Question

1. A bank had a leverage ratio of 12.5 at the end of January. In February, bankís capital decreased by 10 percent, but bankís liabilities remained the same. In March, bankís assets further decreased by 0.5 percent and there was no change in bankís liabilities. (a) What was the percentage change in bankís capital in March? Approximately 6:89% (b) What is the bankís leverage ratio at the end of March? Approximately 14:7

Answer 1

1. Leverage ratio = 12.5

Let the capital in January be X

Let Liabilities in January = Y

Capital = Assets - Liabilities

Therefore, Assets in January = X + Y

Leverage ratio = 12.5

=> Y/X = 12.5 => Y = 12.5X

In February,

Capital = X(1 - 0.1) = 0.9X

Liabilities = Y (same as in January)

Therefore, Asset in February = 0.9X + Y

In March,

Asset = (0.9X + Y)*(1 - 0.005) = (0.9X + Y)*(0.995)

Liabilities in March = Y

Capital = (0.9X + Y)*(0.995) - Y = 0.8955X - 0.005Y = 0.8955X - 0.0625X = 0.83X

% Change in Capital = [(0.9X - 0.8X)/0.9X]*100 = 7.7%

Leverage ratio = Y/0.83X = 15.06