Can somebody who's better at math, please explain this to me?

[Coffee]

Can somebody who's better at math, please explain this to me?

Here's where I'm getting confused:

When a PP asset class drops by 50% in one year (for example) it must go up 100% in the next year to recoup it's losses.  Now, multiply by four different asset classes -- and it seems like a scenario where the house always wins in the long run (you lose) because you're diversified across four different asset classes?

Thanks,
Adam.
http://www.lasvegasdogtraining.com

[Coffee]

I'm guessing the rebalancing/buying low, is where the magic comes into play?

[craigr]

I'm not sure I understand your question. But yes, rebalancing is normally taking money off the table of the winners and putting it where it is most likely to do better going forward.

[MediumTex]

As a case in point, over 2008-2009 stocks lost 40% of their value.  Since then they have gained 80% off of the depressed levels, while LT treasurys have had modest overall gains and gold has gone through the roof.

Advantage: PP.

[Gumby]

When a PP asset class drops by 50% in one year (for example) it must go up 100% in the next year to recoup it's losses.

Not exactly. If an asset goes down by 50% this would almost certainly trigger a rebalancing. Now you buy more of that asset and that means your cost basis has changed. You end up with a greater quantity of that asset than what you originally started with and at a lower average purchase price. So, you don't need to have a 100% return to recoup the losses because you've lowered your cost basis. You only have to recover a portion of the original loss in order to profit from that asset.

[Coffee]

Thanks, Gumby.  That makes sense.

The whole thing just feels funky though, as it goes against the whole, "Cut your losses and let your winners ride" mantra.
[Edit: Of course, I guess you could counter that with, "Buy low, sell high." ]

[MediumTex]

Thanks, Gumby.  That makes sense.

The whole thing just feels funky though, as it goes against the whole, "Cut your losses and let your winners ride" mantra.
[Edit: Of course, I guess you could counter that with, "Buy low, sell high." ]

The PP does both.  By holding an asset until it hits 30% or 35% of your portfolio (depending upon your preference) you are letting your winners run.  When you rebalance you aren't selling ALL of your winning holdings, you are just banking some gains and maintaining your original 25% position.

HB addressed this point on a few different occasions.

[Gumby]

Thanks, Gumby.  That makes sense.

The whole thing just feels funky though, as it goes against the whole, "Cut your losses and let your winners ride" mantra.
[Edit: Of course, I guess you could counter that with, "Buy low, sell high." ]

The PP does both.  By holding an asset until it hits 30% or 35% of your portfolio (depending upon your preference) you are letting your winners run.  When you rebalance you aren't selling ALL of your winning holdings, you are just banking some gains and maintaining your original 25% position.

HB addressed this point on a few different occasions.

Exactly right.

The whole, "Cut your losses and let your winners ride" mantra is the overall message from the financial products industry. And the financial media is mostly about chasing returns when you get right down to it. Think about all of the forecasting and past returns you are given by brokerage firms, analysts and columnists. It's just lots of chaotic data designed to excite, confuse and generate more transactions — often resulting in bad decisions, which generates even more transactions, and so on. But true investing and speculation (according to HB) is about buying the assets that are out of favor and knowing when to sell them.

Most people don't have the discipline to buy things that are in the toilet and sell them when the time is right. The PP forces you to speculate in a very smart and balanced way.

[moda0306]

The PP combines both "buy low sell high" with "let your winners ride" (which seems impossible in a way), by holding assets that are not correllated, and "letting the winners ride" until what I like to think as a "risk breaking point."

In the mid 80's through the 90's gold was dropping/stagnant and LT treasuries were seeing great gains from the high interest rates of the early 80's slowly coming down.  If you started with 25% each, letting the winners ride helped you see some great returns...

but at what point are you taking too much risk that the trend will flip??  Most people here like the 15/35 bands.  If gold dropped to 15% of your portfolio while LT treasuries were really booming, at that point you're becoming increasingly exposed to currency failures or inflation and you may want to say "Ok, this trend thing has worked great for me, but it's time to reset, as it's not worth the risk anymore."  Letting the winner ride, or the loser fall, past the 35/15 bands can start to really skew your exposure to risks in the PP, but until that point you've successfully captured any "trend" bias that the PP assets have... and they have shown to have that bias.

Interestingly, some people, myself included, see the PP as too conservative, as a 25% stock allocation (Same as cash for crying out loud) is just too paltry, but if you think about it, during the boom of the 80's and 90's, your stocks wouldn't have been at 25% starting out every year, but instead bouncing between 25% and 35%, while gold would have been bouncing between 15% and 25%.  The 35/15 bands really help capture the trends while being very tax efficient and more easy to maintain.

[Pkg Man]

I haven't reached a rebalance point yet (other than selling some assets from the VP which caused cash to exceed 35%), but I think for me it would be very difficult to watch LT bonds grow much past 30% of the portfolio without getting antsy.  With the other assets I think I could handle it easier.  That said, I intend to use the 15-35% bands if possible.

[moda0306]

Pkg Man,

I feel the same way about Cash or even Gold to a lesser degree... and even though it's probably frowned upon by the PP faithful, you and I could probably set our rebalance bands to meet certain biases we have about the market and our risk tolerances.

If I practiced an otherwise perfect PP, I'd probably never let stocks go below 20% and let them hit 40% before rebalancing.

[Pkg Man]

Pkg Man,

I feel the same way about Cash or even Gold to a lesser degree... and even though it's probably frowned upon by the PP faithful, you and I could probably set our rebalance bands to meet certain biases we have about the market and our risk tolerances.

If I practiced an otherwise perfect PP, I'd probably never let stocks go below 20% and let them hit 40% before rebalancing.

I have considered that as an option as well (using different rebalance bands for different assets).  I think if it makes one sleep better at night then it is fine to deviate a bit from the original design. 

[upside]

When a PP asset class drops by 50% in one year (for example) it must go up 100% in the next year to recoup it's losses.  Now, multiply by four different asset classes -- and it seems like a scenario where the house always wins in the long run (you lose) because you're diversified across four different asset classes?

If you only have one asset class and it drops 50% in one year it must go up 100% in the next year to recoup it's losses. But if you add another asset class and both asset classes are equally weighted, then in the same scenario, when asset class (A) drops 50%, asset class (B) "only" has to increase 50% to recoup a loss. Add in two other asset classes and each asset class that didn't drop by 50% has to pull less weight for the lagging asset class.

[KevinW]

If you only have one asset class and it drops 50% in one year it must go up 100% in the next year to recoup it's losses. But if you add another asset class and both asset classes are equally weighted, then in the same scenario, when asset class (A) drops 50%, asset class (B) "only" has to increase 50% to recoup a loss. Add in two other asset classes and each asset class that didn't drop by 50% has to pull less weight for the lagging asset class.

Yes.  Since the returns of the four assets are averaged together, you don't need an asset to overcome its own losses, but merely need the average of the other three assets to overcome an asset's losses.  Since all four assets are viable investments and so have positive expected returns, it is unlikely that the portfolio as a whole will have negative returns.

On top of that, we have the economic condition analysis that claims that at least one asset will be rallying at any given time.  If the PP's total return is the average of one very-positive asset plus three other assets following their usual random distributions*, then the probability of the portfolio as a whole going negative is very, very small.

(* Actually you can't quite make that assumption since the condition analysis also says that stocks and cash are statistically dependent with each other, as are bonds and gold.  But I think the intuition behind this explanation still works.)

[cowboyhat]

For reference, when I ran a simulated PP using the the year over year changes from Clive's Periodic Chart and a fixed starting investment in 1972 in an Excel sheet the only assets that triggered a re-balance due to becoming >35% of the portfolio were stocks and gold. The only asset that triggered a re-balance due to dropping to <15% was gold, and that only happened twice in the simulation.

[D]

So does this mean that it's maybe better to have different rebalancing bands like 20-30 for cash and bonds, and 15-35 for gold and equity?

[cowboyhat]

Clive,

Your simulation is better than mine. I didn't attribute the re-balances as being due to gold where stocks were > 35% and gold was < 15%, and I rounded up decimals so I missed the 1995 gold re-balance. But doesn't really change the point, which is that typically stocks and gold drive the re-balances and typically gold alone drives the < 15% re-balances. As I recall, leaving out the <15% driven re-balances slightly improves returns.

Comparing an annual rebalancing scheme with using 35-15% bands, I see that using the band system gives a better return. This made me reflect on my plan to put new money into short term cash and then automatically re-balance at the end of each year to allocate the accumulated cash.

Do you know what is orthodox with regard to adding new funds? Re-balance from cash? Close up the gap on biggest loser? Buy 25% of each asset and then re-balance if necessary?

[cowboyhat]

Clive,

What happens to the PP out of sample if you ignore the <15% rule? In sample it hasn't added value and it has only occurred 2 or 3 times in 40 years.

Theoretically ignoring the <15% rule would avoid repeatedly plowing money into assets in severe secular decline. I'm thinking about a future where long bonds are get hammered over a multi-year period. Probably gold is soaring, but this would be a time where being slow to re-balance would improve performance. After an economic re-normalization you would expect gold to go into a multi-year decline, and again be slow on the re-balancing trigger is better.

[LNGTERMER]

Theoretically ignoring the <15% rule would avoid repeatedly plowing money into assets in severe secular decline

That is a good observation, however you do need to re-balance during periods of pull backs within a predominant bull market.
You need to add a filter to spot the change from a dominant bull cycle and a bear market. If that is not convenient then simply keep re-balancing since that is better that the alternative. If you avoid that you are simply forgoing the built-in buy low sell high component of the PP.

[KevinW]

Do you know what is orthodox with regard to adding new funds? Re-balance from cash? Close up the gap on biggest loser? Buy 25% of each asset and then re-balance if necessary?

I'm not Clive but I think the orthodox approach is to add new funds to the cash allocation, and follow the usual advice of rebalancing when any asset is outside the 15/35 bands.  All inflows and outflows go through the cash allocation.

[cowboyhat]

From an empirical perspective in the US data set the <15% re-balancing trigger is essentially a minor footnote, and one that has not added value to the PP. Re-balancing based on the >35% trigger is a reasonably frequent event that clearly improves performance. As I recall, craigr pointed out somewhere that there is no way to make any money from holding gold unless you re-balance since gold has 0% yield. So I embrace the >35% trigger for re-balancing from a theoretical and empirical perspective. Right now I don't understand the <15% trigger.

The <15% trigger provides design symmetry, but that doesn't mean it improves performance. I could see the logic for a <15% trigger for an asset like stocks that can have rapid year to year fluctuations in price and thus provide only a narrow window to buy them cheap. But using a system of annual re-balancing (which is advantageous from a investor behavior perspective) may make it impossible in practice to take advantage of the short windows when stocks are on sale. For an asset like gold, or perhaps long bonds, that may suffer long periods of under performance there may not be any need to hurry to find a bargain.

[MediumTex]

The 15% rebalancing trigger is helpful when one is drawing down the PP, as in retirement.

You spend from the cash portion until it reaches 15%, then you rebalance.

It's the same as when you were contributing cash to the PP in the accumulation phase, except in reverse.

[Lone Wolf]

But using a system of annual re-balancing (which is advantageous from a investor behavior perspective) may make it impossible in practice to take advantage of the short windows when stocks are on sale.

My understanding has always been that you could either choose to balance based on bands (such as 15%\35%) or rebalance annually.  This would mean that you rebalance any time one of the bands is crossed or just simply have a once-yearly time where you sit down and fully rebalance, regardless of where things are.  I didn't think it was necessarily recommended to use the 15/35 bands and then to furthermore only check those bands once per year.

Anyhow, interesting results.  Thanks for sharing.

[Pkg Man]

I can't remember the details as I did this several months ago, but I used monthly data on the PP components and compared rebalancing with the 15-35 bands vs rebalancing each month.  The results between the two approaches were not very different.  As I recall the monthly rebalancing produced somewhat lower returns but also with lower standard deviation (as expected). 

Of course I did not factor trading costs into this exercise, and I wouldn't recommend rebalancing that often.  It was just a thought exercise.  But to me the take-away is that either annual, 15-35, or 20-30 will pretty much leave you in the same place, at least over a fairly long investment horizon.

[goldfinger]

Hi, Clive, very nice chart!

I have a question about your balance timing. In this chart, do you rebalance as soon as one asset reach 15/35 or you use the year end figure to caculate the balance? Foe example, in 1973, the gold reached 45%, but if we follow the rule, the rebalance should be done when gold reach 35%, thus the year end number should not be 45%, or you already put that into consideration? I guess this difference will dramatically change the pattern over the years.

Thanks.

For reference, when I ran a simulated PP using the the year over year changes from Clive's Periodic Chart and a fixed starting investment in 1972 in an Excel sheet the only assets that triggered a re-balance due to becoming >35% of the portfolio were stocks and gold. The only asset that triggered a re-balance due to dropping to <15% was gold, and that only happened twice in the simulation.

I think it triggered more frequent rebalancing than that, but as you say rebalancing arose out of either stocks or gold only hitting the <15% >35% bands



Since the early 1980's gold declined down to or below <15% levels 4 times up to 1996, which would have added around +10% of the fund value at each such instance into gold, making +40% being added in total.  With the 25% original weighting that makes 65% in effect having been directed into gold.  In 2007 and to more recent gold has performed well hence making that allocation into gold a good choice at recent times.  Over the 1980's to early 2000's however that weighting into gold significantly dragged down the rewards relative to other alternative investments.  With the large declines/poor performance of stocks and good performance of gold since 2000 overall its narrowed/reversed the gap between alternative more pure stock only like investments and the PP.

Compared to pure stock only investments over the full 1972 to 2009 period the PP has done OK.  Over subset periods within that such as 1980 to 2000 the PP has lagged.  A fairer comparison is not to compare solely with 100% stock alternatives, but perhaps 60/40 stock bond type allocations as that is more like what many investors actually invest in.  The Coffee House Portfolio is one such example of a 60/40 stock/bond type investment and compared to that the PP has much more frequently relatively under-performed.  2007 to recent is one of the few exceptions when the PP has bettered the CHP.

Where shorter term (yearly) paper value (only becomes real if you actually sell) fluctuations are a concern then the PP provides good stability in those yearly fluctuations.  Assuming you're investing for the longer term then If you're worried about the yearly paper value fluctuations then probably you'll also be concerned about yearly relative performance compared to alternative investments as likely that means that you're looking at the paper valuations on a relatively regular basis.  Where however you prefer a comfortable ride (relatively stable paper value) and are happy to be rewarded with inflation plus a few percentage points (i.e. real gains) without relatively comparing actual total rewards achieved compared to (potentially higher rewarding) alternatives then you'll probably be less likely to capitulate out of the PP.