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1. The position consists of one 5-yr, zero-coupon bond with a face value of $1,000,000. The bond is trading at a YTM of 7 %. You estimated that the historical mean change in daily yields is 0.0 percent and the standard deviation is 12 basis points. Compute the 10-day value at risk of the position.

2. The portfolio consists of two independent investments, A and B.

Each investment has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, a 94% chance of a gain of $1 million.

a. Compute the VaR of investment A at 95% confidence level

b. Compute the Conditional VaR of investment A at the 95% confidence level

c. Compute the 95% VaR of the portfolio

d. Compute the Expected Shortfall of the portfolio for the 95% confidence level

3. The trading portfolio consists of the following securities:

i) A $1 million position in a six-year zero bond with a face value of $1,543,302. The bond is trading at a y of 7.50 percent. The historical mean change in daily yields is 0.0 percent, and the standard deviation is 22 basis points.

ii) A 12-year zero bond with a face value of $1,000,000. The bond is trading at a yield to maturity of 6.75 percent. The price volatility if the potential adverse move in yields is 65 basis points.

iii) A €2.0 million long trading position in spot euros. The exchange rate is €0.80/$1, or $1.25/€, at the daily close. The estimate of the daily volatility ( standard deviation (s)) of the spot exchange rate is 55.5 basis points .

iv) A $2.5 million trading position in U.S. stocks. The ß = 1. The estimate of the daily volatility of the stock market index is 175 basis points.

 The estimated correlation among assets is given below:6-yr

zero

12-yr zero

€/$

S&P500

6-yr zero

0.75

-0.2

0.4

12-yr zero

-0.3

0.45

€/$

0.25

S&P500