Demographics (source: gapminder.org) Births per Woman, 1800-2010 7 - PowerPoint PPT Presentation

Demographics (source: gapminder.org)

Births per Woman, 1800-2010 7 1

Life Expectancy, 1800-2018 80 30

2020 Source: Gapminder.org

Mortality

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A 2009 Actuarial Table with Progression

A Scenario Matrix

Projections

Inflation

Percentage Changes in the Consumer Price Index Source: Federal Reserve Bank of St. Louis Economic FRED Database

U.S. Treasury Inflation-Protected Securities (TIPS)

20-Year TIPS Real Yields Source: Federal Reserve Bank of St. Louis FRED database

A World Bond Stock Fund

VT Vanguard Total World Stock ETF

BNDW Vanguard Total World Bond ETF

Proportions in Bonds and Stocks ( Ftse Asset Allocation Policy Calculator) May 2019 Equity: 48.2% Bonds: 51.8% equity bonds

Market Returns

The Market Return Distribution Market Value-relatives, year and month VR y = VR m1 * Vr m2 *...* VR m12 Thus: log(VR y ) = log(VR m1 )+ … + log(VR m12 ) If monthly value-relatives are independently distributed: then log(VR y ) will be approximately normally distributed i.e. VRy will be approximately lognormally distributed

The Pricing Kernel

Price per chance: PPC st = f ( cumRm st ) Present value: PV st = PPC st ∗π st Probability: Probability: every π st = 1 / number of scenarios Constant Elasticity: log ( PPC st )= a − b log ( cumRm st )

Constant Elasticity and CAPM Pricing Kernels

Constant Elasticity and CAPM Pricing Kernels on loglog scales

Constant Elasticity Pricing Kernel ● Pricing for any given year is a function of the cumulative market return up to that year ● ● This can only be true for one year for the CAPM ● ● This kernel can provide a present value for any set of cash flows for various times and scenarios from any income source or sources

Present Values of Possible Incomes from Social Security

Market Parameters

The RISMAT program Market Data Structure function market = market_create() % create a market data structure with default values % cost of living % expected cost of living ratio market.eC = 1.02; % standard deviation of cost of living ratios market.sdC = 0.01; % risk-free real investments % risk-free real return rate market.rf = 1.01; % market portfolio returns % market portfolio expected return over risk-free rate market.exRm = 1.0425; % market portfolio standard deviation of return market.sdRm = 0.125; end

Implied Marginal Utility And Cost Efficiency

Glide Path with Proportional Spending

Reducing Cost Price Price A A' P1 Cost savings P2 B' B Y1 Y2 Income To minimize cost, income should be a non-increasing function of PPC

Glide Path with Proportional Spending

Lockbox Strategies

A Lockbox for Year 2029

A Lockbox Strategy 0 2 0 2 1 2 0 2 2022 2022 2023

Lockbox Annuities