Final answer:
In the case of differing CDS and spot market spreads, there is an opportunity for arbitrage. When interest rates rise, the price of pre-existing bonds drops to provide a yield that aligns with the new rates. For the water company bond, one would pay less than $10,000 due to the rise in market interest rates from 6% to 9%.
Step-by-step explanation:
If a trader notices that the credit default swap (CDS) spread on a bond (bond b) is 6%, but the spot market spread between a risky bond and a risk-free bond is 7%, they should consider an opportunity for an arbitrage trade. In this situation, the trader could buy the bond in the spot market and simultaneously sell CDS protection, assuming they can service the CDS if the bond defaults. The net effect would be to capture the 1% spread differential as a gain.
Now turning to a case where interest rates rise impacting the bond price, we have a bond that originally paid 8% interest. If the prevailing interest rates increase to 12% and there is only one year left for the bond's maturity, the bond's price will have to decrease to offer a yield that is competitive with the current market rates. This is because as interest rates rise, the price of existing bonds usually falls to adjust the yield upwards for new investors.
Calculation of Bond Price with Interest Rate Change
With the given scenario of a local water company's bond with an initial rate of 6%, and the market rates rising to 9% a year before the bond's maturity, we would expect the price of the bond to be less than $10,000. This is because the bond's fixed interest payments are now less attractive compared to new bonds issued at 9%. To calculate the price one would be willing to pay for the bond, we can use the present value formula which discounts the remaining cash flows at the new market interest rate (9% in this case).