.711. Both bonds have a par value of 100 dollars. What is the two-year spot rate (in percent)?  

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A floating rate bond and an inverse floating rate bond are backed by $100 million portfolio of 10-year bonds. The coupon rate on the inverse floater equals: 12% – 2r. The market value of the portfolio of 10-year bonds rises to $105 million. Assume the credit quality of the portfolio does not change. At the reset date, the value of the inverse floating tranche will:

Consider the following basic $100 million CDO structure. The senior tranche has a par value of $70 million dollars and a coupon rate of LIBOR + 1.0%. The mezzanine tranche has a par value of $20 million and a coupon rate equal to 8.25%. The equity tranche has a par value of $10 million. Fees are equal to 5.2% of the equity tranche’s par value. The collateral consists of bonds with a coupon 9.75% that mature in ten years. A ten-year interest rate swap with notional principal of $70 million dollars is available that receives fixed rate of 5.25% and pays the LIBOR. Design a CDO that satisfies the above requirements. What is the potential annual return (in percent)  to the equity tranche assuming no defaults?

A company can invest funds for five years at LIBOR minus 50 basis points. The five-year swap rate is 4%. What fixed rate of interest can the company earn by using the swap? 

Consider the following basic $100 million CDO structure. The senior tranche has a par value of $70 million dollars and a coupon rate of LIBOR + 1.0%. The mezzanine tranche has a par value of $20 million and a coupon rate equal to 8.25%. The equity tranche has a par value of $10 million. Fees are equal to 4.2% of the equity tranche’s par value. The collateral consists of bonds with a coupon 9.75% that mature in ten years. A ten-year interest rate swap with notional principal of $70 million dollars is available that receives fixed rate of 5.25% and pays the LIBOR. Design a CDO that satisfies the above requirements. What is the potential annual return (in percent)  to the equity tranche assuming no defaults?