Question

1) A risk analyst is trying to estimate the credit VaR for a risky bond. The credit VaR is defined as the maximum unexpected loss at a confidence level of 99.9% over a one-month horizon. Assume that the bond is valued at $1,000,000 one month forward, and the one-year cumulative default probability is 2% for this bond. What is the credit VaR for the bond, assuming no recovery?

2) Mr. Rosenqvist, asset manager, holds a portfolio of 100 million, which consists of BBB-rated bonds. Assume that the one-year probability of default is 7%, the recovery rate is 60%, and defaults are uncorrelated over years. Required • The one-year expected credit loss on Mr. Rosenqvist’s portfolio • The three -year expected credit loss on Mr. Rosenqvist’s portfolio

3) Credit risk includes three risk factors. Please list them and also illustrate their definition.

4) Justify the statement “credit losses only occur at the event of default”. Is this true?why?

Answer 1

Soln : 1) Given Data, Bond value = $1000000, Var at 99.9, alpha value = 3.09 (use z table)

Probability = 2% and LGD = 1 as no recovery is given,

Hence VaR = EL * alpha value = 1000000*2%*1* 3.09 = $61800

2) Data, portfolio value = $100 mn, RR = 60%, PD = 7% , uncorrelated defaults over years

So, 1 year expected credit loss = $100 *7% *(1-60%) = $2.8 million

Need to calculate 3 year expected loss, As we have calculated that in 1 year EL = $2.8 million, hence, net value remaining of portfolio = 100- 2.8 = $97.2 million, again the 1 year PD = 7% and RR = 60%

So, Expected loss in 2nd year = 97.2*7%*0.4 = $2.722 mn

Similarly in the 3rd year Expected loss = (97.2-2.722) *7%*40% = $2.65 mn

Total 3 year expected loss = 2.65 +2.72+ 2.8 = $ 8.12 million

3) Three risk factors of a credit risk are : 1) Probability of default (PD) i.e. probability of a default of the credit given to the borrower based on their position or rating and any other analysis.

2) Loss given default : It is the rate or percentage of loan that will remain unpaid by the defaulter i.e. the amount remaining after some recovery from the default account.

3) Exposure at default : It is defined as the total outstanding that the borrower needs to pay as he defaults.

4) Credit losses is a definition given in such cases where there are chances of default , for other losses separate risks are defined. As credit loss arises from the definiton of credit itself, when credit is given the willingness and capability of the person defined the repayment strength, there would not be any other reason , other than defalt that will be covered by the credot risk definiion.