Saturday, February 9, 2008

Finding Out How Much is Enough

In our last post we described projecting a set of 100 possible time paths for Total Assets after retirement. Each time path is associated with a different set of possible future rates and prices drawn from historical prices and rates. We are going to evaluate alternative retirement plans by comparing the possible time paths they imply. The time paths are going to look sort of like the final chart on the last post. Lots of lines.

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. 

    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. 

6 comments:

Charlotte said...

That looks very encouraging. I always thought 1 million was about the least you should plan to have to retire (maybe by the time we retire, that will be the case). My only concern is, I still have a bit of anxiety when we start to talk about budgeting/spending less, etc. Do you think you will have to spend a lot of time thinking of that? I don't want to spend a lot of my retirement time stressed.

L Huntz said...

I think that budgeting and spending less is always a bit stressful. Our spending "plans" are based on what we have been spending living here -- so they shouldn't be too hard to implement. If you think about what I have figured out, there is a big assumption -- that things will go along pretty much like they have; both for society (and the economy) and for Judy and I personally. Health problems for either of us could totally undo everything -- and if the economy falls apart in a big way that would also totally undo everything -- but that's why we have food storage.

Finally, it comes down to -- plan the best you can and then just take what comes.

Thanks for reading and commenting. I appreciate your feedback.

Take it easy and try your best to have Tucker be healthy.

Love,
LaVar

Tyler H said...

can you explain the spending adjustments again maybe with the actual numbers you are using for examples?
I am having a really hard time figuring that part out, but it looks like with small adjustments you are getting majorly different results. That is good. Also, if you are able to have the outcomes so different from such minor changes finding a pastime that produces even a small income could change the outcomes fairly significantly?

L Huntz said...

Yes, Tyler you are right finding activities that produce income would have the same effect as reducing spending. Now for an example. If spending wasn't being adjusted it would be $45,000 (adjusted for inflation every year. For the 5th worst case with our adjustment rules, spending is $45,000 the first year then at the first of the following year we check our total assets(adjusted for inflation) and find the total is $565,717 which is less than what we started with ($600,000) so we lower our spending for the following year to .95 x $45,000 which is $42,750. That means we eat out less, make fewer trips to Utah, etc. The next year we find total assets are still low so we lower our spending again to .95 x $42,750 = $40,612. Then again the next year to $38581.87 and so on to the minimum we set which was .75 x $45,000=$33,750. And for this case it stays there at that minimum value for the rest of our retirement. Remember that is the 5th worst case. For the 5th best sometimes the spending gets reduced and sometimes increased. In that case it ends at about $60,000 (adjusted for inflation) per year.
The example shows that the changes are perhaps bigger than you thought. But our lower limit of .75 is based on looking at our spending and determining that we could get by on that. However, we would rather spend more if we can.
The objective of our "analysis" was to find "How much is enough" (the least that would work). It is always the case that more would be better -- but it turns out that it takes A LOT more to make a big difference. Or we can just assume that we will be really lucky and have outcomes like the best few. Actually, I don't think that is likely. More likely that we will need our food storage!

Tyler H said...

I would be interested in seeing a scenario where you are able to make a small additional income without changing spending like maybe 10,15,and/or 20 thousand. If that isn't hard

tim said...

I've always heard, like Charlotte, that we'd need about $1 million before we could plan to retire. I guess by the time that roles around for us that is expected to be true? That has always had me a little nervous. I guess I just figured we'd never get a chance.