Asset and Liability Management: The Banker’s Guide to Value Creation and Risk Control, Second Edition

Solution to Stage Nineteen

1:

Step 1. Variance of total income = total risk2 = standard deviation of total income2 = σ2   = (£ gap2 × £ rate volatility2)     + ($ gap2 × $ rate volatility2)     + (2 × £ gap × $ gap × correlation£,$ × £ rate volatility × $ rate volatility)   = (200,0002 × 0.00122)     + (150,0002 × 0.00182)     + (2 × 200,000 × 150,000 × 0.7 × 0.0012 × 0.0018)   = 221,220 Step 2. Calculate the volatility (standard deviation) of total income. Volatility of total income = 1 standard deviation of total income = σ   = squared root of variance = √221,220   = £470.34