Note:

Daily earnings at risk (DEAR), aka. 1-day VaR, calculations should be based on 1-day and 99% confidence, i.e. the 1 bad day in 100 days. That is, all calculations should address the following: What is the most the bank can lose till tomorrow on its trading portfolio with 99% confidence?

Please show solutions to problem.

An FI wants to obtain the DEAR on its trading portfolio. The portfolio consists of the following securities. Fixed-income securities: The FI has a long position in a seven-year, zero coupon bond with a face value of $2,000,000. The bond is trading at a yield to maturity of 6.50 percent. The historical mean change in daily yields is 0.0 percent and the standard deviation is 22 basis points. (ii) The FI also holds a 10-year, zero-coupon bond with a face value of $1,700,000. The bond is trading at a yield to maturity of 6.35 percent. The price volatility of the potential adverse move in yields is 55 basis points. Foreign exchange contracts: The FI has a 2.5 million long trading position in spot euros at the close of business on a particular day. The exchange rate is 0.90/$1, at the daily close. Looking back at the daily percentage changes in the exchange rate of the euro to dollars for the past year, the FI finds that the volatility or standard deviation () of the spot exchange rate was 45.5 basis points (bp). Equities: The FI holds a $2.35 million trading position in stocks that reflect the U.S. stock market index (e.g., the S&P 500). The B = 1.25. Over the last year, the standard deviation of the stock market index was 275 basis points. Correlations (pij) among assets are as follows: 7-year, zero coupon 12-year zero coupon L | 7-year, zero coupon 12-year zero coupon /S U.S. stock index E S -0.3 -0.5 . U.S. stock index 0.5 0.15 0.35 Problems 1. Calculate the DEAR of this trading portfolio. 2. If the correlation matrix changes as follows, what will the FI's DEAR be? 7-year, zero coupon 12-year zero coupon L E S U.S. stock index 7- Vear, zero coupon 0.25 -OS 0.35 12-year zero coupon 0.2 -0.25 /S 0.5 U.S. stock index 3. If the standard deviation of the stock market index increases to 125 basis points, what will the FI's DEAR be? Use the original correlation matrix. 4. If the FI's FX position were changed to 4.0 million, what will the FI's DEAR be? Use the original correlation matrix. An FI wants to obtain the DEAR on its trading portfolio. The portfolio consists of the following securities. Fixed-income securities: The FI has a long position in a seven-year, zero coupon bond with a face value of $2,000,000. The bond is trading at a yield to maturity of 6.50 percent. The historical mean change in daily yields is 0.0 percent and the standard deviation is 22 basis points. (ii) The FI also holds a 10-year, zero-coupon bond with a face value of $1,700,000. The bond is trading at a yield to maturity of 6.35 percent. The price volatility of the potential adverse move in yields is 55 basis points. Foreign exchange contracts: The FI has a 2.5 million long trading position in spot euros at the close of business on a particular day. The exchange rate is 0.90/$1, at the daily close. Looking back at the daily percentage changes in the exchange rate of the euro to dollars for the past year, the FI finds that the volatility or standard deviation () of the spot exchange rate was 45.5 basis points (bp). Equities: The FI holds a $2.35 million trading position in stocks that reflect the U.S. stock market index (e.g., the S&P 500). The B = 1.25. Over the last year, the standard deviation of the stock market index was 275 basis points. Correlations (pij) among assets are as follows: 7-year, zero coupon 12-year zero coupon L | 7-year, zero coupon 12-year zero coupon /S U.S. stock index E S -0.3 -0.5 . U.S. stock index 0.5 0.15 0.35 Problems 1. Calculate the DEAR of this trading portfolio. 2. If the correlation matrix changes as follows, what will the FI's DEAR be? 7-year, zero coupon 12-year zero coupon L E S U.S. stock index 7- Vear, zero coupon 0.25 -OS 0.35 12-year zero coupon 0.2 -0.25 /S 0.5 U.S. stock index 3. If the standard deviation of the stock market index increases to 125 basis points, what will the FI's DEAR be? Use the original correlation matrix. 4. If the FI's FX position were changed to 4.0 million, what will the FI's DEAR be? Use the original correlation matrix