# CS – 15 Risk Premium for Insurance Product Pricing Steve Mildenhall, AON Re Dave Ingram, Milliman USA Don Mango, AM Re.

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CS – 15 Risk Premium for Insurance Product Pricing Steve Mildenhall, AON Re Dave Ingram, Milliman USA Don Mango, AM Re

Risk Premium for Insurance Product Pricing Stephen Mildenhall CAS/SOA ERM Symposium Washington DC, July 2003

Why a Risk Premium? Need to make a profit Need to be reasonably confident of making a profit Risk Premium is an all encompassing term –Covers frictional costs –Covers pure risk (toss of fair coin) –Compensation for bearing risk under uncertainty Philosophical distractions should be resisted

Risk Premium: 2000BC-today Financial Consequences of policy Probabilities State of the world Policy Payout L  All of the above

Risk Premium Standard deviation Variance Semi-Variance Percentile/VaR Tail-VaR Wang Transform Esscher Transform Utility-based Micro-view of single risk SD, Variance,… of what? Which measure is appropriate?

Measures of Risk Problem: collapse distribution to a number –All moments may not be enough to determine distribution! No consensus methodology Rothschild-Stiglitz offer four possible definitions of when X is “more risky” than Y 1. X = Y + noise 2. Every risk averter prefers Y to X (utility) 3. X has more weight in the tails 4. Var(X) > Var(Y) 1, 2, and 3 are equivalent and are different from 4

Parameter Risk: don’t delude yourself Variance of losses in your model is not the same thing as variance of losses! –Hayne’s Loss Reserving Example (CLRS) Leverage, Excess Policies and Jensen’s inequality –Need to compute the mean correctly –Risk load should not be used to compensate for miscellaneous actuarial inadequacies Don’t believe a risk load formula that says a new small line is a good thing!

Size: what is a large risk? Parameter risk is all that matters…almost Process risk matters for large risks Large? –100M households in US –\$1M loss = 1¢ per household –\$100M loss = \$1 per household –\$1B loss = \$10 per household –\$10B loss = \$100 per household Large

Size: what is a large risk? Heterogeneous distribution of wealth Demographics –Ultimate risk bearers are individual insureds –Population concentrations correlated to risk loads Frequency of losses, size of market Don’t believe a risk load formula that does not account for population demographics

Big Picture: moving beyond individual policy risk All states of the world Policy Payout L States of the world relevant for one policy  Projection with loss of information Multiple states yielding same loss L for one policy

Big Picture: moving beyond individual policy risk

Rodney Kreps, co-measures P/C: Catastrophe (re-)insurance –Cat models explicitly quantify correlation Life: Hedging interest rate and investment risk

Three Points to Remember Parameter Risk Size Think Big-Picture

Pricing for Risk David Ingram ERM Symposium Washington DC, July 2003

Pricing for Risk 1.RMTF Survey of current Practices 2.Methods for Setting Risk Margins a.Charge for Risk Capital b.Risk Adjusted Hurdle Rates c.Adjusted Target Calculation d.Replication

How Do you Price for Risk?

What is the basis for Risk Adjustment?

Methods for Setting Risk Charge Judgment Methods Quantitative Methods

Judgment Methods Risk Premium based on –Prior products –Market prices –Comfort with particular risks –Relative perceived risk of company products

Quantitative Methods 1.Charge for Risk Capital 2.Risk Adjusted Hurdle Rates 3.Adjusted Target Calculation 4.Replication

Charge for Risk Capital Most common quantitative risk adjustment to pricing Charge is: –(HR – i s ) * RC t Where HR is Hurdle Rate i s is the after tax earnings rate on surplus assets RC t is the risk capital in year t

Charge for Risk Capital Is it actually a charge for risk? –Or just a cost of doing business? It is a charge that is proportionate to risk If there are other risk charges or adjustments, need to be careful not to double charge for risk

Risk Adjusted Hurdle Rates Efficient Frontier Analysis Market Analysis

Efficient Frontier Analysis Process A.Brainstorming B.Modeling C.Display / Identify Frontier D.Determine Risk/Reward Trade-off Parameters

Efficient Frontier

Market Analysis Study Relationship between Return and –Product Concentration –Income/ ROE volatility For a group of successful companies. Develop Target returns –Based on Products –Based on volatility

Market Analysis Product Concentration Product A – 12% Product B – 15% Product C – 10% ROE Volatility Target ROE = Risk-free rate + 3.7  22.83% +1.83% ln(  ) 7.5% + 

Market Analysis While this is “quantitative”… Data is so thin that much judgment is needed to develop targets

Study of Insurance Company ROE ROE Std DevRatio Group I13.96% 6.71% 48% Group II10.52%11.32%107% Group III10.12%16.02%158% Group IV 4.86%25.96%534% Group V(3.69%)21.13% NM

Adjusted Target Instead of concentrating on 50 th Percentile results (or average results) –In a stochastic pricing model Pricing Target adjusted to 60 th, 70 th or 80 th Percentile

Replication Finance – Law of One Price –Two sets of securities that have the same cashflows under all situations will have the same price Replication – if you can replicate the cashflows of an insurance product with marketable securities then market price of securities is the correct price for product

Risk & Return Bonds – Volatility of Bond Prices 8.6% –Average Return on Bonds – 5.8% compound Average, 6.1% Arithmetic Average –Risk/Reward = 139% to 148% Stocks – Volatility of Stock Returns 20.5% –Average Return – 10.5%, 12.2% –Risk Reward = 168% to 194%

Insurance Products Cannot easily hedge with 100% efficiency But can compare…

VA Product vs. Common Stocks Insurance Product – VA –\$10 B AV –Std Dev = 200, CTE 90=429 Compare to Common Stock Fund A –\$300 M Fund –Std Dev= 200, CTE 90= 390 Common Stock Fund B –\$330 M Fund –Std Dev= 220, CTE 90= 429

Returns Insurance Product – VA –75 Expected Return Common Stock Fund A –100 Expected Return Common Stock Fund B –110 Expected Return

Recommendations 1.Work on evolving from Judgment to Quantitative 2.Quantitative methods need to be based on Pricing Risk Metric 3.Ultimately should tie to market pricing for risks

Risk Premiums Don Mango AM Re

Where Are We Going? Commonalities Simulation Modeling Explicit Valuation Aggregate Risk Modeling Interaction Effects

Commonalities Valuation of Contingent Obligations (“VALCON”) Levered investment trusts Strong dependencies on economic and capital market conditions

Commonalities Long time horizons and held-to-maturity (“HTM”) portfolios We sell “long-dated, illiquid, OTC derivatives” We have an incomplete, inefficient secondary market We retain magnitudes of risk that bankers would never dream of

Commonalities IMPLICATIONS: This seminar should be the norm, not the exception. There may be hybrid products in our future. We may not be able to simply borrow capital market techniques.

Simulation Modeling Aka “Monte Carlo valuation” Financial engineers use it to price long- dated, illiquid, OTC derivatives Devil is in the parameters and dependence structure

Simulation Modeling IMPLICATIONS: We are heading the same direction. We need transparency or at least explicitness of assumptions.

Explicit Valuation Complete, efficient market affords participants the luxury of not having to think or care or have any opinion of the fundamental value of a product Counting on the continued presence of counterparties to limit downside Bloomberg gives you “the price”

Explicit Valuation Incomplete, inefficient market requires some explicit valuation by its participants True, you could be a “delta” off a content provider –10% below Swiss Re or Met Life

Explicit Valuation IMPLICATION: If you want to be a leader, formulate a risk appetite and apply it. –Read Karl Borch, 1961 What are your desired payoff profiles, and please be specific and use quantities!

Aggregate Risk Modeling Valuation  develop indicated price based on the impact of the product on your portfolio – a “MARKET OF ONE” “One Price” does not mean One Value Value is idiosyncratic and in the eye, mind, interpretive filter, and model of the beholder

Aggregate Risk Modeling Requires aggregate portfolio risk modeling Integration of disparate risks A critical goal of our ERM efforts Sounds like it might require actuaries of all kinds …

Aggregate Risk Modeling IMPLICATIONS: Get information content into the indicated prices and (hopefully) the quotes. Risk Management is that Content Provider.

Interaction Effects Indicated price meets market strategy, premium goals, expense ratios, relationships, history, culture, decision process, … Multiple participants selling promises with indistinguishably small probabilities of non- performance

Interaction Effects Throw in some “momentum sellers” going delta off the content providers Result is an unstable system dynamic = “the insurance market” Mutually reinforcing behaviors, for good or bad

Interaction Effects IMPLICATIONS: Theory aside, the attainable risk premium will rarely be where it “should be.” Market Price represents somebody’s quote (usually the LCD – winner’s curse) – no “exogenous” source No more isolated strategy development – we have seen the enemy, and it is us.

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