1. Assume the dollar market value of an FI\'s position is $200 000 with a modifi

Question

1. Assume the dollar market value of an FI's position is $200 000 with a modified duration of four years. The potential adverse move in the yield is 16.5 basis points. What is the VAR of the position if the FI is required to hold the position for 6 days (round to two decimals)?

2. Assume the dollar market value of an FI's position is $200 000 and the calculated price volatility is 1.25%. What is the VAR of the position if the FI is required to hold the position for 6 days (round to two decimals)?

3. Consider the case of ABC Company. The company's marginal probability of default in year 1 is 0.03 and 0.08 in year 2. What is ABC Company's cumulative default probability (round to two decimals)?

Explanation / Answer

1.

PRICE VOLATILITY = - MODIFIED DURATION X POTENTIAL ADVERSE MOVE IN THE YIELDS

PRICE VOLATILITY = - 4 X 0.00165 = - 0.0066

DEAR = DAILY EARNINGS AT RISK = $ VALUE OF POSITION X PRICE VOLATILITY

DEAR = DAILY EARNINGS AT RISK = $200000 X 0.0066 = $1320

VAR = DEAR X SQRT(N)

VAR = $1320 X SQRT(6) = $1320 X2.4495 = $3233.34

2.

DEAR = DAILY EARNINGS AT RISK = $ VALUE OF POSITION X PRICE VOLATILITY

DEAR = DAILY EARNINGS AT RISK = $200000 X 0.0125 = $2500

VAR = DEAR X SQRT(N)

VAR = $2500 X SQRT(6) = $2500 X2.4495 = $6123.75

3.

CUMULATIVE PROBABILITY OF DEFAULT = 1 - (1 - PROB OF DEFAULT IN YEAR 1)*(1 - PROB OF DEFAULT IN YEAR 2)

CUMULATIVE PROBABILITY OF DEFAULT= 1 - (1-0.03)*(1-0.08) = 1- 0.8924 = 0.1076 = 10.76% = 11%

ANSWER IS 11%

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