Page 58 - Risk Management in current scenario

The objective of managing the interest rate risk can be achieved by just
concentrating on delta(P)/delta(i) and not dividing by P.

The objective is achieved, if following equality can be reached
delta(A)/delta(i) = delta(L)/delta(i) Where A is the Assets and
L is Liability cash flows.
This is equivalent to
Sum(t*A(t)*V^(t) = Sum(t*L(t)*V^(t), where
V(t) = 1/(1+i)
The values of both side of the equation are sensible. This equation
provides an “objective” way in allowing life companies purchasing assets
so that left hand side of the equation comes in close proximity to right
hand side of the equation.

The right hand side of the equation has a fi xed value at each time as all
the variables are known on the date of valuation, the key challenge in fi
nding the assets because assets term run for shorter length compared
to liability term, for example under whole life product, t/ runs would run
to 100 years whereas t for assets would runs to 30 to 40 years depending
upon the availability of assets.
There are two key elements that that need attention that may bring the
sensitivity of assets close to the sensitivity of liability, they are
• “Timing” of Cash fl ows of coupons and redemptions
• “Amount” of coupons and redemptions
This boils down to two variable problems with one equation to identify
the timing and the amount. This can be done on trial and error basis by
pushing the coupon and redemptions to an optimum distance from origin
so that the value to LHS of the equation could be maximized to achieve
RHS. The “Optimum distance” is important because by too far pushing
the assets, the discounting effect would nullify their effect.

A typical life company may have following fi rst derivative of assets and
liability on base assets CFs and revised assets cash fl ows as shown below.

56 | Risk Management in Current Scenario