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Births per Woman, 1800-2010
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Demographics (source: gapminder.org) Births per Woman, 1800-2010 7 - - PowerPoint PPT Presentation
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 A 2009 Actuarial Table with Progression A Scenario Matrix Projections Inflation Percentage
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Life Expectancy, 1800-2018
30 80
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Source: Gapminder.org
2020
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Mortality
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A 2009 Actuarial Table with Progression
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A Scenario Matrix
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Projections
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Inflation
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Percentage Changes in the Consumer Price Index
Source: Federal Reserve Bank of St. Louis Economic FRED Database
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U.S. Treasury Inflation-Protected Securities (TIPS)
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20-Year TIPS Real Yields
Source: Federal Reserve Bank of St. Louis FRED database
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A World Bond Stock Fund
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VT Vanguard Total World Stock ETF
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BNDW Vanguard Total World Bond ETF
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Proportions in Bonds and Stocks ( Ftse Asset Allocation Policy Calculator)
May 2019 Equity: 48.2% Bonds: 51.8% equity bonds
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Market Returns
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The Market Return Distribution
Market Value-relatives, year and month
VRy = VRm1 * Vrm2 *...* VRm12
Thus:
log(VRy) = log(VRm1)+ … + log(VRm12)
If monthly value-relatives are independently distributed: then log(VRy) will be approximately normally distributed i.e. VRy will be approximately lognormally distributed
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The Pricing Kernel
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PPC st= f (cumRmst) PV st=PPC st∗πst every πst=1/number of scenarios
Price per chance: Present value: Probability: Probability: Constant Elasticity:
log(PPC st)=a−blog(cumRmst)
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Constant Elasticity and CAPM Pricing Kernels
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Constant Elasticity and CAPM Pricing Kernels on loglog scales
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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
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Present Values of Possible Incomes from Social Security
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Market Parameters
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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
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Implied Marginal Utility And Cost Efficiency
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Glide Path with Proportional Spending
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Price Price Income P1 P2 Y1 Y2 A A' B B'
Reducing Cost
Cost savings
To minimize cost, income should be a non-increasing function of PPC
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Glide Path with Proportional Spending
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Lockbox Strategies
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A Lockbox for Year 2029
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2 2 2 2 1 2022 2022 2023
A Lockbox Strategy
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