07. Credit Risk Management// Credit Risk

Question 1

Credit Risk
* Can we get an …
* How much capital should we hold against potential losses?
* Economic capital: …
* Regulatory capital.
* Banks use various measures and models such as … to calculate economic/regulatory capital.

Answer 1

estimate of potential losses?

What they would have hold without regulation

Value-at-Risk (VaR) models and Expected Shortfall (ES)

Question 2

Economic & Regulatory Capital

• Bank wants to keep the probability of default at most at 2.5%.
• Regulator wants to keep the probability of default at most at 0.5%.

How does the economic and regulatory capital change with increasing mean and standard deviation of the normally distributed expected returns?

Answer 2

Increasing mean -> Higher expected returns -> Lower probability of loss-> bank would need less buffer to protect against unexpected losses-> lower economic/regulatory capital

Increasing standard deviation -> uncertainty around the expected return grows-> widening the tails of the distribution-> increases the potential for extreme losses-> higher economic/regulatorycapital

Question 3

Economic Capital
* The return at t=1 is R1.
* The bank defaults if R1 < d.
* The bank wants this probability to be 2.5%: Pr(R1 < d) = 0.025.
* This corresponds to the 2.5% lower tail of the Normal distribution.
* …
* The bank defaults with a probability of 2.5% when …
* Max amount of debt bank can have is …
* Thus economic capital is…

Answer 3

At the 2.5% tail of the Normal distribution R1 = mean – 1,96*std dev.

d = mean - 1,96 * std dev.

Since d + e = Ro, d = mean - 1,96* std dev.
and Ro - d = e

Economic Capital is given as e = Ro - mean + 1,96 * std dev

Question 4

Regulatory Capital
* Regulator keeps the probability of default at most at 0.5%.
* The bank defaults if R1 < d.
* At the 0.5% tail of the Normal distribution R1 = mean – 2,57std dev.
* The bank defaults with a probability of 0.5% when R1 = ….
* This corresponds to d < mean – 2,57std dev

Answer 4

mean – 2,57* std dev.

Since debt cannot be lower than R1=> d = mean - 2,57*std dev. at critical point

Since Ro = d + e
=> e = Ro - mean + 2,57*std dev.

Question 5

What is widely used risk measure for losses on a portfolio of assets?
Commonly used for:
* Risk management
* …
* Financial Reporting
* …

Answer 5

VaR

Financial control

Computing regulatory capital

Question 6

Explain the components of VaR.

100p% VaR is the threshold loss value such that:
…

Answer 6

Components:
* Portfolio of assets
* Time horizon
* Probability denoted by p.

Probability that the loss on the portfolio over the given time horizon exceeds this value is p.

Question 7

p=0.01. Time horizon is 1 week. Explain what 1% VaR of €10m means.

Answer 7

There is a 0.01 probability that the losses on the portfolio will exceed €10 million over a week.

Question 8

Expected Shortfall
* One of the shortcomings of VaR is that it …
* However, losses can be …
* VaR can …
* Expected shortfall tries to …
* Also called conditional VaR (CVaR), average VaR (AVaR) and expected tail loss (ETL).

Answer 8

gives the minimum loss for a given probability.

much larger in the tail.

miss tail risk.

address this shortcoming.