AIM 1: Describe factors contributing to expected and unexpected loss.

1、Unexpected loss is best characterized as:

A) variance of expected loss.

B) variance of unanticipated loss.

C) standard deviation of expected loss.

D) standard deviation of unanticipated loss.

The correct answer is C

Unexpected loss is defined as the variation in potential loss around the expected or average loss level.

2、Which of the following is TRUE concerning expected loss and unexpected loss from a bank loan portfolio?

A) Expected loss > unexpected loss.

B) Indeterminate.

C) Expected loss < unexpected loss.

D) Expected loss = unexpected loss.

The correct answer is B

Based on the relative magnitudes of expected loss and its standard deviation, i.e. unexpected loss, expected loss may be greater, less or equal to unexpected loss. Without further information, 'indeterminate' is the best answer choice.

3、Under the option view of the firm, which of the following is TRUE?

A) The firm will default on its obligations if the value of the firm exceeds the value of the debt.

B) The firm will default on its obligations if the value of its equity exceeds the value of the debt.

C) The firm will default on its obligations if the value of its equity is less than the value of the debt.

D) The firm will default on its obligations if the value of the firm is less than the value of the debt.

The correct answer is D

Under the option view of the firm, the strike price is set at the level of outstanding debt. As long as the value of the firm exceeds the outstanding debt (strike price), the firm will repay its obligation.

4、Which of the following statements about loan returns is (are) TRUE?

Unexpected loss on the loan can result from default.

Unexpected loss on the loan can result from credit migration.

Loan returns increase as recovery rates decrease.

A) I and II only.

B) I only.

C) II and III only.

D) I, II, and III.

The correct answer is A

Default and credit migration (downgrade) will decrease loan return. Similarly, loan returns increase as recovery rates increase.

AIM 2: Define, calculate and interpret the unexpected loss on an asset.

1、Decreasing the recovery rate will do which of the following to unexpected loss?

A) Recovery rate does not influence UL.

B) Increase UL.

C) Decrease UL.

D) No change.

The correct answer is B

Reducing the recovery rate increases the variability around the expected loss level, increasing standard deviation (unexpected loss).

2、If the adjusted exposure for Bank X is $15 million, the probability of default is 2%, the recovery rate is 20%, and the standard deviation of EDF and LGD is 5% and 3%, respectively. What is the unexpected loss for Bank X?

A) $603,366.

B) $302,242.

C) $240,000.

D) $24,270.

The correct answer is A

3、Unexpected loss will increase under which of the following circumstances?

A) Variance of default frequencies increases.

B) Expected default frequency decreases.

C) Usage given default decreases.

D) Adjusted exposure increases but default frequency decreases.

The correct answer is

Unexpected loss is defined as :

As usage given default goes up, adjusted exposure increases, thus ‘usage given default decreases’ is incorrect. If expected default frequency decreases UL will decrease. ‘Adjusted exposure increases but default frequency decreases’ is ambiguous. ‘Variance of default frequencies increases’ will increase UL as the last term in the square root will increase.

4、John Clayburn is trying to parameterize a credit risk model for his employer, Syacmoor Bank. Based on a large sample of loans, he has estimated a default frequency of 12%. John knows that this is a necessary input to calculate the unexpected loss. Which of the following is closest to the standard deviation of Sycamoor’s default frequency?

A) 88%.

B) 35%.

C) 12%.

D) 11%.

The correct answer is B

The standard default model assumes a two-state (binary) default process. Therefore, the variance = EDF × (1 ? EDF) = (0.12) × (1 ? 0.12) = 0.1056. Thus, standard deviation of default frequency (0.1056)0.5 = 0.3496.

5、Which of the following statements about unexpected loss is TRUE?

A) Unexpected loss is a non-linear function of adjusted exposure.

B) Adjusted exposure is a non-linear function of unexpected loss.

C) Unexpected loss is a linear function of adjusted exposure.

D) Adjusted exposure is a linear function of unexpected loss.

The correct answer is C

The answer is clear from the equation of unexpected loss:

For example, doubling adjusted exposure will double the unepected loss.

6、Which of the following statements about unexpected loss is TRUE?

A) Unexpected loss is a linear function of loss given default.

B) Loss given default is a non-linear function of unexpected loss.

C) Loss given default is a linear function of unexpected loss.

D) Unexpected loss is a non-linear function of loss given default.

The correct answer is D

The answer is clear from the equation of unexpected loss:

For example, doubling LGD will not double the unexpected loss (as it appears inside the square root).

7、Smallville Savings Bank (SSB) has a loan portfolio totaling $20,000,000 in commitments. Currently 60% is outstanding. The bank has assessed an average internal credit rating equivalent to 2% default probability over the next year. Drawdown upon default is assumed to be 75%. The bank has additionally estimated a LGD of 60%. The standard deviation of EDF and LGD is 5% and 25%, respectively. The ratio of unexpected loss to expected loss is closest to:

A) 2.0.

B) 4.0.

C) 0.50.

D) 0.25.

The correct answer is B

We can calculate the expected loss as follows:

EL = AE × EDF × LGD

Adjusted exposure = OS + (COM ? OS) × UGD = $20,000,000 × (0.6) + ($800,000) × (0.75) = $18,000,000.

EL = ($18,000,000) × (0.02) × (0.60) = $216,000.

Ratio = $834,626 / $216,000 = 3.86 (closest to 4.0).

8、Smallville Savings Bank (SSB) has a loan portfolio totaling $20,000,000 in commitments. Currently 60% is outstanding. The bank has assessed an average internal credit rating equivalent to 2% default probability over the next year. Drawdown upon default is assumed to be 75%. The bank has additionally estimated a recovery rate of 60%. The standard deviation of EDF and LGD is 5% and 25%, respectively. The unexpected loss for SSB falls within which of the following ranges?

A) Greater than $750,000.

B) $250,001 to $500,000.

C) Less than $250,000.

D) $500,001 to $750,000.

The correct answer is D

Note that a recovery rate of 60% implies a loss given default of 40%. We can calculate the expected loss as follows:

EL = AE × EDF × LGD

Adjusted exposure = OS + (COM ? OS) × UGD = $20,000,000 × (0.6) + ($8,000,000) × (0.75) = $18,000,000.

EL = ($18,000,000) × (0.02) × (0.40) = $144,000.

UL = 18,000,000×√(0.02 × 0.252 + 0.42×0.052) = $731,163

9、Which of the following formulas for unexpected loss is CORRECT?

A)  

B)  

C) 

D) 

The correct answer is C

You can eliminate the two equations with LGD2 since LGD does not have square term. Then, you can eliminate the equation where the EDF term is multiplied by the VAR(LGD) term instead of VAR(EDF).

AIM 3: Explain the relationship between economic capital and unexpected loss.

1、The type of capital used to buffer a bank from unexpected losses is known as:

A) regulatory capital.

B) unexpected capital.

C) risk-adjusted capital.

D) economical capital.

The correct answer is D

It is imperative that a bank hold capital reserves (i.e., economic capital) to buffer itself from unexpected losses so that it can absorb large losses and continue to operate.

2、Which of the following best describes the relationship between loan losses and economic capital?

A) Unexpected loss typically exceeds economic capital.

B) Economic capital typically exceeds unexpected loss.

C) Economic capital typically equals expected loss.

D) Expected loss typically exceeds economic capital.

The correct answer is B

Economic capital represents the capital a bank sets aside to cover losses in atypical conditions. Thus, economic capital will reasonably be set above the unexpected loss level, e.g. two standard deviations.

AIM 4: Derive, mathematically, the unexpected loss on an asset.

1、The derivation of unexpected loss followed from which basic statistical identity?

VH = horizon value; V0 = current asset value.

A) VAR(V0) = E(V0)2 ? E(V20).

B) VAR(VH) = E(VH)2 ? E(V2H).

C) VAR(VH) = E(V2H) ? E(VH)2 + COV(V0, VH).

D) VAR(VH) = E(V2H) ? E(VH)2.

The correct answer is D

Current asset value is not relevant to determining the distribution on the horizon date. Choice A has the squared terms in the wrong place. COV is not used in the derivation.