Morse Code Glide Path

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Morse Code
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Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 8:42 am

I use a glide path method I was introduced to on these forums, but I don't see it talked about often, so I don't think many others have adopted it. I'm not sure why because I think it's better than a target DATE glide path. I characterize it as a target BALANCE glide path. Let me explain:

If I determine I would like to have a balance of $1.5M and a 50/50 stock/bond allocation at retirement, a simple spreadsheet formula can tell me how to re-balance so when I arrive at "my number", my AA will be exactly 50/50. For example, if my current retirement fund balance is $500K, I am a third of the way to my target and my AA will be 83/17. As my balance reaches $750K (half-way), I will have moved to 75/25, etc.

The beauty of this is in down markets, the bond allocation actually decreases, forcing you to buy more stocks than you would with a target date glide path and when markets are hot, it increases your bond allocation, forcing you to take more off the table than otherwise. With this method you may reach your target balance at any age, but when you do you're presumably free to punch out of the work force and your AA will match your predetermined risk tolerance.

Of course, this method has it's flaws, which I'm sure will be brought up quickly, but I still like it better for the reasons stated above. What do you think?
Last edited by Morse Code on Fri Oct 12, 2018 9:31 am, edited 1 time in total.
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Re: Morse Code Glide Path

Post by willthrill81 » Fri Oct 12, 2018 8:50 am

Would you elaborate on the "simple spreadsheet formula" used to derive this glide path?
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Re: Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 8:55 am

willthrill81 wrote:
Fri Oct 12, 2018 8:50 am
Would you elaborate on the "simple spreadsheet formula" used to derive this glide path?
(Current Balance/Target Balance) X Target Bond Allocation = Current Bond Allocation
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Re: Morse Code Glide Path

Post by goblue100 » Fri Oct 12, 2018 9:17 am

Interesting, I am doing something in a similar fashion, though I don't have a formula. For a $1.5 million portfolio, my max equity balance would be $750K. I check balances quarterly. Anything over $750K goes to bonds. If its under do nothing. Once bond balance gets to $750K allow both to grow equally. If for some reason(large decline in equities) I get to a 50/50 portfolio short of $1.5 million I will have to decide if I want to move some from bonds to equities to take advantage of the decline.
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Re: Morse Code Glide Path

Post by cherijoh » Fri Oct 12, 2018 9:18 am

willthrill81 wrote:
Fri Oct 12, 2018 8:50 am
Would you elaborate on the "simple spreadsheet formula" used to derive this glide path?
I'm not the OP, but it looks pretty simple.

Given
PV= present value in Dollars = $500K
T= Target in Dollars = $1.5M
TB = target % bonds = 50%
TS = Target % stocks = 50%

Calculated
B= current % bonds = TB*PV/T = 50%* $500K/$1.5M = 16.667% ~ 17%
S= current % Stocks = 100 - B = 83.333% ~83%

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Re: Morse Code Glide Path

Post by willthrill81 » Fri Oct 12, 2018 9:19 am

Morse Code wrote:
Fri Oct 12, 2018 8:55 am
willthrill81 wrote:
Fri Oct 12, 2018 8:50 am
Would you elaborate on the "simple spreadsheet formula" used to derive this glide path?
(Current Balance/Target Balance) X Target Bond Allocation = Current Bond Allocation
Have you backtested the performance of such a glide path?
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 9:26 am

willthrill81 wrote:
Fri Oct 12, 2018 9:19 am
Morse Code wrote:
Fri Oct 12, 2018 8:55 am
willthrill81 wrote:
Fri Oct 12, 2018 8:50 am
Would you elaborate on the "simple spreadsheet formula" used to derive this glide path?
(Current Balance/Target Balance) X Target Bond Allocation = Current Bond Allocation
Have you backtested the performance of such a glide path?
No. I wouldn't know how, but I'd be really curious to see the results if someone did. Just speculating, since stocks go up more than they go down, this method may be a bit more conservative. In other words, it may take a little longer to get to a given balance this way, but you would arrive there more safely, if that makes any sense.
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Re: Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 9:27 am

goblue100 wrote:
Fri Oct 12, 2018 9:17 am
Interesting, I am doing something in a similar fashion, though I don't have a formula. For a $1.5 million portfolio, my max equity balance would be $750K. I check balances quarterly. Anything over $750K goes to bonds. If its under do nothing. Once bond balance gets to $750K allow both to grow equally. If for some reason(large decline in equities) I get to a 50/50 portfolio short of $1.5 million I will have to decide if I want to move some from bonds to equities to take advantage of the decline.
Same concept. Go Blue!
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Re: Morse Code Glide Path

Post by cheese_breath » Fri Oct 12, 2018 9:30 am

When I saw Morse Code I was expecting dots and dashes. :D
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Re: Morse Code Glide Path

Post by cheese_breath » Fri Oct 12, 2018 9:31 am

Morse Code wrote:
Fri Oct 12, 2018 9:27 am
goblue100 wrote:
Fri Oct 12, 2018 9:17 am
Interesting, I am doing something in a similar fashion, though I don't have a formula. For a $1.5 million portfolio, my max equity balance would be $750K. I check balances quarterly. Anything over $750K goes to bonds. If its under do nothing. Once bond balance gets to $750K allow both to grow equally. If for some reason(large decline in equities) I get to a 50/50 portfolio short of $1.5 million I will have to decide if I want to move some from bonds to equities to take advantage of the decline.
Same concept. Go Blue!
Except when they play MSU. :D
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Re: Morse Code Glide Path

Post by willthrill81 » Fri Oct 12, 2018 9:31 am

cheese_breath wrote:
Fri Oct 12, 2018 9:30 am
When I saw Morse Code I was expecting dots and dashes. :D
When I learned it, all we had were dits. :wink:
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 9:38 am

cheese_breath wrote:
Fri Oct 12, 2018 9:30 am
When I saw Morse Code I was expecting dots and dashes. :D
Yeah. I thought that subject line would pique some curiosity, get more views. :D
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Re: Morse Code Glide Path

Post by jhfenton » Fri Oct 12, 2018 9:39 am

I use different starting and ending points, but I use a similar formula in my spreadsheet. I got the idea from a discussion with klangfool at some point. We have very different ideas on a reasonable asset allocation--I am much more aggressive--but I appreciated his glidepath theory.

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Re: Morse Code Glide Path

Post by cheese_breath » Fri Oct 12, 2018 9:43 am

Morse Code wrote:
Fri Oct 12, 2018 9:38 am
cheese_breath wrote:
Fri Oct 12, 2018 9:30 am
When I saw Morse Code I was expecting dots and dashes. :D
Yeah. I thought that subject line would pique some curiosity, get more views. :D
Well it worked, at least for me. :happy
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Re: Morse Code Glide Path

Post by retiringwhen » Fri Oct 12, 2018 9:50 am

I like this idea, I had been on a slow mechanical glide path that was not really tied to anything but age. This drives you to use a target $ amount instead. I just added this formula to my normal AA sheet as an experiment, I think I'll watch it for a while before formally starting to drive off it. Ironically, my current bond % is within 1% of what this algorithm says it should be :-)

Of course, this forces you decide what your target Retirement $ is, I have a minimum, but not an optimal number......

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Re: Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 9:59 am

retiringwhen wrote:
Fri Oct 12, 2018 9:50 am
I like this idea, I had been on a slow mechanical glide path that was not really tied to anything but age. This drives you to use a target $ amount instead. I just added this formula to my normal AA sheet as an experiment, I think I'll watch it for a while before formally starting to drive off it. Ironically, my current bond % is within 1% of what this algorithm says it should be :-)

Of course, this forces you decide what your target Retirement $ is, I have a minimum, but not an optimal number......
Yes. This method requires you pick your number and future risk tolerance now. We all know these can change, but there's nothing that says you can't adjust as you go, just like anything else when new information or circumstances present themselves.

The other method requires you to pick your retirement age and risk tolerance now, which may be even more of an uncertainty.
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Re: Morse Code Glide Path

Post by retiringwhen » Fri Oct 12, 2018 10:07 am

Morse Code wrote:
Fri Oct 12, 2018 9:59 am
The other method requires you to pick your retirement age and risk tolerance now, which may be even more of an uncertainty.
Exactly, at least at this phase of life, I think the $ is now more realistic to specify with some accuracy.

Although when I was 29, I calculated my target retirement $ and used that as a planning number for nearly 20 years. Only in my 50s did I change it (up) mostly due to increased expectations on retirement spending (probably mostly an underestimation of inflation actually).

I would have been well served all those years to use that number though in the algorithm.

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Re: Morse Code Glide Path

Post by dcabler » Fri Oct 12, 2018 10:10 am

Interesting concept - I generally don't use a glidepath but hold a fixed allocation.

With this method, as you approach you target dollar amount, the percentage of your bond holdings increase. If your bond holdings increase, then you can expect your long term returns to decrease. It's sort of gently applying your brakes as you get closer to your final destination, possibly making it take a little longer to get there...

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Re: Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 10:20 am

dcabler wrote:
Fri Oct 12, 2018 10:10 am
...It's sort of gently applying your brakes as you get closer to your final destination, possibly making it take a little longer to get there...
I agree. I like the way you said that. But there's little doubt it would get you to your destination faster than a fixed allocation of 50/50, for example.
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Re: Morse Code Glide Path

Post by retiringwhen » Fri Oct 12, 2018 10:32 am

Morse Code wrote:
Fri Oct 12, 2018 10:20 am
dcabler wrote:
Fri Oct 12, 2018 10:10 am
...It's sort of gently applying your brakes as you get closer to your final destination, possibly making it take a little longer to get there...
I agree. I like the way you said that. But there's little doubt it would get you to your destination faster than a fixed allocation of 50/50, for example.
Have you looked at the Glide-path research done by ERN?

https://earlyretirementnow.com/2016/12/ ... t-1-intro/

The whole series is worth your time, but he especially digs into Sequential Risk or Returns and outcomes using Glide Paths in articles: 14 and 19.

I have been on the fence about moving to a glide path of 50/50 at retirement that turns around and goes to 80/20 as we age. I am currently working my "official" plan as targeting a permanent 60/40 for retirement and a glide into it the last few years of working.

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Re: Morse Code Glide Path

Post by Elysium » Fri Oct 12, 2018 10:36 am

Excellent idea. The merits of this approch isn't disucussed here often although many of us do this or started doing.

I started doing this since 2015 or so when I reached critical mass regarding my retirement assets, and nearing retirement. Before that I had a static 80/20 allocation for many years during accumulation.

I tried explaining it in a different way in the "backing up truck" thread but it failed since I focused more on backing up part than the method behind it. The formula takes away any emotion based decision out of the picture. Although in my case I haven't developed a formula but doing it by intution, and a quick check with this method tells me I am not way off.

My goal is too use a glidepath using portfolio balance now that I am looking at the home stretch of final 10 years or so before retirement. This makes sense for those of us who have already reached critical mass and more concerned about preserving what we have while at the same time not giving up totally on the gains that are there. Buying more when stocks go down and accumulating more bonds when stocks go up is a good way to participate in the gains while safe guarding the principal.

This may not be the path to best returns possible, and may not be recommended for those in accumulation. But a combination of static AA with re-balancing plan until you are on the home stretch then switching to a glide path based on this strategy is a good method in my opinion.

There are other variants to this such as buiding a bond tent during the final 10 years to retirement where you start building a larger bond portion than needed then spending that down in early retirement years and finally returning to a static AA path 5-10 years into retirement.

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Re: Morse Code Glide Path

Post by PaulF » Fri Oct 12, 2018 11:01 am

This reminds me of Phineas J Whoopee's approach. He gives a more intuitive explanation here:

viewtopic.php?f=10&t=126809&start=50#p1862535

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Re: Morse Code Glide Path

Post by oldcomputerguy » Fri Oct 12, 2018 11:06 am

cheese_breath wrote:
Fri Oct 12, 2018 9:30 am
When I saw Morse Code I was expecting dots and dashes. :D
You mean dits and dahs?
:wink:
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Re: Morse Code Glide Path

Post by cheese_breath » Fri Oct 12, 2018 11:09 am

oldcomputerguy wrote:
Fri Oct 12, 2018 11:06 am
cheese_breath wrote:
Fri Oct 12, 2018 9:30 am
When I saw Morse Code I was expecting dots and dashes. :D
You mean dits and dahs?
:wink:
OK for sound. But the forum doesn't have sound features, ergo dots and dashes here. :D
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Re: Morse Code Glide Path

Post by vineviz » Fri Oct 12, 2018 11:34 am

This method seems reminiscent of the approach popularized by by Ayres and Nalebuff in their book "Lifecycle Investing ".

http://lifecycleinvesting.net/index.html

The idea is to calculate the present value of your future savings contributions, use this to determine your target equity allocation at each point in your life, and invest in equities (possibly leveraged) until you reach that target.

They provide this calculator to estimate the PV of your future savings. http://lifecycleinvesting.net/Resources ... lator.xlsx
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Re: Morse Code Glide Path

Post by oldcomputerguy » Fri Oct 12, 2018 11:35 am

cheese_breath wrote:
Fri Oct 12, 2018 11:09 am
oldcomputerguy wrote:
Fri Oct 12, 2018 11:06 am
cheese_breath wrote:
Fri Oct 12, 2018 9:30 am
When I saw Morse Code I was expecting dots and dashes. :D
You mean dits and dahs?
:wink:
OK for sound. But the forum doesn't have sound features, ergo dots and dashes here. :D
Point taken. :beer
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Re: Morse Code Glide Path

Post by #Cruncher » Fri Oct 12, 2018 11:57 am

Morse Code wrote:
Fri Oct 12, 2018 8:42 am
The beauty of this is in down markets, the bond allocation actually decreases, forcing you to buy more stocks than you would with a target date glide path ...
Following this approach would require an iron will (and stomach!) in a severe downturn in stock prices. Consider the crash from 2007 to 2009. Many investors had trouble just keeping from bailing out of stocks. Keeping a constant percentage in stocks, required even more fortitude to buy stocks when many were predicting Armageddon. Your approach would actually increase the percentage in stocks. I know that I wouldn't have had the stomach to do this.

Consider someone with a target retirement "number" of $1,080,000; and who wishes to have a 40:60 stock:bond allocation at that time. Assume that on 10/9/2007, when Vanguard's Total Stock Market Index Fund (VTSAX)'s price peaked at $37.80, his total portfolio value was $540,000. Since this is 50% of his retirement target, the desired bond allocation would be 30% (60% X 540 / 1080) or $162K. This leaves $378K (540K X 70%) or 10,000 shares in VTSAX. At the bottom on 3/9/2009 these 10,000 shares would have been worth only $164,000. Assume at this time the bond portion of the portfolio retained its value. (This was true for Vanguard's Total Bond Market Index Fund (VBTLX) which was $9.96 / share on 10/9/2007 and $9.99 on 3/9/2009.)

So over this period, the stock allocation dropped from 70% to 50%. The "To 70%" column in the table below shows the exchange from bonds to stocks necessary to restore the 70% stock allocation. But since the total portfolio value has fallen, the recommended approach reduces the bond allocation from 30% down to only 18%. (60% X 326 / 1080), and the stock allocation up to 82%. The "To 82%" column below shows the additional exchange from bonds into stocks needed to attain this new allocation. How many of us would have been psychologically able to do this?

Code: Select all

                                   ------- Rebalance ------
             10/09/07  03/09/09    To 70%   To 82%   Result
             --------  --------   -------  -------  -------
VTSAX Price     37.80     16.43
VTSAX Value   378,000   164,000   +64,000  +39,000  267,000
VBTLX Value   162,000   162,000   -64,000  -39,000   59,000
              -------   -------                     -------
Total Value   540,000   326,000                     326,000
Stock Alloc       70%       50%                         82%
Bond  Alloc       30%       50%                         18%

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Re: Morse Code Glide Path

Post by retiringwhen » Fri Oct 12, 2018 12:04 pm

#Cruncher wrote:
Fri Oct 12, 2018 11:57 am
Morse Code wrote:
Fri Oct 12, 2018 8:42 am
The beauty of this is in down markets, the bond allocation actually decreases, forcing you to buy more stocks than you would with a target date glide path ...
Following this approach would require an iron will (and stomach!) in a severe downturn in stock prices. Consider the crash from 2007 to 2009. Many investors had trouble just keeping from bailing out of stocks. Keeping a constant percentage in stocks, required even more fortitude to buy stocks when many were predicting Armageddon. Your approach would actually increase the percentage in stocks. I know that I wouldn't have had the stomach to do this.

Consider someone with a target retirement "number" of $1,080,000; and who wishes to have a 40:60 stock:bond allocation at that time. Assume that on 10/9/2007, when Vanguard's Total Stock Market Index Fund (VTSAX)'s price peaked at $37.80, his total portfolio value was $540,000. Since this is 50% of his retirement target, the desired bond allocation would be 30% (60% X 540 / 1080) or $162K. This leaves $378K (540K X 70%) or 10,000 shares in VTSAX. At the bottom on 3/9/2009 these 10,000 shares would have been worth only $164,000. Assume at this time the bond portion of the portfolio retained its value. (This was true for Vanguard's Total Bond Market Index Fund (VBTLX) which was $9.96 / share on 10/9/2007 and $9.99 on 3/9/2009.)

So over this period, the stock allocation dropped from 70% to 50%. The "To 70%" column in the table below shows the exchange from bonds to stocks necessary to restore the 70% stock allocation. But since the total portfolio value has fallen, the recommended approach reduces the bond allocation from 30% down to only 18%. (60% X 326 / 1080), and the stock allocation up to 82%. The "To 82%" column below shows the additional exchange from bonds into stocks needed to attain this new allocation. How many of us would have been psychologically able to do this?

Code: Select all

                                   ------- Rebalance ------
             10/09/07  03/09/09    To 70%   To 82%   Result
             --------  --------   -------  -------  -------
VTSAX Price     37.80     16.43
VTSAX Value   378,000   164,000   +64,000  +39,000  267,000
VBTLX Value   162,000   162,000   -64,000  -39,000   59,000
              -------   -------                     -------
Total Value   540,000   326,000                     326,000
Stock Alloc       70%       50%                         82%
Bond  Alloc       30%       50%                         18%
And on the way back in 2009 to 2011 the investor would have been moving back to bonds every quarter and would have been very well compensated for the move to equities...

[edited, as I read the table wrong, the first time, so the to 82% column is additional over just keeping the 70% constant.]

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Re: Morse Code Glide Path

Post by Grogs » Fri Oct 12, 2018 12:16 pm

jhfenton wrote:
Fri Oct 12, 2018 9:39 am
I use different starting and ending points, but I use a similar formula in my spreadsheet. I got the idea from a discussion with klangfool at some point. We have very different ideas on a reasonable asset allocation--I am much more aggressive--but I appreciated his glidepath theory.
I'm doing something similar, and I also got the idea from Klang. My goal is to have 30X my basic annual expenses saved before retirement, and I want to be at a 50/50 AA then. I started at 80/20, and for each "X" I accumulate I reduce the stocks by 1%. I also decided that the glide path is one-way. That is, if I'm at 60/40 and stocks suddenly drop 50%, I will only rebalance back to 60/40, not 66/34.

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Re: Morse Code Glide Path

Post by icetrap » Fri Oct 12, 2018 12:19 pm

I saw a similar concept in my exam for Pension Plan using the Funding Ratio. If the more the funding ratio gone to 100%, the more the conservative asset allocation was. It seems that it was the recommended method since Pension Plan do not get one retirement age.

The classic issue with Glide path, is that they are more or less equivalent to you doing a constant asset allocation at the average asset allocation of your glide path. See the PWL whitepaper.

Using your strategy I agree that it would tell you to buy more stocks when the fund is down and thus probably the stock market. However, last month (Sept 2018) saw both Bonds(VFV -0.53%) and Equity(VBU -0.61%) down. Why buy more stocks in this situation than bonds?

Also if you are well after retirement (say age 70), would you be willing to go with a more risky asset allocation if the market plummet 40%?

The answer is probably yes, you should do it from an historical and rational perspective. However, perhaps your risk tolerance may change through time or circumstance.

Knowing the exponential curve of fund accumulation(ie: going from 0 to 50% is much slower than going from 50% to 100%). I would try to tweak the formula to be exponential. Why not go for ((2)^(Current Balance/Target Balance)-1) X Target Bond Allocation = Current Bond Allocation.

In the end, your risk tolerance should drive your asset allocation. This is why the classic glide path is based of age since age seems to be a strong indicator of a general person risk tolerance.

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Re: Morse Code Glide Path

Post by Morse Code » Fri Oct 12, 2018 12:24 pm

#Cruncher wrote:
Fri Oct 12, 2018 11:57 am
Following this approach would require an iron will (and stomach!) in a severe downturn in stock prices.
To me, this is one of the great features of this method. To take the analogy one more step, as you approach your destination, you gently apply the brakes, but as you encounter detours along the way, you put your foot back on the accelerator until you're back on the highway. This method also provides more protection from downturns the closer you get to your target, just as it should.
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Re: Morse Code Glide Path

Post by andrew99999 » Fri Oct 12, 2018 8:30 pm

Very interesting approach.

Also interesting that there are only 2 downsides people have mentioned

1. Takes you a little longer to reach FI since you are taking more off the table as you get closer, although as they said, it is more like "gently applying the brakes", not slamming on the breaks.
I would think this is countered at least in part by the idea that in down markets, the bond allocation decreases, and when markets are hot, it increases your bond allocation, so you get a better than normal rebalancing bonus.

2. If it's hard to rebalance into equities when they are falling and many are freaking out wanting to take money out, then this would be even more difficult.
I would think as long as I am still working and as long as I am not "running out" of bonds to rebalance into stocks, I would happily continue steadily rebalancing as the market dropped, but of course this is conjecture since I was not invested in 2008.

It's rare to see a non-standard idea here that is not severely criticised (for the sake of finding the truth), so it seems like it's a pretty big sign that there have been almost no criticism of this method.

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Re: Morse Code Glide Path

Post by #Cruncher » Sat Oct 13, 2018 2:25 pm

retiringwhen wrote:
Fri Oct 12, 2018 12:04 pm
#Cruncher wrote:
Fri Oct 12, 2018 11:57 am
… The "To 70%" column in the table below shows the exchange from bonds to stocks necessary to restore the 70% stock allocation. But ... the recommended approach reduces the bond allocation from 30% down to only 18%. (60% X 326 / 1080), and the stock allocation up to 82%. The "To 82%" column below shows the additional exchange from bonds into stocks needed to attain this new allocation. How many of us would have been psychologically able to do this? ...
And on the way back in 2009 to 2011 the investor … would have been very well compensated for the move to equities. (underline added)
I agree with "compensated", but question the "very well". I extended the analysis in my previous post. Instead of just comparing the results at the bottom on 3/9/2009 to the peak on 10/9/2007, I ran every month from 10/9/2007 to 12/9/2011. Every month I rebalanced stocks and bonds using the recommended approach of varying the stock allocation based on the ratio of current portfolio value to target portfolio value at retirement. This only added about 2% to the portfolio value on 12/9/2011 ($501K vs $492K) compared to holding the allocation steady at 70% stocks. For me this wouldn't be worth the additional gut wrenching the recommended approach required during the throes of the crash.

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        Rebalancing
          Method       10/9/07    3/9/09    8/9/09   12/9/10   12/9/11
        -----------    -------   -------   -------   -------   -------
Case 0: None           540,000   326,000   411,000   473,000   476,000
Case 1: Constant 70%   540,000   308,000   416,000   487,000   492,000
Case 2: Recommended    540,000   293,000   415,000   493,000   501,000
  • 3/9/2009 (the bottom): With no rebalancing (case 0) the portfolio falls from $540,000 to $326,000. Rebalancing monthly to 70% stocks (case 1) causes it to fall further to $308,000. But rebalancing to the recommended varying allocation (case 2) causes it to fall even more to $293,000.
  • 8/9/2009: After five months, the portfolio value for case 2 has "caught up" with both case 0 and case 1.
  • 12/9/2011: After August 2009 the portfolio value for case 2 grows fastest. By 12/9/2011 it is $25,000 more than case 0 and $9,000 more than case 1.
Here are the detailed month-by-month figures for the constant 70% allocation and for the recommended varying allocation. They're based on the following assumptions:
  • Target portfolio value at retirement is $1,080,000 with a 40:60 stock:bond allocation.
  • Start out with a total portfolio value of $540,000 on 3/9/2007 composed of 10,000 shares of Vanguard Total Stock Market Index (VTSAX) at $37.80 / share and $162,000 invested in bonds.
  • The initial bond allocation is 30% = 60% X 540 / 1080.
  • Use monthly prices for VTSAX obtained from historical price information. For simplicity ignore dividends and assume no price change for bonds.
  • Rebalance every month. For Case 1, keep stocks at the initial 70%. For Case 2 adjust the stock allocation based on the ratio of total portfolio value to the $1,080,000 target retirement portfolio value.
Case 1: Constant 70% stock allocation

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             VTSAX   --------- Value ---------   --- Stock Pct --              VTSAX
   Date      Price    Stocks   Bonds    Total     Actual  Desired   $ Exch    Shares

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10/09/2007   37.80   378,000  162,000  540,000   70.000%  70.000%        0   10,000.0
11/09/2007   35.19   351,900  162,000  513,900   68.476%  70.000%    7,830   10,222.5
12/09/2007   36.41   372,201  154,170  526,371   70.711%  70.000%   (3,741)  10,119.7
01/09/2008   33.76   341,643  157,911  499,554   68.390%  70.000%    8,045   10,358.1
02/09/2008   32.21   333,633  149,866  483,499   69.004%  70.000%    4,816   10,507.6
03/09/2008   31.27   328,572  145,050  473,622   69.374%  70.000%    2,963   10,602.3
04/09/2008   32.65   346,167  142,087  488,253   70.899%  70.000%   (4,389)  10,467.9
05/09/2008   33.63   352,036  146,476  498,512   70.617%  70.000%   (3,078)  10,376.4
06/09/2008   33.35   346,053  149,554  495,606   69.824%  70.000%      872   10,402.5
07/09/2008   30.27   314,885  148,682  463,567   67.927%  70.000%    9,612   10,720.1
08/09/2008   31.65   339,290  139,070  478,360   70.928%  70.000%   (4,438)  10,579.8
09/09/2008   29.95   316,866  143,508  460,375   68.828%  70.000%    5,396   10,760.0
10/09/2008   22.01   236,828  138,112  374,940   63.164%  70.000%   25,630   11,924.5
11/09/2008   22.47   267,943  112,482  380,425   70.433%  70.000%   (1,646)  11,851.3
12/09/2008   21.38   253,380  114,128  367,508   68.946%  70.000%    3,875   12,032.5
01/09/2009   21.55   259,301  110,252  369,553   70.166%  70.000%     (614)  12,004.0
02/09/2009   21.11   253,405  110,866  364,271   69.565%  70.000%    1,585   12,079.1
03/09/2009   16.43   198,460  109,281  307,741   64.489%  70.000%   16,959   13,111.3 <===
04/09/2009   20.87   273,633   92,322  365,955   74.772%  70.000%  (17,464)  12,274.5
05/09/2009   22.72   278,876  109,787  388,663   71.753%  70.000%   (6,812)  11,974.7
06/09/2009   23.19   277,692  116,599  394,291   70.428%  70.000%   (1,688)  11,901.8
07/09/2009   21.56   256,604  118,287  374,891   68.448%  70.000%    5,820   12,171.8
08/09/2009   24.90   303,078  112,467  415,545   72.935%  70.000%  (12,196)  11,682.0 <===
09/09/2009   25.56   298,592  124,663  423,255   70.546%  70.000%   (2,313)  11,591.5
10/09/2009   26.48   306,943  126,977  433,919   70.737%  70.000%   (3,199)  11,470.7
11/09/2009   26.86   308,102  130,176  438,278   70.298%  70.000%   (1,308)  11,422.0
12/09/2009   26.99   308,279  131,483  439,763   70.101%  70.000%     (445)  11,405.5
01/09/2010   28.25   322,205  131,929  454,134   70.949%  70.000%   (4,311)  11,252.9
02/09/2010   26.42   297,301  136,240  433,541   68.575%  70.000%    6,178   11,486.7
03/09/2010   28.40   326,222  130,062  456,285   71.495%  70.000%   (6,823)  11,246.5
04/09/2010   29.70   334,020  136,885  470,905   70.931%  70.000%   (4,386)  11,098.8
05/09/2010   27.61   306,437  141,272  447,709   68.446%  70.000%    6,959   11,350.8
06/09/2010   26.29   298,413  134,313  432,726   68.961%  70.000%    4,495   11,521.8
07/09/2010   26.75   308,208  129,818  438,026   70.363%  70.000%   (1,590)  11,462.4
08/09/2010   28.04   321,404  131,408  452,812   70.980%  70.000%   (4,436)  11,304.2
09/09/2010   27.47   310,525  135,844  446,369   69.567%  70.000%    1,933   11,374.5
10/09/2010   29.03   330,202  133,911  464,113   71.147%  70.000%   (5,323)  11,191.1
11/09/2010   30.34   339,539  139,234  478,773   70.919%  70.000%   (4,398)  11,046.2
12/09/2010   31.06   343,095  143,632  486,727   70.490%  70.000%   (2,386)  10,969.4 <===
01/09/2011   31.92   350,142  146,018  496,160   70.570%  70.000%   (2,830)  10,880.7
02/09/2011   33.19   361,131  148,848  509,979   70.813%  70.000%   (4,146)  10,755.8
03/09/2011   33.26   357,738  152,994  510,732   70.044%  70.000%     (226)  10,749.0
04/09/2011   33.49   359,984  153,220  513,204   70.145%  70.000%     (742)  10,726.9
05/09/2011   33.98   364,499  153,961  518,460   70.304%  70.000%   (1,577)  10,680.5
06/09/2011   32.54   347,542  155,538  503,080   69.083%  70.000%    4,614   10,822.3
07/09/2011   33.97   367,632  150,924  518,556   70.895%  70.000%   (4,643)  10,685.6
08/09/2011   29.30   313,088  155,567  468,654   66.806%  70.000%   14,971   11,196.5
09/09/2011   28.94   324,027  140,596  464,624   69.740%  70.000%    1,209   11,238.3
10/09/2011   28.69   322,427  139,387  461,814   69.817%  70.000%      843   11,267.7
11/09/2011   30.70   345,918  138,544  484,462   71.402%  70.000%   (6,794)  11,046.4
12/09/2011   31.42   347,077  145,339  492,416   70.485%  70.000%   (2,386)  10,970.4
Case 2: Recommended approach with varying stock allocation

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             VTSAX   --------- Value ---------   --- Stock Pct --              VTSAX
   Date      Price    Stocks   Bonds    Total     Actual  Desired   $ Exch    Shares

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10/09/2007   37.80   378,000  162,000  540,000   70.000%  70.000%        0   10,000.0
11/09/2007   35.19   351,900  162,000  513,900   68.476%  71.450%   15,282   10,434.3 [*]
12/09/2007   36.41   379,911  146,718  526,630   72.140%  70.743%   (7,359)  10,232.2 [*]
01/09/2008   33.76   345,437  154,077  499,515   69.155%  72.249%   15,458   10,690.0
02/09/2008   32.21   344,326  138,619  482,945   71.297%  73.170%    9,044   10,970.8
03/09/2008   31.27   343,057  129,576  472,633   72.584%  73.743%    5,475   11,145.9
04/09/2008   32.65   363,913  124,101  488,014   74.570%  72.888%   (8,209)  10,894.5
05/09/2008   33.63   366,381  132,310  498,690   73.469%  72.295%   (5,853)  10,720.4
06/09/2008   33.35   357,526  138,162  495,689   72.127%  72.462%    1,658   10,770.2
07/09/2008   30.27   326,013  136,504  462,517   70.487%  74.305%   17,659   11,353.5
08/09/2008   31.65   359,339  118,845  478,184   75.147%  73.434%   (8,188)  11,094.8
09/09/2008   29.95   332,290  127,034  459,323   72.343%  74.482%    9,824   11,422.8
10/09/2008   22.01   251,416  117,210  368,626   68.204%  79.521%   41,718   13,318.2
11/09/2008   22.47   299,261   75,492  374,753   79.856%  79.180%   (2,530)  13,205.6
12/09/2008   21.38   282,336   78,022  360,358   78.349%  79.980%    5,878   13,480.6
01/09/2009   21.55   290,507   72,143  362,650   80.107%  79.853%     (921)  13,437.9
02/09/2009   21.11   283,673   73,064  356,737   79.519%  80.181%    2,363   13,549.8
03/09/2009   16.43   222,623   70,701  293,324   75.897%  83.704%   22,901   14,943.7 <===
04/09/2009   20.87   311,875   47,800  359,674   86.710%  80.018%  (24,070)  13,790.3
05/09/2009   22.72   313,317   71,870  385,186   81.342%  78.601%  (10,557)  13,325.7
06/09/2009   23.19   309,022   82,427  391,449   78.943%  78.253%   (2,702)  13,209.1
07/09/2009   21.56   284,789   85,129  369,919   76.987%  79.449%    9,107   13,631.6
08/09/2009   24.90   339,426   76,022  415,448   81.701%  76.920%  (19,865)  12,833.8 <===
09/09/2009   25.56   328,031   95,887  423,918   77.381%  76.449%   (3,950)  12,679.2
10/09/2009   26.48   335,746   99,837  435,583   77.080%  75.801%   (5,570)  12,468.9
11/09/2009   26.86   334,914  105,407  440,321   76.061%  75.538%   (2,306)  12,383.0
12/09/2009   26.99   334,218  107,713  441,931   75.627%  75.448%     (789)  12,353.8
01/09/2010   28.25   348,995  108,502  457,497   76.284%  74.584%   (7,778)  12,078.5
02/09/2010   26.42   319,114  116,280  435,393   73.293%  75.811%   10,965   12,493.5
03/09/2010   28.40   354,815  105,315  460,130   77.112%  74.437%  (12,307)  12,060.1
04/09/2010   29.70   358,186  117,622  475,809   75.280%  73.566%   (8,152)  11,785.7
05/09/2010   27.61   325,402  125,774  451,177   72.123%  74.935%   12,685   12,245.1
06/09/2010   26.29   321,924  113,089  435,013   74.003%  75.833%    7,958   12,547.8
07/09/2010   26.75   335,654  105,131  440,785   76.149%  75.512%   (2,808)  12,442.8
08/09/2010   28.04   348,897  107,940  456,836   76.372%  74.620%   (8,004)  12,157.4
09/09/2010   27.47   333,962  115,944  449,907   74.229%  75.005%    3,491   12,284.4
10/09/2010   29.03   356,617  112,453  469,070   76.026%  73.941%   (9,784)  11,947.4
11/09/2010   30.34   362,484  122,237  484,721   74.782%  73.071%   (8,293)  11,674.1
12/09/2010   31.06   362,596  130,530  493,127   73.530%  72.604%   (4,566)  11,527.0 <===
01/09/2011   31.92   367,943  135,097  503,040   73.144%  72.053%   (5,486)  11,355.2
02/09/2011   33.19   376,878  140,583  517,461   72.832%  71.252%   (8,176)  11,108.8
03/09/2011   33.26   369,480  148,759  518,239   71.295%  71.209%     (447)  11,095.4
04/09/2011   33.49   371,584  149,206  520,791   71.350%  71.067%   (1,473)  11,051.4
05/09/2011   33.98   375,526  150,679  526,206   71.365%  70.766%   (3,150)  10,958.7
06/09/2011   32.54   356,596  153,829  510,425   69.863%  71.643%    9,088   11,238.0
07/09/2011   33.97   381,754  144,741  526,496   72.509%  70.750%   (9,258)  10,965.5
08/09/2011   29.30   321,288  153,999  475,287   67.599%  73.595%   28,500   11,938.2
09/09/2011   28.94   345,490  125,499  470,989   73.354%  73.834%    2,259   12,016.2
10/09/2011   28.69   344,746  123,239  467,985   73.666%  74.001%    1,567   12,070.9
11/09/2011   30.70   370,575  121,672  492,247   75.282%  72.653%  (12,943)  11,649.3
12/09/2011   31.42   366,020  134,615  500,635   73.111%  72.187%   (4,627)  11,502.0
* Example calculations for 11/9/2007 and 12/9/2007:

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11/9/2007
   351,900 = 10000  * 35.19              = stock value
   513,900 = 351900 + 162000             = total value
    71.45% = 100% - 60% * (513.9 / 1080) = new stock allocation
    15,282 = 513900 * 71.45% - 351900    = $ exchange from bonds to stocks
  10,434.3 = 10000  + 15282  / 35.19     = new shares of stock
12/9/2007
   379,911 =   10434.3 * 36.41           = stock value
   146,718 =  162000   - 15282           = bond value

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