1. We start with C (initial capital) and we want to retire. We want to calculate "w" or how much we can withdraw a month and have a safe future.
2. We are going to hedge the longevity risk by creating a perpetuum mobile, meaning, we are going to keep the principal intact taking inflation into account.
3. Our portfolio will consist of 5% cash, and the rest: 8/13 dividend shares and 5/13 gold.
4. w is going to come exclusively from the dividends. Why? Because we are going to suppose that the inflation will be hedged by the increase in the value of shares and gold.
Solution:
PORTFOLIO=5/100[CASH]+95/100x(8/13[SHARES]+5/13[GOLD])
w=1/12xDIVIDENDx95/100x(8/13xC)x0.7, being DIVIDEND the dividend yield. 0.7 comes from taking 30% taxes into account. The final equation can be rewritten as follows:
w=34103xDIVIDENDxM, being M the number of initial millions.
Practical point of view:
If we happen to have 2.2 million dollars for retirement and we buy shares of solid companies with an average dividend of 3.5%, we can spend 2625 USD a month and feel safe.
From another angle, we think we can live with 4000 USD a month and will receive a pension of 2500 USD a month, how much do we need to retire? w=4000-2500=1500 M=w/(34103x0.035)=1.26 millions.
Some of you might think:
1. Why gold? To hedge the risk of the stock market.
2. Isn't it too much money for such a tiny yield? Inflation is a very powerful enemy, and to overcome it we cannot overspend.
