- Forms of Risk
- Interest rate duration risk - C-3
- insurance co can be selected against when int rates move
- if rates increase - disintermediation risk
- if rated decline - reinvestment risk
- Valn Actuary's concern - how to make good and sufficient opinion w/r to reserves when faced w/ C-3 risk

- Credit (or default) Risk - C-1
- real default in asset value or a mkt value change in the common stock

- Pricing Risk - C-2
- ins co can suffer loss due to unforseen changes in experience levels w/r to mortality, morbidity, expenses, etc

- Interest rate duration risk - C-3
- Valuation Actuary's Job
- have skills and tools necessary to measure C1, C2 adn C3 risk
- understand and obey SOP established by profession adn regulations regarding messurement of risk
- recognize that need to rely on key indiv in co (COO, CEO, CIO (inv)) for continuation of stated policy and good business judgement in managing co's affairs
- let them take responsibility for what is theirs

- render an opinion as to adequacy of reserves, taking into account nature of assets supporting the reserves
- NOT the Valn Actuary's job to guarantee solvency

- Statement of Opinion
- two levels to the various opinions
- reasonable reserves
- reasonable reserve + designated surplus to cover plausible deviations

- current opinion
- reasonable - probability of reserves being inadequate < x% where x% > 1
- plausible - probability of reserves & designated surplus being inadequate < 1%
- actually probability of ruin

- two levels to the various opinions
- Elements of Cash Flow
- insurance (liability) adn asset cash flows projected into future under various int rate scenarios
- some assumptions used in projection are dynamic (vary w/ int)
- main elements of cash flow
- liab side
- income components - premiums, policy loan repayments, policy loan interest
- outflow - benfit payments, surr, divs, comm, expenses, taxes, policy loans
- policy loans on liab side (asset on B/S) b/c investment people can't invest in policy loans

- asset side
- income - bond maturities, mort prin & int pmts, coupons, calls, prepayments, stock divs, real estate, rental income, liquidations adn borrowed money
- outflow - repayment of borrowed money and capital losses

- liab side

- actuary must select: scenario set, lapse function, prepayment functions adn reinv function
- information on assets more extensive than traditional valuation methods
- Scenarios
- definitions
- int rate scenario defined as sequence of yield curves
- yield curves - function showing relationship of yield to duratino
- scenario - sequence of yield curves - one for each period-end in teh future

- cash flow analysis requires choosing a scenario set
- can arbitrarily select a set of scenarios that seem to cover possibilities (NY7)
- drawbacks
- # possible scenarios unlimited therefore no singel scenario likely to occur in real life
- no unique way to make probability statement about outcome of testing

- advised (in absense of regulation) to use approach that attempts to capture statistical meaning
- common methods: transitional probability and successive ratios

- definitions
- Transitional Probability Approach
- begin by defining universe of std yield curves
- one approach, 10yr and 1yr rates w/ intermediate rates set by fitting exponential curve

- define matrix of transitional probabilities
- P(ij) -> prob c(j) follows c(i)
- often set in consultation w/ investment officers
- most of the time, probabilites equal and opposite moves set equal

- set c(0) to std yield curve most like current rates
- monte carlo simulation used to pick future yield curves
- repeat using same c(0) and transition matrix until adequate # scenarios choses

- begin by defining universe of std yield curves
- Successive Ratios Model
- stochastic model of ratios of successive interest rates
- y(1)...y(n)... sequence of historical int rates
- ratio of y(n+1)/y(n) calculated for last 10 years for 1 long and 1 short dur
- dist function determined which models frequency values appear
- correlations between long and short rates studied historically
- bivariate dist w/ proper correlation coefficient constructed

- simulation performed on bivariate dist to get N pairs of rates for each scenario

- Morgan Stanley research shows promise using ln(y(n+1)/y(n))
- distribution not precisely normal
- close enough to justify simplifying assumption

- significance of number 40 - can get 40-50 scenario results on a single sheet of paper
- when testing stochastically generated scenarios, quite a few boring ones and on a few exciting ones
- most extreme scenarios don't necessarily give most extreme results
- function relationships - formerly known as setting assumptions
- ways to choose assumptions
- dart board
- xerox - using someone else's assumptions
- rules of thumb - similar to Delphi technique

- key element sto consider when choosing functional relationships
- relationships
- consistency
- validation
- should validate reasonably to whatever experience is available
- should validate reasonable results (sniff test)

- Market Rate Assumption
- possibly most important functional relationship - between credited rates, mkt rates, and lapse rates
- mkt rate - rate PO can get by lapsing policy and buying comparable new policy
- generally rate competing co offering on similar products

- when defining mkt rate, keep in mind what mkt rate used for
- if intest to set credited rate = mkt rate, mkt rate definition for model should match definition for way intend to credit
- sometimes results very sensitive to mkt rate definition and sometimes not
- relationship between earned rate adn mkt rate may not be rational, but there is a relationship
- when choosing mkt rate assumption, dont give too much weight to current situation
- mkt does not always react as quickly as scenario rates doo
- assumption should make sence for the long term
- s/b consisten w/ historical past
- apply common sense when looking forward

- mkt rate assumption typically based on current int and sometimes a rolling avg int rate (for cos crediting based on portfolio rate)
- common assumption - mkt rate = max(current, rolling avg)

- Credited Rate Strategy
- not an assumption, but a strategy
- decide whether crediting strategy matches what in in CF projection
- strategies key off of one or more of 3 rates
- fixed rate - initial guar rate, bailout rate, min guar rate
- earned rate less spread
- mkt rate

- SC may complicate matters - somewhat safer to have lower credited rate if SC is present
- consider increasing spread for higher int rates
- applying relationship to mkt rate as well could produce some reasonable answers

- for UL, trend is credit current money rate for 3-5 years
- then roll into new money rate at end of period

- special considerations for div scales on par policies
- such as pegged divs

- Lapse Rate Function
- largely based on intuition and judgement
- littel experience available for many types of plans

- considerations
- if product has SC, less sensitive to difference between credited and mkt
- PO/Agent characteristics important (stockbroker sold -> higher lapses)
- bailout
- "hidden" interest (not obvious to PO like Par WL pols)
- aging of business - possibility that excess lapses decrease over time
- core group of PO not sensitive to int rates

- sample SPDA laspe formulas
- 1982-C3 study - min(5%+ (M-C)^1.5,75%)
- VA Handbook ex - 15% + 2*(M-C)^2 - 3*SC
- Case Study - min(5%+2(M-C)^2, 50%)

- excess lapses increase dramatically as spread widens
- exponential term seems to be fairly well accepted

- largely based on intuition and judgement
- Policy Loan Utilization
- policy loan environment changed a lot
- direct recognition and tax law changes

- less likely to take loan and more likely to lapse
- sample utilization rate (mkt rate - loan rate)^1.8
- function of % of unloaded values and % total avail CV

- SP policies w/ 0 net cost loans - loan assumption could be key assumption to CF analysis

- policy loan environment changed a lot
- Premium Suspension
- very littel experience available
- new money product premium suspensions should nto be greatly interest sensitive
- lapses could be problem if PO looks at overall credited rate

- premium suspenstion can be very sensitive to credited rate of interest

- Expense Inflation
- generally a valuation concern only for effect on maint expenses
- common assumption - inflation = gov't bond int rate - spread
- overhead might not get appropriate weight in high lapse scenarios

- Mortality
- generally accepted - if extra lapses, future mortality will increase
- impaired lives more likely to keep life ins policy since unable to get equiv policy elsewhere
- several models available for calculating excess mortality due to excess lapse

- after assumptoins created, run through scenarios
- look at results and see if reasonable

- Role of the actuary and the Investment Officer: A discussion
- no agreement on what exactly the Actuary's role s/b w/r to setting inv assumptions
- Larger role in determing investment philosophy
- actuary determining for LOB responsible for
- type of assets, type of maturities, type of risks willing to take
- quality of assets and probability of net realizing expected returns

- strong communications w/ investment dept a must
- actuary shoudl decide if CF volatility for a type of asset is acceptable

- actuary determining for LOB responsible for
- Reliance Role
- one of jobs as Valn Actuary is to rely on other key people
- rely - work with them, not tell them what to do
- collaborative effort
- let the investment people select teh assets they deem appropriate given some guidelines w/ explanations of ramifications of choosing certain types of assets, maturity, structures
- investment people understand modeling, but modeling not "real world"
- inv people look at what's happening in mktplace daily and try to take advantage of mkt conditions

- What is an Investment Philosophy?
- used day-to-day basis by inv dept
- need assumptions re: investment philosophy in the future
- may not match what inv people doing today

- future inv philosophy is an actuarial assumption - actuary responsible for it
- ought to know current inv philosophy
- think about possibility that other philosophies will be used in the future

- inv philosophy may be different depending on purpose of projection
- stat solvency - only need a 1 year projection

- Valn Actuary's role is to evaluate effects of an investment philosophy
- Sr Mgmt's role is to choose the inv philosophy

- if not sure what your co is going to do in the future
- run projections w/ different inv philosophies

- one method - bring in Inv officer, show him the int scenarios and ask "How would you invest?"
- inv officer will buy into projection and feel comfortable with results

- Reinvestment Function
- Positive Cash Flows
- 3 methods
- continuatino of current strategy
- follow stated policy (set of rules)
- keep dur matched and x% to type A assets etc

- mkt timing - important to get investment person involved
- if mkt does A, invest in B
- inv officer will "do whatever is best"

- 3 methods
- Negative Cash Flows
- borrow funds - reflect cost of borrowing in projections
- liquidate assets - pro-rata across all assets or involve specific assets

- Positive Cash Flows
- Activeness of Asset Portfolio
- how will assets be managed
- buy and hold
- trading or purposeful disinvestment

- how will assets be managed
- Valn Actuary needs ot deal w/ pos cash flows, neg cash flows and asset mgmt when doing cash flow analysis

- which assets backing products valuing?
- s/b consistent w/ investment philosophy statement filed w/ state

- if assets not segmented, either set up segmented pool or use pro-rata share of all assets
- obtain listing of current assets from inv dept (hopefully inv database)
- Treasuries
- 100% guar by govt adn non-callable
- perfect asset except don't earn enough interest to support credited rates
- amortization of prem or discount as CF item
- Donna Claire would not use since not real cash
- better to recognize prem/discount @ sale/maturity

- Corp Bonds
- used to be most popular asset for ins co investments
- major problem - generally callable
- range where very few bonds called - generally 1% of original int environment
- fairly simple approx - 2% greater than current coupon rate - it gets called
- another approx: .25*(coupon rate - current coupon rate - .25*call prem) min 0, max 1.0
- also check other provisions, such as sinking fund provisions

- Commercial Mortgages
- characteristics similar to bonds - take coupons and pay back principal at end
- some have sinking fund payments
- prepayment provision - some have very generous provisions
- current prepayment penalties - such that if investor took payment and invested it in T-bills for remaining period, still wind up w/ same amt int
- could be modeled as non-callable bonds since little reinvestment risk
- have a default risk
- depending on rating, C-1 default risk charge s/b subtracted (similar to corps)

- Agricultural Mortgages
- generally short mortgages
- can be variable int - appear to be well suited for I/S products
- problem: many are defaulting - approx 25% industry wide
- C-1 charge s/b enough to cover this type of default (worse than junk)
- charge must be large enough to cover
- int forfeited
- opportunity loss when owning property
- principal loss on sale of asset

- can be as high as 75bps

- Gov't Backed Mortgages
- GNMA, FNMA, FHLMC - some of most popular inv for ins cos
- give fairly high int rate
- major problem is duration risk
- very important to model correctly in terms of effect of int scenarios on GNMAs
- sample prepayment equation: 5% + 3*S + 2*S^2 where S and 5 <= P <= 60
- # factors affecting prepayments
- moving, years left on mort, general economy in area, employment stats

- Junk Bonds
- begun to play important role in portfolio
- subtract approx 2.5% of principal to cover default in models
- check diversification - very important in junk

- Real Estate
- becoming more popular in I/S portfolios b/c asset is inflation adaptive
- problems modeling real estate
- need to check w/ inv dept as to expected cash flows, not just expected avg returns over expected holding period
- when do you assume you sell property
- what will price be when real estate is sold
- good approx is that it appreciates at economic int rate + x% (typically around 3%)

- Case Study Life
- additional reserve req'd to make probably of inadequacies < 1%
- take PV of cashflows from each trian using that trials int rates
- assuming results normally distributed, use std dev and mean to determine point probability that PV < 0 is <= 1%

- generation of scenarios - monte carlo & lognormal method
- monte carlo - randomly generated using starting yield curve, yield curve universe and probability of movement matrix
- lognormal - randomly generated using starting yield curve, volatility factor and lognormal dist function
- differences between two not enough to say which is better

- reserves should cover reasonable deviations
- reserves and surplus should cover reasonable and plausible deviations

- additional reserve req'd to make probably of inadequacies < 1%

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