Page 57 - Risk Management in current scenario

The problem is, it is impossible to match the duration of liability with the
duration of assets during these initial years.

This is a perennial problem prevalent in all long term regular premium
paying life insurance products mainly resulting from the definition of the
duration. The purpose of duration matching is to purchase the assets of
similar interest rate sensitivity as liability so that when interest rate
changes, their value moves in same direction and in same quantity. This
can be achieved through altering the defi nition of duration and yet
achieving the purpose thereby enabling an objective way of purchasing
the assets to back liability.

The duration definition is
D = - (1/P) x delta(P)/Delta(i) where P is the price of the asset and i is
the interest rate.

delta(P)/delta(i) Is change in the price of assets (or liability) with the
change in the interest rate. When this change in price is divided by P, it
gives the percentage change per unit value of assets (or liability).

In life insurance regular premium paying products, the problem in
duration number comes out due to dividing “change in price” by P. It is
the P that creates the problem.

This happens because liability cash fl ows in initial years are negative
followed by positive cash fl ows, when these cash fl ows are discounted
and added to calculate the value of P, it gives a smaller value of P
compared to delta(p)/delta(i) and when divided, it gives infl ated value
of duration (divided by smaller value). This happens till the time the
liability cash fl ows changes its sign. After this change in the sign of liability
cash fl ows, duration value becomes sensible. Till the time the Company
has mature portfolio; writing new business would cause change in sign
of liability cash fl ows and duration calculation would be tricky.

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