AIM 1: Describe the relationship between economic capital and risk-adjusted return on capital.

1、An analyst simulates the distribution of operational losses for her employer. She finds that the loss that corresponds to the 99th percentile of potential losses is $1,500,000 and the mean of the distribution is $250,000. The estimate of operational risk economic capital is closest to:

A) $250,000.
 
B) $1,500,000.
 
C) $1,250,000.
 
D) $1,750,000.

The correct answer is C

Operational risk economic capital is the difference between the loss at a given confidence level and the expected loss. In this case, $1,500,000 – $250,000 = $1,250,000.

2、The primary purpose of operational risk economic capital is to:

A) protect the company against insolvency due to expected and unexpected operational losses. 
 
B) meet financial reporting requirements. 
 
C) protect the company against insolvency due to unexpected operational losses. 
 
D) meet regulatory guidelines. 

The correct answer is C

The primary purpose of operational risk economic capital is to protect the company against insolvency due to unexpected operational losses.

3、Economic capital protects the company against insolvency due to unexpected operational losses. In identifying the appropriate level of economic capital, a bank should focus on the part of the loss probability distribution represented by losses:

A) in excess of the loss at a given level of confidence.
 
B) between the loss at a given level of confidence and the expected loss.
 
C) below the loss at a given level of confidence.
 
D) greater than the expected loss.

The correct answer is B

Economic capital is the difference between the loss at a given confidence level and the expected loss.

4、Which of the following is TRUE about economic capital?

For most financial institutions, economic capital held exceeds regulatory capital.
It protects financial institutions from expected and unexpected losses.
It is the capital required to keep the banking system safe.
It is a function of the risk of the financial institutions and inversely related to performance.
A) I and IV.
 
B) I and II.
 
C) II and III.
 
D) II and IV.

The correct answer is A

Statement II is not true. Economic capital protects financial institutions from unexpected losses; reserves protect the financial institutions from expected losses. Statement III is the function of regulatory capital.

AIM 2: Compute the RAROC for a loan.

1、Given the following information, calculate the RAROC.

Gross revenue: $8 million.
Interest expense: $4 million.
Economic capital: 10 million.
Return on invested economic capital: 500,000.
Operating costs associated with making the loan: $1.5 million.
Expected loss on the loan: 300,000.
A) 27%.
 
B) 42%.
 
C) 40%.
 
D) 5%.

The correct answer is A

RAROC: (8 - 0.3 – 4 + 0.5 - 1.5) / 10 = 27%.

2、A bank loan has expected gross revenue of $300,000, interest expense of $200,000, expected return on the $200,000 of economic capital of $20,000, expected loss on the loan of $10,000 and operating costs associated with the loan of $70,000. What is the risk adjusted return on capital (RAROC) for this loan?

A) 20%.
 
B) 10%.
 
C) 30%.
 
D) 55%.
 

The correct answer is A

RAROC = (300 ? 200 ? 10 + 20 ? 70) / 200 = 20%.

AIM 3: Explain how capital is attributed to market, credit, and operational risk.

1、What is the major source of market risk for a bank?

A) Credit risk.
 
B) Gap risk.
 
C) Operational risk.
 
D) Exchange rate risk.

2、A credit institution is allowed to reduce its total operating risk charge by up to 20% through the use of insurance if it adopts the:

A) basic indicator approach (BIA).
 
B) advanced measurement approach (AMA).
 
C) advanced standardized approach (ASA).
 
D) standardized approach (SA).

The correct answer is B

A credit institution is allowed to reduce its total operating risk charge by up to 20% through the use of insurance if it adopts the advanced measurement approach (AMA).

AIM 4: Compute the capital charge for market risk and credit risk.

1、Given the following information what is the daily RAROC charge for market risk?

The appropriate adjustment factor for the day-to-day event risk that is not captured by the VAR model is 2.25.
The multiplier used to determine the unused portion of the VAR limit is 0.30.
The mulitiplier used to determine the charge for exceeding the VAR limit is 3.20.
The VAR limit over a 10-day period is $2,530,000.
The daily VAR is $950,000.
A) $3,040,000. 
 
B) $1,100,000. 
 
C) $2,587,500. 
 
D) $2,617,500. 

The correct answer is D

The RAROC capital charge = F1(VAR) + F2(VAR limit – VAR) + F3 (VAR – VAR limit)

Where:
F1 = constant that adjusts for day to day event risk not captured in the VAR model
F2 = the multiplier used to determine the unused portion of the VAR limit
F3 = the multiplier used to determine the charge for exceeding the VAR limit

2.25($950,000) + 0 + 3.20($950,000 - $800,000) = $2,617,500.

2、Calculate the RAROC capital charge for market risk assuming:

The appropriate adjustment factor for the day-to day event risk that is not captured in VAR is 3.
The multiplier used to determine the charge for the unused portion of the VAR limit is ?0.20.
The multiplier used to determine the charge for exceeding the VAR limit is 5.
The VAR limit is $10 million.
VAR is $9 million.
A) $28,200,000.
 
B) $30,200,000.
 
C) $26,800,000.
 
D) $435,200,000.

The correct answer is C

RAROC capital charge = 3($9 million) + (?0.20)($1 million) + 5($0) = $26,800,000.

AIM 6: Explain how the second-generation RAROC approaches improve economic capital allocation decisions.

1、The flaw in the first-generation risk-adjusted return on capital (RAROC) approach is that it:

A) assumes that the default probability remains constant.
 
B) attempts to align the risk of the business with the firm’s equity. 
 
C) only estimates the RAROC hurdle rate.
 
D) is poorly understood by investors and directors.

The correct answer is A

The flaw in the first-generation RAROC approach is that it assumes that the default probability remains constant. This assumption is inconsistent with a constant expected return on the firm’s equity.

AIM 7: Compute the adjusted RAROC for a project to determine viability.

1、What is the adjusted RAROC for a business if its RAROC is 22%, the company’s beta is 1.1, and the risk-free rate is 5%?

A) 15.45%.
 
B) 17%.
 
C) 4.84%.
 
D) 24.2%.

The correct answer is A

ARAROC = (RAROC – RF) / Beta

ARAROC = (22 – 5) / 1.1 = 15.45%.

2、Assume RAROC is 10%, the risk free rate is 4%, the market return is 10%, the firm’s required return on equity is 12%, and the firm’s beta is 1.1. What is the ARAROC and should the project be accepted?

A) 5.5%; reject.
 
B) 5.5%; accept.
 
C) 10%; accept.
 
D) 7.3%; accept.

The correct answer is A

ARAROC = (RAROC ? Rf) / beta = (10% ? 4%) / 1.1 = 5.4545%; Accept when ARAROC > (Rm ? Rf); Rm ? Rf = (Rs ? Rf) / beta (from the SML equation) = (12% ? 4%) / 1.1 = 7.2727%; Reject since 5.5% < 7.3%.