Chapter 19: Actuarial techniques (1) Flashcards
Asset pricing
Relates to the systematic determination of the value of risky securities such as equities, bonds and derivatives.
Modern asset pricing models derive from the notion that price equals the expected discount payoffs from an asset.
Approaches used in asset pricing
- consumption-based models where asset price equals the expected discounted value of asset’s payoff, using investor’s marginal utility to discount the payoff.
- Capital Asset Pricing Model (CAPM)
- Arbitrage Pricing Theory
- Multifactor models
- Option pricing models
- Term structure models
Functions that asset pricing help us perform
- To determine whether an asset is mispriced (and represents a trading opportunity for the shrewd investor)
- To determine what price the asset should be (where it cannot be observed)
Absolute pricing
Prices assets by reference to exposure to fundamental sources of macroeconomic risk, e.g. consumption based and general equilibrium models (CAPM)
- prices obtained are capable of economic interpretation
Relative pricing
Considers the value of an asset given the price of some other assets, e.g. Black Scholes option pricing and arbitrage free pricing theory.
- use as little information about the fundamental risk factors as possible and do not ask where the prices of the assets came from
General asset pricing formula
Interpretation of the general asset pricing formula
First equation tells us that the price of an asset is equal to the expected value of the discounted future payoffs.
Second equation tells us where the stochastic discount factor comes from. It is derived either from an economic model (and so reflects the parameters of the model) or emphirical data
ALM for banking
Used ensure any mismatches between assets and liabilities are not so large as to expose them to serious risk if there’s a sudden sharp market movement in near future – use VaR to help assess such risks.
ALM for pension funds and insurers
- Use ALM to investigate longer-term issues – project the assets and liabilities (and of related characteristics such as solvency levels) over periods of several years to review investment policy
- Pension funds becoming focussed on hedging liabilities. This is called Liability Driven Investing (LDI) = underlying benchmark is more linked to actual liabilities
ALM for institutional investors
- ALM used when setting investment strategy
ALM results in an investment strategy using one of the two techniques (historically):
- Benchmark consisting of specific fixed percentages allocated to each asset class which the investment manager is expected to follow (within suitable ranges)
- Extraction of ‘core’ portfolio, typically of bonds, with the remaining assets invested in a ‘balanced’ fashion
Dynamic liability benchmark
The benchmark for investing the assets changes as the underlying liabilities change. It is a better reflection of the underlying liabilities than the static benchmark
Stages in the ALM exercise
- Clarify key objectives of the investment and funding policy.
- Agree suitable assumptions to use in study
- Collect data to be used to carry out the projections
- Consider overall nature of liabilities
- Analyse how scheme might progress in future if different investment strategies were adopted
- Analyse different asset mixes in more detail
- Summarise and present the results
What objectives could be involved in the ALM
Involve objectives like:
- Future ongoing funding levels
- Future solvency levels
- Future company contribution rates
- Level of risk (performance mismatch between assets and liabilities) prepared to be taken
In what dimensions does ALM provide more information on?
- Projections into the future (time dimension)
- Estimate of range of likely outcomes (probabilistic dimension)
- Effect of changing investment strategy (asset mix dimension)
Why is Monte Carlo simulation usually used in practice?
- the vast majority of important practical problems are not amenable to analytical solutions
- it’s relatively easy to master the basic steps of Monte Carlo simulation techniques, certainly compared to setting up and solving analytical models
Presentation of ALM results
- Graphic format & looks at distribution of target objective (level of solvency of funding) resulting from investment strategy over projection period
- Investor not decided to fully hedge assets and liabilities – results show range of results based on projected asset and liability performance based on different economic scenarios
- Alternative way of presenting: select single projection date and plot Favourable, Median and Unfavourable results using the asset mix as the variable on horizontal axis
- Results resemble an expanding funnel of doubt – uncertainty associated with output increases further into the future
= ALMs are essentially a qualitative method for explaining risks
Choosing between different investment strategies
- ALM can provide an assessment of the likelihood of a shortfall
- Assess ‘ruin probabilities’ of insolvency for a fund
- These probabilities cannot be translated directly into assessments of the value of different strategies except by using the concept of risk neutral probabilities or by adopting a deflator (stochastic discounting) methodologies
Asset liability mismatching reserve
Emerging asset and liability position is projected under range of possible conditions to establish extent to which assets and liabilities are mismatched. Supplementary reserves then set up to cover possible level of shortfall identified
Absolute matching
Involves structuring the flow of income and maturity proceeds from the assets so that they will coincide precisely with the outgo in respect of the liabilities under all circumstances
Deterministic modelling
- Up to modeller to decide nature and extent of scenarios to be tested for purpose of setting the reserve
- Resilience testing: Investigation restricted to current portfolio of assets & liabilities & impact of immediate change in condition is considered, rather than involve projections of the emerging state of the fund
- More dynamic approaches are typically adopted now with modern computer modelling power readily available
Stochastic modelling
- Include the use of stochastic techniques, where multiple projections are made to generate many possible future scenarios
- Stochastic element of the projections would apply to the asset portfolio and investment returns to assess exposure to systematic risk
- Given a finite number of projections must be performed, assessment of results often carried out in the form of ruin probability
- Additional reserves set up to cover all but specified proportion of such shortfalls.
