Consider a $10-$year bond that has a yield$-$to$-$maturity of $4\%$ and a credit rating of BBB$.$ Assume that the probability that the company will default on the bond during next year is $0\mathrm{.}5\%$ and that investors' recovery rate upon default is $40\%.$ In addition, assume that the $10-$year risk free rate is $2\mathrm{.}5\%.$

Question $4(11$ points$)$

The CDS $($credit default swap$)$ premium on this bond should be approximately Suppose that the probability of default on this bond increases to $1\%$ a year. Which of the following options is correct?

Question $5$ options:

The CDS premium goes up to $1\%.$

Banks and insurance companies would be more likely to sell CDS protection on this company's debt because the premium has increased.

An investor who holds the bond and a CDS would still be earning a $2\mathrm{.}5\%$ return despite the change in default risk.

The CDS premium will decrease because the bond's expected return is lower