Learn / Risk & ALM

Shock and net impact

This is the classroom book under one combined shock. You can move the shocks. Every dollar is a labeled coefficient from the lessons above. Nothing here is a live market revaluation, a solved swaption price, or a forecast.

Bond assets are $80 million, modified duration 6, spread duration 5. Equity assets are $20 million. Liabilities are $100 million, duration 12, and they respond only to the yield shock. The payer hedge is worth $40,000 per basis point of that yield shock and $150,000 per volatility point.

How the four lines add

Surplus change equals the asset change, minus the liability change, plus the hedge change. Minus the liability change means a fall in the value of the promise increases surplus. A rise in the value of the promise decreases surplus.

A liability mark-down increases surplus, because the promise is worth less. Read the sign of the liability line with that in mind.

At the starting sliders the yield is +100 basis points, so the bonds move by −$80 million × 6 × 0.01 = −$4.8 million. The liabilities move by −$100 million × 12 × 0.01 = −$12 million. Credit at +50 basis points moves only the bonds: −$80 million × 5 × 0.005 = −$2 million. Equity at −20% moves only the stock sleeve: −$4 million. The hedge’s rate piece is $40,000 × 100 = $4 million, and its volatility piece is $150,000 × 10 = $1.5 million.

Assets are −$4.8 million − $2 million − $4 million = −$10.8 million. Surplus is −$10.8 million − (−$12 million) + $5.5 million = $6.7 million. The rate rise marked the longer liabilities down by more than the bonds, so surplus rose before the hedge was added. The hedge, as specified here, gains when yields rise too. It is not canceling the duration gap. The receive-fixed swap on the hedging page is the instrument that closes that gap. This payer coefficient is the teaching stand-in for an option that gains if yields and volatility rise.

Move the shocks

Teaching lab

Move the four shocks

The sliders start at +100 basis points of yield, +50 basis points of credit spread, −20% equity, and +10 volatility points. Every dollar uses the classroom coefficients printed above. This is not a solved swaption price.

10-year yield +100 bpCredit spread +50 bpEquity -20%Volatility +10 pts

Piece	Change	Why
Bond assets, rates	-$4,800,000	Duration 6 on $80 million of bonds.
Bond assets, credit	-$2,000,000	Spread duration 5 on the same bonds. Liabilities ignore this shock.
Equity assets	-$4,000,000	The $20 million stock sleeve moves by the equity percent.
Liabilities	-$12,000,000	Duration 12 on $100 million. A mark-down of a liability raises surplus.
Hedge, rates	$4,000,000	$40,000 per basis point. A teaching coefficient, not a market DV01.
Hedge, volatility	$1,500,000	$150,000 per volatility point. A teaching vega, not a solved price.
Surplus	$6,700,000	Asset change minus liability change plus hedge change.

What the surplus line is not

The surplus line is an economic classroom total. It is not earnings, and it is not OCI. The GAAP page is why those can differ. It is also not a reverse stress test by itself. To use it that way, compare the surplus change with a limit you state, as on the stress testing page, where an $8 million surplus and a $5 million floor means a decline larger than $3 million is the breach.