Noris: Asset/Liability Management Strategies for P&C Companies

Question 1

Describe the three different ways to value the portfolio equity. (what values of bonds, stocks, and liabilities are used?)

Answer 1

1. Book Value (Statutory Surplus): Bonds are discounted according to their yields at the time of purchase (i.e. book value), stocks are valued at market value, liabilities are not discounted at all.
2. Current Value Surplus: Values all assets at current market value and liabilities on an undiscounted basis.
3. Market Value Surplus: Assets at their current market value and also discounts the liabilities to a present value based on any number of possible interest rates, including the historic portfolio yield, the current yield of its assets, or some conservative figure (risk free rate).

Question 2

Why should a company manage its MVS?

Answer 2

1. MVS is leading indicator of the future book value of the firm, since book value converges to market value as assets and liabilities mature.
2. It helps mangement to achieve their goals of maximizing shareholder wealth and providing higher future divedends.
3. It assists in addressing regulator’s concern regarding capital adequacy

Question 3

What is the formula for the duration of MVS?

Answer 3

D_MVS = (D_MVAMVA - D_MVLMVL)/MVS

This is more specifically call the Duration Gap of Surplus (DG(s)).

Question 4

What is a firm’s “duration gap”?

Answer 4

The amount that the D_MVS exceeds zero.

Larger duration gap => MVS is more susceptible to changes in interest rate

A positive duration gap => assets are longer than liability. This means that any rise in interest rates would lower the absolute value of MVS (asset market value would decline relatively more than liability market value).

A negative duration gap => rising interest rates would improve the amount of MVS.

A natural target for managing DG would be to achieve a DG =0, which would mean that the value of MVS will be immune to changes in interest rates.

Question 5

What is the approximation for a stock’s duration? Why does this approximation often produce unrealistic values?

Answer 5

1/d, where d is the current dividend rate.

Because the value of stock is influenced by many other factors in addition to interest rate

Question 6

Three different targets for duration gap to manage towards

Answer 6

i. Duration Gap of Surplus — One target for the duration gap of surplus (DGS ) is to set it to zero, thus immunizing the surplus from the effects of changes in interest rates. This might be desirable in some contexts but it would result in large fluctuations in earnings and would be unduly restrictive.
ii. Duration Gap of Total Return — Recall from BKM Chapter 16 that the Macaulay duration indicates the holding period over which the rate of return is immunized. Therefore, insurers might want to set their DG_S equal to a specific holding period (e.g. one year) and thereby achieve a target return on surplus over that period. If H is the desired holding period, then DG_TRS can be used to indicate the duration gap of the total return on surplus and then DG_TRS ƒ= DG_S - H.
iii. Duration Gap of Leverage — Others might be interested in the degree of leverage, which can be denoted as either MVS/MVA or its reciprocal. It should be clear that if both MVS and MVA change by the same percentage amount, then the leverage ratio will remain unchanged and will therefore be immunized against changes in rates. To do this, we simply set the duration of assets equal to the duration of surplus, since the (modified) duration tells us the percentage change in the surplus or assets. Noris then defines the duration gap of leverage as DG_EL ƒ = D_MVS - D_MVA.

Question 7

What is “economic leverage”?

Answer 7

MVA to MVS ratio. The economic leverage of a firm will remain unchanged only when the duration of surplus = duration of assets. => Duration gap for Economic Leverage DG (el) = D(mvs)-D(mva)=0.

Question 8

Miscellaneous Issues 1: Unexpected Loss Development

What are the three alternative approaches to hedge against unexpected change in inflation?

Answer 8

i. One way to do this is to invest more heavily in common stocks or real estate, two asset classes that arguably contain an exposure to inflation. Noris dismisses this because these asset classes introduce too much non-interest rate volatility.
ii. Another approach is to have assets that roll over frequently, but this will require more short-term assets and will likely require a deviation from duration matching.
iii. Another approach is to simply overstate the liabilities in the form of contingency reserves.