Question 1

Suppose we have a zero-coupon bond that pays $1 after one year if the issuing firm is not in default. If the firm is in default the recovery rate is 40%. The one-year risk free interest rate in simple terms is 5% and the risk-neutral probability that the firm defaults is 10%. What is today's fair price for this bond?

Accepted Answer

A)   $0.875
B)   $0.895
C)   $0.915
D)   $0.935 B

Question 2

The current one-year and two-year zero-coupon rates are 6% and 7%, respectively. The one-year and two-year credit spreads are 1% and 2%, respectively. If the recovery rates on this class of bonds is 40% of face value, which of the following numbers most closely approximates the forward probability of default in year 2? Assume that interest rates and yields are in continuously-compounded and annualized terms. Assume also that if default occurs in any year, the recovered amount is received at the end of that year.

Accepted Answer

A)   1%
B)   2%
C)   5%
D)   9% C

Question 3

A zero coupon bond with a maturity of one-year pays $1,000 if the issuing firm is not in default. If the firm is in default, the recovery rate is 35%. The risk-free interest rate for one year is 5% and the risk-neutral probability that the firm defaults is 20%. What is the credit spread (over the risk-free rate) on the bond? All yields are in simple terms with annual compounding.

Accepted Answer

A)   7.90%
B)   12.90%
C)   15.69%
D)   20.69% C

Question 4

There are different recovery conventions. Two common ones are RMV (recovery of market value) and RT (recovery of Treasury value). For a given dollar value recovered on a default bond, it is generally the case that

Accepted Answer

A)   RMV  ⇔\Leftrightarrow⇔  RT.
B)   RMV  ⩾\geqslant⩾  RT.
C)   Which one is greater depends on the level of interest rates.
D)   None of the above.

Question 5

ABC Inc. has a risk-neutral probability of default of 5% over every half-year period. The loss-given-default (LGD) is 75% of the face value of the debt in ABC Inc. If the risk-free interest rate for one year is 10% on a semiannual compounding basis, find the fair spread for a one-year maturity, semiannual pay CDS contract. Assume that the spread is paid at the beginning of each half-year, while default, if it occurs, occurs at the end of each semiannual period.

Accepted Answer

A)   228 bps
B)   357 bps
C)   428 bps
D)   551 bps

Question 6

There are two ratings in a very simple world: non-default (ND) and defaultd. The real-world rating transition matrix per year is given by: $$P = \left[ \begin{array} { c c } 
0.95 & 0.05 \
0 & 1
\end{array} \right]$$ i.e., the probability of defaulting when the current state is non-default is 0.05, and a defaulted bond never leaves that state and has zero recovery. The two-year zero-coupon risk-free rate is 4% (continuously-compounded). The price of a default-risk-bearing two-year $100 face value zero-coupon bond is $88. If the off-diagonal one-period transition probabilities in the real-world transition matrix are multiplied by a premium adjustment $\pi$ to get the risk-neutral transition matrix (as in the Jarrow-Lando-Turnbull model), then given the price of the two-year bond, what is the value of $\pi$ ?

Accepted Answer

A)   1.97
B)   2.00
C)   2.03
D)   2.10

Question 7

Empirically, recessions witness a rise in default rates. Which of the following scenarios also accompanies the rise in default rates?

Accepted Answer

A)   Recovery rates rise.
B)   Loss given default (LG
D)   falls
C)   LGD rises
D)   LGD becomes highly volatile.

Question 8

Consider a two-year, annual pay CDS contract, where premiums are paid at the end of the year and if default occurs, it is also assumed to happen at the end of the year (but immediately after the premium payment). Each year there is a 5% risk-neutral probability of the firm defaulting. In default, recovery is 50% (recovery of par, RP). Assume that interest rates are zero. The fair price of this CDS is a spread of

Accepted Answer

A)   200 bps
B)   225 bps
C)   250 bps
D)   275 bps

Question 9

Suppose we have a zero-coupon bond that pays $100 after one year if the issuing firm is not in default. If the firm is in default the recovery rate is 50%. The simple risk-free interest rate for one year is 5% and the risk-neutral probability that the firm defaults is 10%. What is todayÕs fair credit spread for this bond?

Accepted Answer

A)   5.5%
B)   6.5%
C)   7.5%
D)   8.5%

Question 10

The average default rate in the economy is 1.5% of the face value of outstanding debt defaults per year. How many years will it be on average before half the firms are no longer in existence if no new firms enter the economy?

Accepted Answer

A)   44 years
B)   45 years
C)   46 years
D)   47 years

Question 11

Suppose we have a zero coupon bond that pays $1 after one year if the issuing firm is not in default. If the firm is in default, the recovery rate is 42%. The risk free interest rate for one year is 5%. If the credit spread on the bond is 2.5%, what is the risk-neutral probability of default of the bond? Assume all yields are stated in simple terms with annual compounding.

Accepted Answer

A)   0.01
B)   0.02
C)   0.03
D)   0.04

Question 12

Suppose the default intensity of a firm is 0.10. What is the five-year survival probability of the firm closest to?

Accepted Answer

A)   45%
B)   50%
C)   55%
D)   60%

Question 13

A zero coupon bond with a maturity of one-year pays $1,000 if the issuing firm is not in default. If the firm is in default, the recovery rate is 35%. The risk-free interest rate for one year is 5% (in simple terms with annual compounding) and the risk-neutral probability that the firm defaults is 20%. What is todays price for this bond?

Accepted Answer

A)   $781.28
B)   $828.57
C)   $885.71
D)   $912.92

Question 14

If the hazard rate is $\lambda = 0.2$ , the risk-free rate is zero, then if the price of a one-year $100 face value discount bond is $85, then what is the expected recovery rate $\phi$ on default of the bond?

Accepted Answer

A)   17%
B)   24%
C)   40%
D)   55%

Question 15

The average default rate in the economy is 1.5% of the face value of outstanding debt defaults per year. What is the average time between defaults if there are 1000 firms alive on average?

Accepted Answer

A)   20 days
B)   24 days
C)   38 days
D)   41 days

Question 16

Consider a one-year zero-coupon defaultable bond. Let $r$ and $S$ denote, respectively, the risk-free interest rate and the spread on the bond, where both are expressed in simple terms with annual compounding. Suppose the risk-neutral probability of default $\lambda$ and the recovery rate of the bond in default $\phi$ remain fixed. Then, an increase in the risk-free rate must be accompanied by

Accepted Answer

A)   An increase in the spread.
B)   A decrease in the spread.
C)   No change in the spread.
D)   A change in the spread that can be positive, negative, or zero.

Question 17

The hazard rate for a firm evolves as follows: $\lambda ( t ) = 0.2 + 0.5 t$ . The probability of the firm defaulting in the next year is:

Accepted Answer

A)   0.24
B)   0.36
C)   0.48
D)   0.60

Question 18

Suppose the default probability of a firm, conditional on it not having defaulted so far, is 0.10 per year. What is the 5-year survival probability of the firm?

Accepted Answer

A)   49%
B)   51%
C)   59%
D)   61%

Question 19

Suppose we have a zero-coupon bond that pays $100 after one year if the issuing firm is not in default. If the firm is in default the recovery rate is 50%. The simple risk free interest rate for one year is 3% and the risk-neutral probability that the firm defaults is 5%. What is today's fair price for this bond?

Accepted Answer

A)   $87.55
B)   $89.23
C)   $92.59
D)   $94.66

Question 20

Suppose we have a zero-coupon bond that pays $1 after one year if the issuing firm is not in default. If the firm is in default the recovery rate is 40%. The one-year risk free interest rate in simple terms is 5% and the risk-neutral probability that the firm defaults is 10%. What is the fair credit spread on the bond (again, in simple terms)?

Accepted Answer

A)   5.0%
B)   6.7%
C)   10.5%
D)   11.7%

Exam 31: Reduced-Form Models of Default Risk

There are different recovery conventions. Two common ones are RMV (recovery of market value) and RT (recovery of Treasury value) . For a given dollar value recovered on a default bond, it is generally the case that

Empirically, recessions witness a rise in default rates. Which of the following scenarios also accompanies the rise in default rates?

The average default rate in the economy is 1.5% of the face value of outstanding debt defaults per year. How many years will it be on average before half the firms are no longer in existence if no new firms enter the economy?

Suppose the default intensity of a firm is 0.10. What is the five-year survival probability of the firm closest to?

If the hazard rate is $\lambda = 0.2$ , the risk-free rate is zero, then if the price of a one-year $100 face value discount bond is $85, then what is the expected recovery rate $\phi$ on default of the bond?

The average default rate in the economy is 1.5% of the face value of outstanding debt defaults per year. What is the average time between defaults if there are 1000 firms alive on average?

The hazard rate for a firm evolves as follows: $\lambda ( t ) = 0.2 + 0.5 t$ . The probability of the firm defaulting in the next year is:

Suppose the default probability of a firm, conditional on it not having defaulted so far, is 0.10 per year. What is the 5-year survival probability of the firm?

Exam 31: Reduced-Form Models of Default Risk

There are different recovery conventions. Two common ones are RMV (recovery of market value) and RT (recovery of Treasury value) . For a given dollar value recovered on a default bond, it is generally the case that

Empirically, recessions witness a rise in default rates. Which of the following scenarios also accompanies the rise in default rates?

The average default rate in the economy is 1.5% of the face value of outstanding debt defaults per year. How many years will it be on average before half the firms are no longer in existence if no new firms enter the economy?

Suppose the default intensity of a firm is 0.10. What is the five-year survival probability of the firm closest to?

If the hazard rate is λ=0.2\lambda = 0.2λ=0.2 , the risk-free rate is zero, then if the price of a one-year $100 face value discount bond is $85, then what is the expected recovery rate ϕ\phiϕ on default of the bond?

The average default rate in the economy is 1.5% of the face value of outstanding debt defaults per year. What is the average time between defaults if there are 1000 firms alive on average?

The hazard rate for a firm evolves as follows: λ(t) =0.2+0.5t\lambda ( t ) = 0.2 + 0.5 tλ(t) =0.2+0.5t . The probability of the firm defaulting in the next year is:

Suppose the default probability of a firm, conditional on it not having defaulted so far, is 0.10 per year. What is the 5-year survival probability of the firm?

If the hazard rate is $\lambda = 0.2$ , the risk-free rate is zero, then if the price of a one-year $100 face value discount bond is $85, then what is the expected recovery rate $\phi$ on default of the bond?

The hazard rate for a firm evolves as follows: $\lambda ( t ) = 0.2 + 0.5 t$ . The probability of the firm defaulting in the next year is: