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William Sharpe interview - "lockbox strategy for retirement spending"
Old 05-12-2008, 12:45 PM   #1
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William Sharpe interview - "lockbox strategy for retirement spending"

Interesting interview with William Sharpe:

http://www.stanford.edu/~wfsharpe/retecon/rotman.pdf

He alludes to his work on alternatives to the "inefficient" 4% rule that can be found here: SSRN-Efficient Retirement Financial Strategies by William Sharpe, Jason Scott, John Watson

Tough read with alot of math and no practical implimentation described. He discusses several scenarios using a "lock box" approach whereby you a prior designate funds to be spent each year in the future. Each one makes assumptions about how you will be investing and how you will be spending.

DD
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Old 05-12-2008, 01:02 PM   #2
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Old 05-12-2008, 02:15 PM   #3
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This is very closely related to the "Smart Guys Question 4% ..." thread.

As a number of people mentioned there, this paper works real hard to get the "right" investment and spending strategy, given that you know exactly when you are going to die.

He says that you should spend everything you have available in every period because there is no utility in dying with assets. That's where the "lockbox" comes in - it gives you a firm spending rule. If you have some good investment years, you spend everything in the maturing lockboxes, never carrying any good results forward. Similarly with bad years, you never "borrow" from future spending.

But, as soon as you realize that your date of death is uncertain, you can't optimize with Sharpe's rules. You've got some chance of dying before you spend all your lockboxes, and some chance of living beyond the last one. (He mentions the problem early in the paper, but clearly hasn't thought about it seriously.)

My "feel" for this is that he made some simplifying assumptions to get to a problem that had an elegant solution. But, one of his simplifying assumptions was so extreme that the answer isn't very useful.

I've thought that you could so something like this with most of your assests if you had a life annuity with a deferred start date to cover the longevity risk. But that's a whole different thread.
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Old 05-12-2008, 02:29 PM   #4
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I've thought that you could so something like this with most of your assests if you had a life annuity with a deferred start date to cover the longevity risk. But that's a whole different thread.
... and a popular one ...

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Old 05-12-2008, 02:45 PM   #5
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Longevity is an easy issue... just have a robotic monkey with a gun in the last lockbox.
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Old 05-12-2008, 10:28 PM   #6
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Longevity is an easy issue... just have a robotic monkey with a gun in the last lockbox.
Unless, of course, you're already married...
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Old 05-13-2008, 10:06 AM   #7
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Unless, of course, you're already married...
If you are then you don't mind making sure the monkey has two bullets.
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Old 05-13-2008, 02:26 PM   #8
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The more I peruse that article, the more I wonder why Sharpe expended his effort.

He has a day job and his company's growing extremely fast. He presumably already has tenure (along with the Nobel) and isn't too worried about climbing the ranks, let alone "publish or perish". I don't see that he has any motivation for doing the research and the publicity.

The only "new ground" being broken here is the point that people might be taking on too much principal risk to compensate for longevity risk. Bernstein has already pointed out that most of this concern is so far down in the weeds compared to world events and macroeconomics that Sharpe seems to be tinkering with a butterfly's wing-flapping. So why this apparent fascination with making the money last not too short, not too long, but just right?

When he talks about "low-expense investing", I doubt he's about to annunce a reduction in FinancialEngines.com fees. Unless he's decided to boost the career of a research assistant, my only other conclusion is that he's trying to find the optimum pricing for annuities. Maybe he could hire Ben Stein as a spokesman. And, hey, AIG could be looking for a new business partner.

But Sharpe might just be feeling bored & unfulfilled.

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If you are then you don't mind making sure the monkey has two bullets.
Perhaps the whole clip, just to make absolutely positively sure...
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Old 05-13-2008, 02:30 PM   #9
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Perhaps the whole clip, just to make absolutely positively sure...

But would that be lbym? Seems like the whole clip might be over kill
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Old 05-13-2008, 08:34 PM   #10
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Old 05-14-2008, 07:44 AM   #11
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Unless, of course, you're already married...
Not sure what you're trying to say, but are you saying that there should be a monkey in the first box?
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Old 05-14-2008, 04:44 PM   #12
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Not sure what you're trying to say, but are you saying that there should be a monkey in the first box?
Nah, just fumbling for a punch line. I figured anything involving spouses, robotic monkeys, and ammunition would write its own joke-- and adding an annuity or two would just make it funnier!

Looks like I'm going to have to seek professional help from CFB...
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Old 05-15-2008, 10:30 PM   #13
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Old 05-22-2008, 06:19 AM   #14
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I've set up a spreadsheet to simulate returns for a simple lockbox strategy. I assume
  • I will be 100% invested at all times in my risky asset, in my case this has an estimated return of 5.5% with standard deviation 7.95%.
  • I will take an annual income I until age 75, i.e. the target final value of all lockboxes except the age 75 one is I.
  • At age 75 I will buy an inflation-linked annuity that pays an income of I. The cost of such an annuity would currently be I/7.080%. This is the target final value of the last lockbox.
  • I use a 4% discount rate to allocate all my capital to different years so as to produce the target total for each year. (If my risky asset does indeed return 5.5%, a 4% discount rate means I will have a rising income.)
  • I simulate the cumulative return to year N with the calculation [Cumulative Return]=[Previous years cumulative return]*(100%+5.5%+7.95%*(rand()+rand()+rand()... (12 rand()s in total) - 6))
  • I repeatedly press F9 in Excel to recalculate the spreadsheet to get a feel for different possible futures the strategy produces.
The advantage of this strategy is that it eliminates the risk that bad investment returns early on will wreck the retirement plan. As you only spend whatever the market returns for a given lockbox, later years cannot be affected by over-spending in earlier years.

You can't run out of money with this strategy (unless the cumulative return for your risky asset goes to zero) but your income can drop to a low level if the risky asset delivers a real return lower than your discount rate.

In real life a fund with the given return and standard deviation will produce a narrower range of outcomes than this spreadsheet does, because in real life markets revert to the mean, whereas in the spreadsheet each years investment return is assumed to be completely unconnected to what has happened previously.

One simple refinement to the investment strategy would be to say that if at any time in the last ten years of a given lockbox's life, switching its investments to a safe asset would yield the desired final value, then we do so. This rule helps us avoid having to sell risky assets when they are at a temporary low.
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Old 05-22-2008, 01:19 PM   #15
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I've set up a spreadsheet to simulate returns for a simple lockbox strategy. I assume
  • I will be 100% invested at all times in my risky asset, in my case this has an estimated return of 5.5% with standard deviation 7.95%.
  • I will take an annual income I until age 75, i.e. the target final value of all lockboxes except the age 75 one is I.
  • At age 75 I will buy an inflation-linked annuity that pays an income of I. The cost of such an annuity would currently be I/7.080%. This is the target final value of the last lockbox.
  • I use a 4% discount rate to allocate all my capital to different years so as to produce the target total for each year. (If my risky asset does indeed return 5.5%, a 4% discount rate means I will have a rising income.)
  • I simulate the cumulative return to year N with the calculation [Cumulative Return]=[Previous years cumulative return]*(100%+5.5%+7.95%*(rand()+rand()+rand()... (12 rand()s in total) - 6))
  • I repeatedly press F9 in Excel to recalculate the spreadsheet to get a feel for different possible futures the strategy produces.
The advantage of this strategy is that it eliminates the risk that bad investment returns early on will wreck the retirement plan. As you only spend whatever the market returns for a given lockbox, later years cannot be affected by over-spending in earlier years.

You can't run out of money with this strategy (unless the cumulative return for your risky asset goes to zero) but your income can drop to a low level if the risky asset delivers a real return lower than your discount rate.

In real life a fund with the given return and standard deviation will produce a narrower range of outcomes than this spreadsheet does, because in real life markets revert to the mean, whereas in the spreadsheet each years investment return is assumed to be completely unconnected to what has happened previously.

One simple refinement to the investment strategy would be to say that if at any time in the last ten years of a given lockbox's life, switching its investments to a safe asset would yield the desired final value, then we do so. This rule helps us avoid having to sell risky assets when they are at a temporary low.
Interesting stuff, but it generates questions.

First, what is the beginning age?

Then: What did "I" turn out to be?
and,,, How does that compare to the "I" from using lockboxes until, say, 100?
and,,, What's the downside? for example, how many years do you spend less than 90% of I?
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Old 05-22-2008, 02:11 PM   #16
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Interesting stuff, but it generates questions.

First, what is the beginning age?
For me, 44.
Quote:

Then: What did "I" turn out to be?
4.5% of initial capital.
Quote:
and,,, How does that compare to the "I" from using lockboxes until, say, 100?
As I like the principle of annuities, and roughly half of my current investment capital is legally required to go into an annuity by age 75, the question is a bit to academic for me to pursue.
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and,,, What's the downside? for example, how many years do you spend less than 90% of I?
I haven't measured the income stream variability, but subjectively it usually looks pretty good. Occasionally you end up with a low income at 75, but that happens when cumulative investment returns over 30 years are low. I've just done some runs, and on the 33rd F9 I got my lowest final income of the set, a final income of 58% of I when the cumulative return on the risky asset was 3.2% a year. Also, note my earlier comments; real life variabiliy should be better (i.e. less) due to mean reversion.

What I like about the lockbox strategy is that it essentially solves the problem that firecalc and the 4% rule address, that there is a risk from the sequence of returns.

Note that my use of 4% as a discount rate was somewhat arbitrary. If I were to follow Sharpes thinking about utility I probably ought to use 5.5% as my discount rate. (Edit: doing so increases I from 4.5% to 5.6% for my risky asset.)

I may looking at ways to reduce the variability of the income. I think I will enhance the spreadsheet to explore the effect of switching to safe assets for lockboxes that are within ten years of their target date and are sufficiently "up" that they will beat the 4% benchmark, after taking into account the time remaining and the return on the safe assets. This won't make any difference to scenarios where cumulative return is low, but the difference between 4% and 5.5% means that income getting "to high" is actually a more common problem. I don't want to solve this by changing the discount rate to 5.5% because I want to spend some of my money on reducing the risk of lower incomes in old age.
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Old 05-23-2008, 06:46 AM   #17
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I created a modified version of the spreadsheet, with the annuity omitted and the income lasting until 100. I also changed the discount rate to be the same as the underlying rate of return of 5.5%.

As expected, the income stream still looks fairly stable. Of course if returns are poor then income will be, but there's no easy way to escape that.


The first year income is almost a third higher than when using the annuity option with the same discount rate. That's much more than I expected. I guess if I implemented this strategy I should consider using one of those self-invested annuities I mentioned in another thread, so I could stay invested in my risky asset after 75.
Correction: the first year income isn't different - I was comparing versions with different discount rates. When you use the same rate, the first year income is virtually identical.
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Old 05-23-2008, 10:16 AM   #18
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Thanks. I'm 60, so my "I" turns out to be 5.0%. I get more "lift" out of this strategy (as compared to a 4% SWR) because I'm losing more estate potential. However, I can't assume that "markets revert to the mean", becuase I'm cashing out in 15 years, so I accept more income risk on the annuity than you do.

If I ignore the annuity and simply build lockboxes to age 100, my "I" becomes 4.8%. But that's apples-to-oranges because the strategy that uses the annuity has no expected growth in income after age 75, but lockboxes-to-100 has an expected growth with your assumptions.

I like the comment that the primary advantage of this strategy is that it provides a rule for when to reduce spending. We all sense that the 4% SWR is too conservative for someone who is willing to reduce spending if investment performance is poor. The problem is coming up with a rule for when to cut back. This is an an approach which most of us can understand.

I think it's possible to answer my "downside" question with standard statistics, but I haven't spent any time trying to do that.
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While we are on the subject of monkeys..
Old 05-23-2008, 10:34 AM   #19
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While we are on the subject of monkeys..

Wow, after reading the article, I suspeect this wasn't one of those hypothetical "monkey with a typewriter" scenarios...
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