So we need a systematic way to compare the sets of lines. We do this by drawing particular attention to four of the lines on the chart by making them heavier and different colors – the 5th worst (colored red), the 25th worst (colored magenta), the 25th best (colored dark purple), and the 5th best (colored dark blue). We are interested in these cases as some sort of summary of the whole set of outcomes. Specifically, half of the outcomes are between the 25th worst and the 25th best (so there is 50/50 chance the outcome will be in that range), almost all, 95%, of the outcomes are better than the 5th worst (so unless we are really unlucky we can expect and outcome at least that good), and the 5th best is better than almost all of the outcomes (so we would have to be really lucky to do better than that).
Now suppose I retire just after I turn 62 (Judy will be 58). We can reasonably expect to have about $300,000 in total assets after paying off the houses, $26,000 annual income and expect to spend about $45,000 per year. We start by supposing the income will be fully adjusted for inflation each year, that we will keep 75% of our assets in stocks, and each year we put 20 months of the expected "draw" into a money market account. By "draw" I mean spending minus income which we will need to draw out of the money market account. We then spend out of the money market account for the following year. Each year we rebalance accounts – putting 75% of our assets into stocks and 20 months of draw into the money market account. The following chart shows the implied results.
These results don't look very good (there is too high a likelihood that we will run out of assets before we expect to die). In fact, for all of the cases except the best 7 or better, our total assets don't last 42 years after retirement (when I would be 104 and Judy 100). And for most of the cases the assets run out in just a few years.
So instead, suppose I wait until full retirement age, 66, (judy will be 62). Then we can reasonably expect to have about $600,000 in total assets after paying off the houses, $33,000 annual income and still would expect to spend about $45,000 per year. If we make the same assumptions about how the money will be managed the results are as shown in the following chart.
This is better, but still not good. For the worst 20 cases the assets are exhausted before 38 years after retirement( when I would turn 104 and Judy 100). I probably won't live that long -- but there is a good chance Judy will come close to 100 -- and for fully one fifth of the cases the assets don't last 38 years.
This is better, but still not good. For the worst 20 cases the assets are exhausted before 38 years after retirement( when I would turn 104 and Judy 100). I probably won't live that long -- but there is a good chance Judy will come close to 100 -- and for fully one fifth of the cases the assets don't last 38 years.
So we need more -- how much more? It turns out that we would need about one million in total assets before the results for all but the worst 4 cases have the assets lasting at least 38 years after retirement. That seemed pretty discouraging because I don't see any sure way of getting one million.
Then I had a thought. If we look at the charts carefully we see that each line has lots of ups and downs, which is realistic – it is the way real world results look; but it also means that for each case, when an interval with bad outcomes comes along as it almost always does, the total assets begin to get rapidly used up. Suppose we adjust our spending based on how well our investments fare. When we have bad outcomes we reduce our spending some. It turns out that doing that makes a lot of difference in how long the assets last.
So we plan to reduce our spending (adjusted for inflation) each year when we rebalance accounts, by multiplying by 95% if our total assets (adjusted for inflation) are below the value at retirement; and on the other hand we will increase our spending by multiplying by 103% each year if our total asset value is higher than 125% of the value at retirement. But we will only reduce spending to minimum of 75% of the basic planned amount and raise spending to a maximum of 150% of the basic planned amount.
Then if we retire after I turn 66 (Judy 62) with $600,000 the results are as shown on the following chart.
This is good!! The results for all of the cases are successful. Even for the worst case there is about $140,000 worth of assets remaining 38 years after retirement and for the 25th worst case (the magenta line) there is over $500,000 left 38 years after retirement and we have a 75/25 chance of doing better than that.
It looks like this is enough to retire. In fact, maybe we don't need quite that much. Maybe we could retire a few years earlier -- if things go well.