Replicating portfolio
Encyclopedia
In the valuation of a life insurance
company, the actuary
considers a series of future uncertain cashflows (including incoming premiums and outgoing claims, for example) and attempts to put a value on these cashflows. There are many ways of calculating such a value (such as a net premium valuation
), but these approaches are often arbitrary in that the interest rate chosen for discounting is itself rather arbitrarily chosen.
One possible approach, and one that is gaining increasing attention, is the use of replicating portfolios or hedge portfolios. The theory is that we can choose a portfolio of assets (fixed interest bonds, zero coupon bonds, index-linked bonds, etc.) whose cashflows are identical to the magnitude and the timing of the cashflows to be valued.
For example, to value a set of annual cashflows as follows: 2, 2, 2, 50, 2, 2, 102, you could buy a seven year bond with a 2% dividend, and a four year zero-coupon bond with a maturity value of 48. The cost of those two instruments might be 145 (the cost of buying the replicating portfolio) - and therefore the value of the cashflows is taken to be 145.
It should be clear that the advantages of a replicating portfolio approach include:
Valuing options and guarantees can require complex nested stochastic calculations. Replicating portfolios can be setup to replicate such options and guarantees. It may be easier to value the replicating portfolio than to value the underlying feature (options and guarantees).
For example, bonds and equities can be used to replicate a call option. The call option can then be easily valued as the value of the bond/equity portfolio, hence not requiring one to value the call option directly.
For additional information on economic valuations and replicating portfolios can be found here:
The Economics of Insurance
Life insurance
Life insurance is a contract between an insurance policy holder and an insurer, where the insurer promises to pay a designated beneficiary a sum of money upon the death of the insured person. Depending on the contract, other events such as terminal illness or critical illness may also trigger...
company, the actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
considers a series of future uncertain cashflows (including incoming premiums and outgoing claims, for example) and attempts to put a value on these cashflows. There are many ways of calculating such a value (such as a net premium valuation
Net premium valuation
A Net Premium Valuation is an actuarial calculation, used to place a value on the liabilities of a life insurer.-Background:It involves calculating a present value for the contractual liabilities of a contract, and deducting the value of future premiums. Both contractual liabilities, and future...
), but these approaches are often arbitrary in that the interest rate chosen for discounting is itself rather arbitrarily chosen.
One possible approach, and one that is gaining increasing attention, is the use of replicating portfolios or hedge portfolios. The theory is that we can choose a portfolio of assets (fixed interest bonds, zero coupon bonds, index-linked bonds, etc.) whose cashflows are identical to the magnitude and the timing of the cashflows to be valued.
For example, to value a set of annual cashflows as follows: 2, 2, 2, 50, 2, 2, 102, you could buy a seven year bond with a 2% dividend, and a four year zero-coupon bond with a maturity value of 48. The cost of those two instruments might be 145 (the cost of buying the replicating portfolio) - and therefore the value of the cashflows is taken to be 145.
It should be clear that the advantages of a replicating portfolio approach include:
- an arbitrary discount rate is not required
- the term structure of interest rates is automatically taken into account.
Valuing options and guarantees can require complex nested stochastic calculations. Replicating portfolios can be setup to replicate such options and guarantees. It may be easier to value the replicating portfolio than to value the underlying feature (options and guarantees).
For example, bonds and equities can be used to replicate a call option. The call option can then be easily valued as the value of the bond/equity portfolio, hence not requiring one to value the call option directly.
For additional information on economic valuations and replicating portfolios can be found here:
The Economics of Insurance