Uncertainty and Retirement Planning Lecture for

Transcript:Uncertainty and Retirement Planning Lecture for:
Uncertainty and Retirement Planning Lecture for FIN 352 Professor Dow CSUN 2016 The situation (from the last presentation) Save and invest money until retirement (the accumulation phase) Once retired, withdraw money from investment accounts (the spending phase) We solved the problem in reverse order Spending phase: How much do you need each year in retirement? This determines desired (target) wealth at retirement Accumulation phase Goal is to end with the targeted level of wealth How much do you need to save to reach the target? Timeline of Wealth Now End of Life Date of Retirement Add money each year Withdraw money each year Wealth The accumulation phase Two decisions How much to save each month The asset allocation This affects the portfolio return (and risk) On a financial calculator N: number of years to retirement PV: starting wealth PMT: How much you save each year I: The return to your portfolio FV: Your target wealth Generating an wealth path Wealth grows over time because: Additional savings Under your control given your income Reinvested income generated by your assets Cannot control returns in the markets, but… Average returns and risk depends on asset allocation of your portfolio Equation: Wt+1 = (1+Rt)Wt + St W: Wealth S: Savings R: Portfolio Return Wealth path if no uncertainty Retirement Date Wealth Start Date Target Wealth Uncertainty of portfolio return Treat R as a random variable If asset allocation is between stocks and bonds, Portfolio return in a given year is an average of the return on stocks and the return on bonds Rp = xRs + (1-x)Rb (where x is the share of stock in the stock in the portfolio) Assuming a normal distribution for stock and bond returns E(Rp) = xE(Rs) + (1-x)E(Rb) σp= sqrt( x2σs2 +(1-x)2σb2 +2x(1-x)σsσbρsb ) Portfolio returns ~N(E(Rp), σp) Generating a sample wealth path Each year draw random variable from N(E(Rp), σp) Update wealth using Wt+1 = (1+Rt)Wt + St Continue until you hit the retirement date This is one possible path that your investment future could take. This is called a simulation Generating a wealth path Retirement Date Wealth Start Date Target Wealth Generating a distribution No guarantee of any particular outcome Many possible paths Monte Carlo analysis Randomly generate 1,000’s of possible paths Summarize results by distribution of ending wealth Generating a distribution Retirement Date Wealth Start Date Target Wealth Probability distribution of wealth at retirement Total