The negative value of duration gap that results when the duration of assets is less than the duration of liabilities (i.e., when the weighted duration of assets minus the product of the weighted duration of liabilities and the ratio of total liabilities to total assets is negative):
DGap < 0 when DA < DL × L/A
Where: DA and DL denote the weighted durations of assets and liabilities, respectively; L and A denote the values of liabilities and assets, respectively. Duration gap is also negative when the duration of equity times the ratio of equity to total assets is negative:
DGap < 0 when DE × E/A < 0
Where: DE is the duration of equity and E is the value of equity.
A negative duration gap means that the market value of equity will increase when interest rates rise (this corresponds to a reinvestment position). In other words, a decrease in interest rates with a negative duration gap will cause capital to fall, while an increase in interest rates with negative duration gap will cause it to rise.
Comments