Financial Markets and Market Risk Calculations
Topic 7 – self attempt tute questions Chapter 12
6. The DEAR for a bank is $8500. What is the VAR for a 10-day period? A 20-day period? Why is the VAR for a 20-day period not twice as much as that for a 10-day period? For the 10-day period: VAR = 8500 x [10]½ = 8500 x 3.1623 = $26 879.36
For the 20-day period: VAR = 8500 x [20]½ = 8500 x 4.4721 = $38 013.16
The reason that VAR20 (2 x VAR10) is because [20]½ (2 x [10]½). The interpretation is that the daily effects of an adverse event become less as time moves farther away from the event.
8. In what sense is duration a measure of market risk?
The market risk calculations are typically based on the trading portion of an FI’s fixed-rate asset portfolio because these assets must reflect changes in value as market interest rates change. As such, duration or modified duration provides an easily measured and usable link between changes in the market interest rates and the market value of fixed-income assets.
12. Bank of Ayers Rock’s stock portfolio has a market value of $10 000 000. The beta of the portfolio approximates the market portfolio, whose standard deviation (m) has been estimated at 1.5 per cent. What is the 5-day VAR of this portfolio, using adverse rate changes in the 99th percentile? DEAR = ($ value of portfolio) x (2.33 x m ) = $10m x (2.33 x .015) = $10m x .03495 = $0.3495m or $349 500 VAR = $349 500 x 5 = $349 500 x 2.2361 = $781 505.76 14. Calculate the DEAR for the following portfolio with and without the correlation coefficients. Estimated Assets DEAR S,FX S,B FX,B Stocks (S) $300 000 -0.10 0.75 0.20 Foreign exchange (FX) $200 000 Bonds (B) $250 000
What is the amount of risk reduction resulting from the lack of perfect positive correlation between the various assets groups? The DEAR for a portfolio with perfect correlation would be $750 000. Therefore the risk reduction is $750 000
6. The DEAR for a bank is $8500. What is the VAR for a 10-day period? A 20-day period? Why is the VAR for a 20-day period not twice as much as that for a 10-day period? For the 10-day period: VAR = 8500 x [10]½ = 8500 x 3.1623 = $26 879.36
For the 20-day period: VAR = 8500 x [20]½ = 8500 x 4.4721 = $38 013.16
The reason that VAR20 (2 x VAR10) is because [20]½ (2 x [10]½). The interpretation is that the daily effects of an adverse event become less as time moves farther away from the event.
8. In what sense is duration a measure of market risk?
The market risk calculations are typically based on the trading portion of an FI’s fixed-rate asset portfolio because these assets must reflect changes in value as market interest rates change. As such, duration or modified duration provides an easily measured and usable link between changes in the market interest rates and the market value of fixed-income assets.
12. Bank of Ayers Rock’s stock portfolio has a market value of $10 000 000. The beta of the portfolio approximates the market portfolio, whose standard deviation (m) has been estimated at 1.5 per cent. What is the 5-day VAR of this portfolio, using adverse rate changes in the 99th percentile? DEAR = ($ value of portfolio) x (2.33 x m ) = $10m x (2.33 x .015) = $10m x .03495 = $0.3495m or $349 500 VAR = $349 500 x 5 = $349 500 x 2.2361 = $781 505.76 14. Calculate the DEAR for the following portfolio with and without the correlation coefficients. Estimated Assets DEAR S,FX S,B FX,B Stocks (S) $300 000 -0.10 0.75 0.20 Foreign exchange (FX) $200 000 Bonds (B) $250 000
What is the amount of risk reduction resulting from the lack of perfect positive correlation between the various assets groups? The DEAR for a portfolio with perfect correlation would be $750 000. Therefore the risk reduction is $750 000