20.2 Optimal Porfolio Under 4 Scenarios

From Venter et al. (“Implication of Reinsurance and Reserves on Risk on Investment Asset Allocation”)

1) Assets (No Liabilities) Porfolio

• Short term treasures: risk free and maintain value well

• Long bond and stocks are risky

• Use modern portfolio theory to find alternatives on the efficient frontier

2) Known Liabilities and Known Cash Flows (Fixed in Time and Amount)

• Investment duration:

  • Short duration \(\Rightarrow\) Reinvestment risk

  • Long duration \(\Rightarrow\) Interest rate risk

• Risk and conclusions are different if liabilities are discounted at current rates (Such as using Economic balance sheet)

3) Liabilities are Variable and Timing is Variable

• Precise matching is impossible

• Requires model that incorporate asset and liability fluctuations

• Inflation sensitive liabilities further complicates things

4) Going Concern Company, with Cash Flow from Current Operations

• Can have positive or negative cash flow

  • If asset prices are too low, can pay claims from premium cash flows and use depreciated assets to support loss reserves

• Need to model: premium, income, losses, cat losses, expenses

• Need enterprise wide model with holistic view to handle the complexity

20.2.1 Additional Consideration: Tax

Investment strategy change in responses to u/w cycle

• Profitable period:

  Tax exempt bonds are better

• Unprofitable period:

  Taxable bonds are better as the investment income is reduced by u/w losses

• Assets is also reallocated to maximize income while avoiding Alternative Minimum Tax

20.2.2 Additional Consideration: Equity

Generally considered risky and imply a potentially worst downside risk to capital

However, they can be useful hedge against inflation

Can be tested with an ERModel, but conclusions will be sensitive to input assumptions of the macroeconomic model

20.2.3 VFIC 2002

Published by CAS’ Valuation, Finance & Investment Committee (VFIC)

Testing the optimality of duration matching assets & liabilities

Simulation models were used against the following scenarios:

• Long tailed business vs short tailed business (w/ CAT)

• Profitable vs unprofitable (Generate cash and consumes cash)

• Growing vs shrinking companies

Results were reviewed on GAAP, Stat, Economic B/S basis and several risk measures were used form each accounting basis:

• Duration matching was one of the optimal strategies

• Investment choice depends on:

  • Risk metrics selected

  • Return metrics (Venter used US GAAP pretax \(\Delta\) in surplus)

  • Risk tolerance or preference

Results for Economic Balance Sheet:

• Assets are mark to market, liabilities are discounted at current rates

• Duration match results in low interest rate risk

• Longer duration is better if not matched:

  • Long duration investments: \(\uparrow\) interest rate risk \(\uparrow\) returns

  • Short duration investments: \(\uparrow\) reinvestment rate risk and \(\downarrow\) return

• Choosing longer duration vs matching is a value judgement (i.e. is the extra return worth the extra risk)

Other Remarks:

• Duration match is irrelevant for Stat and GAAP accounting as they are not responsive to interest rate movement

• Adding cash flows from continuing operations complicates this analysis