Fixed-income securities:
1.) The FI has a $1 million incline in a six-year zero seizes with a face lever of $1,543,302. The alignment is trading at a yield to maturity of 7.50 percent. The historical mean change in daily yields is 0.0 percent, and the streamer deviation is 22 basis points.
MD = D/(1 + R) = 6/(1.075) = 5.581395
Potential adverse move in yield at 5 percent = 1.65( = 1.65 x 0.0022 = .00363
Price volatility = MD x potential adverse move in yield
= 5.581395 x .00363 = 0.02026 or 2.026 percent
and the daily earnings at risk for this bond is:
salutary = ($ value of stupefy) x ( harm volatility)
= $1,000,000 x 0.02026 = $20,260
2.) The FI also holds 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.
Dollar value of position = $1m./(1 + 0.0675)12 = $456,652. The modified term of these bonds is:
MD = D/(1 + R) = 12/(1.0675) = 11.24122
Price volatility = (MD) x (potential adverse move in yield)
= (11.24122) x (.0065) = 0.073068 or 7.3068 percent.
DEAR = $456,652 x 0.073068 = $33,367
Foreign exchange contracts:
3.)The FI has a 3.5 million wide trading position in spot euros at the shutdown of business on a particular day. The exchange commit is €1.40/$1, or $0.714286/€, at the daily close.
Looking back at the daily changes in the exchange reckon of the euro to dollars for the past year, the FI finds that the volatility or standard deviation (?) of the spot exchange rate was 55.5 basis points (bp).
Dollar equivalent value of € position = FX position x ($/€ spot exchange rate)
= €3.5 million x $ per unit of foreign currency
Dollar value of € position = €3.5 million x $0.714286/€
= $2,500,000
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