seeking a deeper understanding of the PP

[jomby]

I'm just starting to learn about investing, macroeconomics, portfolio theory, etc., and I'm seriously considering going with the permanent portfolio with most of my money.  It sounds reasonable, and there don't seem to be too many great counterarguments, and the people who are into it seem pretty smart.

However, I still have the problem that I really have no clue what is going on.  I come from a math background, and most of the reasoning for why the permanent portfolio is good doesn't even come close to resembling a proof.  Harry Browne always talked about how "the future is simply too hard to predict".  But that's what probabilities are for, right?  And he said stuff about having uncorrelated assets that are all volatile enough to counteract each other well.  Is there some mathematical reason why the combination of low correlation and high volatility are good?  Also, why are there only four different underlying economic conditions, and how do we know these four assets are the best for each one?  Is this agreed upon by all economists?

If someone could point me in the right direction, I'd really appreciate it.  I've read a bunch about the permanent portfolio now, and I am excited about it, but most of the arguments I have read are too "intuitive" and not mathy enough, and it concerns me.  I want something deeper than metaphors like rudders on ships or a gyroscopes or whatever.  If I don't hear about stuff like expected value, variance, Kelly criterion, Pareto efficiency, etc., I get scared.

[craigr]

I'm just starting to learn about investing, macroeconomics, portfolio theory, etc., and I'm seriously considering going with the permanent portfolio with most of my money.  It sounds reasonable, and there don't seem to be too many great counterarguments, and the people who are into it seem pretty smart.

However, I still have the problem that I really have no clue what is going on.  I come from a math background, and most of the reasoning for why the permanent portfolio is good doesn't even come close to resembling a proof.  Harry Browne always talked about how "the future is simply too hard to predict".  But that's what probabilities are for, right?  And he said stuff about having uncorrelated assets that are all volatile enough to counteract each other well.  Is there some mathematical reason why the combination of low correlation and high volatility are good?  Also, why are there only four different underlying economic conditions, and how do we know these four assets are the best for each one?  Is this agreed upon by all economists?

If someone could point me in the right direction, I'd really appreciate it.  I've read a bunch about the permanent portfolio now, and I am excited about it, but most of the arguments I have read are too "intuitive" and not mathy enough, and it concerns me.  I want something deeper than metaphors like rudders on ships or a gyroscopes or whatever.  If I don't hear about stuff like expected value, variance, Kelly criterion, Pareto efficiency, etc., I get scared.

Ok there are different ways to answer this. But first of all there is no proof that can be applied to the stock market. The primary reason is that the market is made up of millions of people making millions of decisions for various chaotic reasons and modeling that kind thing is impossible.

So it is easier to break it down into economic cycles because that ultimately is the result of these market actions and impact of the monetary supply.

A prosperous market is going to be that way for many reasons and how it got there is not something that is predictable. Same for the other conditions. For instance in 2008 there was no reason to try to predict a real estate crash would cause deflation. The simple fact that you held the asset that does best in deflation is all the mattered, not how we got there or what predictive model could have seen it coming.

Next please understand that engineers can be their own worst enemy when investing. Because they want to apply the precision of science and engineering to the markets. But unfortunately the markets cannot be broken down into a statistical model. In fact, there is serious debate if gaussian type statistical tools are even applicable as have traditionally been used (I believe they are not for various reasons). There is a reason why economics is called the "dismal science." It simply doesn't lend itself to precision.

Lastly when Harry Browne said the future is too hard to predict is the reason why probabilities do not apply. Plenty of very smart mathematicians have been completely surprised by the moves of the markets that their models said would never happen statistically. You may enjoy the book When Genius Failed that details the explosion at Long Term Capital Management by some Nobel Economists. That incident could have taken down the financial markets. Then of course there was the cascading failure of 2008 which other models said couldn't happen either. So when applying the tools of math to the markets you can get a very false sense of security.

Honestly I wish the markets were so easy to predict that some statistical models could be used to eliminate all the risks and get extra reward. But a lot of really smart people using really good hardware have tried to do this repeatedly in the past and as a strategy it is fraught with peril.  

[craigr]

However, I still have the problem that I really have no clue what is going on.  I come from a math background, and most of the reasoning for why the permanent portfolio is good doesn't even come close to resembling a proof.  Harry Browne always talked about how "the future is simply too hard to predict".  But that's what probabilities are for, right?  And he said stuff about having uncorrelated assets that are all volatile enough to counteract each other well.  Is there some mathematical reason why the combination of low correlation and high volatility are good?  Also, why are there only four different underlying economic conditions, and how do we know these four assets are the best for each one?  Is this agreed upon by all economists?

Ok some more specifics.

Although not touted by Harry Browne, his ideas have strong backing in Modern Portfolio Theory. So there is mathematical proofs there for the reasoning behind diversification: http://en.wikipedia.org/wiki/Modern_portfolio_theory

The Efficient Market Hypothesis represents the reasoning for why stock picking doesn't work well (I am closer to the semi-strong form myself): http://en.wikipedia.org/wiki/Efficient- ... hypothesis

I think total market investing is probably the best idea: http://www.norstad.org/finance/total.html

The construction of the Permanent Portfolio indicates that it does not believe in time diversification: http://www.norstad.org/finance/risk-and-time.html

Understanding bond convexity may help you realize why non-callable treasury bonds work best for falling interest rates: http://en.wikipedia.org/wiki/Bond_convexity

Hope that helps get your math fix for now.

[KevinW]

I come from a math background, and most of the reasoning for why the permanent portfolio is good doesn't even come close to resembling a proof.  

This thread covered similar ground:
http://gyroscopicinvesting.com/forum/ht ... 1.msg11851

I also have some math background. IMO you'll never see a satisfying rigorous math proof of this sort of thing because it deals with unknowable future world events and human emotional reactions, neither of which can be modeled satisfactorily. Some people try to model these things as continuous normally-distributed random variables, but I think that's always on thin ice.

***

The logic for the PP goes like this:

The real economy's growth is on a continuum between growth (prosperity) and contraction (recession). In a fiat currency system, the money supply is on a continuum between oversupplied (inflation) and undersupplied (deflation). So at any point in time the economy's state is some linear combination of prosperity-recession and inflation-deflation.

For any quadrant Q except recession, there exists an asset A s.t. if the economy is in Q then A rallies:
if prosperity is happening then stocks rally
if deflation is happening then long term bonds rally
if inflation is happening then gold rallies

And,
if recession is happening then cash's utility is neutral or amplified (but it doesn't quite "rally").

The volatile assets carry risk premia and the non-gold assets appreciate due to the time preference of money. So in the limit, each appreciates.

So we have that, under all circumstances at least one asset is rallying; and that over time each of the four assets appreciates. The combination of one strongly-positive asset and three more-often-positive-than-negative assets, is almost always positive.

(If you assume a probability distribution on asset returns then you can compute the probability of seeing a loss over a time interval. It's very low. But as stated I'm uneasy with making those kinds of assumptions.)

And he said stuff about having uncorrelated assets that are all volatile enough to counteract each other well.  Is there some mathematical reason why the combination of low correlation and high volatility are good?

This is the "rebalancing bonus." It is described in detail in any modern portfolio theory book, e.g. "Asset Allocation" by Gibson. It works because compound interest curves are exponential functions, which are convex.

[stone]

A very crude (I'm sure much too crude for someone like you with a maths background) way to think of the rebalancing bonus is that if an asset class is volatile and more or less maintains its value long term, then the price will be say alternately halving and doubling ie 50% loss then 100% gain. If you shuffle money from a gainer to top up a looser and that then  reverts, then you gain more than you lost. So long as all the assets are not in lockstep, then you tap into the fact that a 100% gain from the same starting point means more dollars than a 50% loss.

The PP relies on that fact that the four assets are chosen so as to link them into contradictory economic conditions. This makes it very hard to get a scenario that is bad for all four at the same time. As a result there is always a reservoir with which to top up the losers.

The PP assets are also chosen to be very very broad and reliable so as to give the most confidence that over the long term each of them will somewhat retain much of their value. That means that a dip in any one of them can be relied on to be followed by a rise at some point in the future (such cycles can take decades though as with stocks in the 1929 to 1950 period or 1970s, LTT in the 1960s and 1970s or gold from 1980 to 2000 or whatever)

[stone]

I'm very ashamed of my innumeracy which is only matched by my spelling. Am I correct in imagining that a coin flip model of the PP, where each of gold, LTT, and stocks doubled or halved depending on whether that year was "heads" or "tails" and cash stayed the same; would give a CAGR of about 14%

0.5+0.5+0.5+1=2.5=x0.625
2+0.5+0.5+1=4=x1
0.5+2+0.5+1=4=x1
0.5+0.5+2+1=4=x1
2+2+0.5+1=5.5=x1.375
2+0.5+2+1=5.5=x1.375
0.5+2+2+1=5.5=x1.375
2+2+2+1=7=x1.75

(0.625x1x1x1x1.375x1.375x1.375x1.75)^(1/8)=1.139

[jomby]

Thanks everyone for the very helpful responses.  I am starting to understand the rebalancing bonus and how it relates to convexity.  This part seems mathy enough for me to eventually be less skeptical.

I am still a little confused about the behavior of the individual components however.  How is it that gold and long-term treasuries can both go up over the long run?  In the simple model in my head, they have to eventually cancel each other out, but I'm sure there is a deeper economic explanation for why this doesn't have to happen.

[craigr]

I am still a little confused about the behavior of the individual components however.  How is it that gold and long-term treasuries can both go up over the long run?  In the simple model in my head, they have to eventually cancel each other out, but I'm sure there is a deeper economic explanation for why this doesn't have to happen.

Over time gold will match inflation more or less. Basically 0% real returns. However over shorter periods it can lag or exceed inflation and those returns can be captured with rebalancing or protect you during serious currency crisis.

Long term bonds will over time pay an interest rate that exceeds inflation by a margin the markets think is adequate reward to compensate for future inflation expectations.

So over time both assets go "up" in price. Gold because the dollar is constantly falling and is repriced in current dollar value. Bonds because they are generating new dollars from interest payments to offset inflation.

At least that's the theory. In reality the assets are moving in jerky movements at times as the markets work out these details.

[stone]

Thanks everyone for the very helpful responses.  I am starting to understand the rebalancing bonus and how it relates to convexity.  This part seems mathy enough for me to eventually be less skeptical.
I am still a little confused about the behavior of the individual components however.  How is it that gold and long-term treasuries can both go up over the long run?  In the simple model in my head, they have to eventually cancel each other out, but I'm sure there is a deeper economic explanation for why this doesn't have to happen.

First off, the rebalancing bonus means that even if none of the four assets showed any long term growth, the overall portfolio could still grow.

I think LTT and gold both benefit from falling interest rates. The spike in interest rates at the end of the 1970s has been slowly unwinding ever since and that has created falling yields (rising prices) for LTT. Interest rates below inflation (negative real rates) are a big driver for higher gold prices. Also both gold and LTT prices benefit when there is more money looking for something to do than the real economy can find a use for. Governments are desperate to engineer economic expansion and yet at the same time to keep wages down. The result is a deluge of cheap money available for investment and yet a dearth of money available for consumption. So the money goes to bidding up LTT and gold prices.

Gold obviously does not move in lockstep with LTT. Inflation makes LTT much much less attractive than gold and a strengthening USD is very bad for gold.

[MediumTex]

Although I am more "wordy" than "mathy", you should also internalize the concept that the value of any non-leveraged asset has a hard floor at zero but no similar ceiling, and thus the asset you buy for $50 might go to $500 or more in favorable market conditions but will NEVER go below 0.  When thinking about the PP, many rookies intuitively seem to believe that the asset you buy for $50 can only go to $100 and then it must stop, since this is the mirror image of the maximum potential loss you could experience on the asset.  When you think about it in more detail, of course, you see that this is not the case.

In other words, when someone says "The PP doesn't actually work because the asset movements cancel one another out" they are normally thinking in the terms I am describing above.

[moda0306]

Also, there's probably a few important things to flesh out that some of the more simplistic explanations don't detail:

Gold during Inflation: Really, it's almost always about Real Interest Rates.  If you can earn positive real yields on risk-free instruments (the gov't is set up so it can ALWAYS pay its bonds back, so there's no default risk), then gold will usually and rightfully decline.  This doesn't mean there's no inflation... but simply that you can save risk-free and beat it.  So when people say "gold isn't a good inflation hedge," they are right in a really screwed up misleading way... but it's EXACTLY what you want in a portfolio with other assets that may or may not be delivering to you REAL returns.

Bonds During Deflation: Technically, we don't have to have overt deflation for LTT's to do great.  Simply lower-than-expected inflation will suffice.  So don't think "well we've had 2 periods of deflation in the last 100 years, and one was recent, so LTT's are barely ever useful."  They're almost what I'd consider the most "perfect" diversifier to stocks you could find: A fixed payment for a long time from the most stable entity in world denominated in your domestic currency AND the world's reserve currency.

So don't let the imperfection of these assets to fit with their supposed economic condition scare you... the whole thing works... it's those nuances about inflation & deflation w/ gold and LTT's that MAKE it work... they're a feature, not a detriment.  If gold crept up with CPI, it wouldn't be what we want in the PP.

[stone]

Clive, is it possible that the pronounced gradual trend of LTT yields during the 1980-2000 "great moderation" made them less choppy than we might see in the future? I've been using 20%-30% bands (a bit tighter than the recommended 15%-35%) and so did hit a rebalance with UK 50year treasuries this winter (they swung in price from 91 to 125 and are now back down to 113). In the short term that has helped a bit but I have no idea whether time will show that that was pointless or counterproductive.

For a UK PP, gold saved the day in 2008. BUT for a US PP, wouldn't 2008 have been much worse with 5year treasuries rather than LTT ?

I'm really wondering whether the 1980-2000 "great moderation" might be a one off event and won't be encountered again at least in our lifetimes

[stone]

moda, I think you are making a good point that it is not the suitability of the assets that is at fault it is the descriptions of the "four economic conditions" that are a bit inadequate.

[stone]

For a UK PP, gold saved the day in 2008. BUT for a US PP, wouldn't 2008 have been much worse with 5year treasuries rather than LTT ?

Yes instead of something like a +2% in 2008 a US PP with 50% cash instead of STT/LTT barbell would have been down something around -5%. In 2009 however likely that gap would have been closed down - didn't US LTT's lose something like -25% in 2009.

Wouldn't the added purchase of stocks from rebalancing out of LTT at the end of 2008 have uplifted the US PP enough to offset the 2009 drop in LTT prices?

[AdamA]

I come from a math background, and most of the reasoning for why the permanent portfolio is good doesn't even come close to resembling a proof. 

You might consider reading the first four chapters of William Bernstein's "The Intelligent Asset Allocator" (will you take about a half hour).    He gives a very aesthetically pleasing description of how modern portfolio theory works.  He only uses stocks and bonds, but you could easily apply the logic to cash and gold as well.

It's as close as you'll get to a "proof," and I definitely agree with what Craig said about applying the laws of the physical sciences to markets...it's dangerous, and it just doesn't work.