Volatlity Harvesting

[melveyr]

I found an interesting paper that can help explain the strong historical performance of the PP:
www.iinews.com/site/pdfs/JWM_Fall_2012_Parametric.pdf

The paper shows how rebalancing low correlation asset classes can be produce positive returns even if the asset classes in isolation have 0 expected return. This is nothing terribly new of course for an avid PP fan, but I thought it was a nice presentation that is reassuring. Diversification offers free lunch with regards to risk reduction, and free dessert with regards to a rebalancing bonus 

[greenv]

Excellent . The paper and your summary!

[MachineGhost]

The paper shows how rebalancing low correlation asset classes can be produce positive returns even if the asset classes in isolation have 0 expected return. This is nothing terribly new of course for an avid PP fan, but I thought it was a nice presentation that is reassuring. Diversification offers free lunch with regards to risk reduction, and free dessert with regards to a rebalancing bonus 

Indeed.  I've come to the conclusion that the PP relies on technical analysis for its just desserts.  Whether it is rebalancing, trend following, momentum or some other kind of technical analysis, it is critical to improving the risk-reward ratio.  I'd like to see a comparison between all of these methods.

[melveyr]

The paper shows how rebalancing low correlation asset classes can be produce positive returns even if the asset classes in isolation have 0 expected return. This is nothing terribly new of course for an avid PP fan, but I thought it was a nice presentation that is reassuring. Diversification offers free lunch with regards to risk reduction, and free dessert with regards to a rebalancing bonus 

Indeed.  I've come to the conclusion that the PP relies on technical analysis for its just desserts.  Whether it is rebalancing, trend following, momentum or some other kind of technical analysis, it is critical to improving the risk-reward ratio.  I'd like to see a comparison between all of these methods.

It is interesting how the more I dig into the surface level areas of quantitative finance the more I come to appreciate the PP. I don't know if Mr. Browne was a genius, lucky, or both. He wrote a lot about explicitly seeking volatility in the markets using LEAPS and zero coupon bonds, so the harvesting mentality was definitely internalized for him.

[AdamA]

The paper shows how rebalancing low correlation asset classes can be produce positive returns even if the asset classes in isolation have 0 expected return. This is nothing terribly new of course for an avid PP fan, but I thought it was a nice presentation that is reassuring. Diversification offers free lunch with regards to risk reduction, and free dessert with regards to a rebalancing bonus 

Indeed.  I've come to the conclusion that the PP relies on technical analysis for its just desserts.  Whether it is rebalancing, trend following, momentum or some other kind of technical analysis, it is critical to improving the risk-reward ratio.  I'd like to see a comparison between all of these methods.

It is interesting how the more I dig into the surface level areas of quantitative finance the more I come to appreciate the PP. I don't know if Mr. Browne was a genius, lucky, or both. He wrote a lot about explicitly seeking volatility in the markets using LEAPS and zero coupon bonds, so the harvesting mentality was definitely internalized for him.

Enjoyed that very much.  Thanks for posting.

What did HB say about LEAPS?

[melveyr]

Indeed.  I've come to the conclusion that the PP relies on technical analysis for its just desserts.  Whether it is rebalancing, trend following, momentum or some other kind of technical analysis, it is critical to improving the risk-reward ratio.  I'd like to see a comparison between all of these methods.

It is interesting how the more I dig into the surface level areas of quantitative finance the more I come to appreciate the PP. I don't know if Mr. Browne was a genius, lucky, or both. He wrote a lot about explicitly seeking volatility in the markets using LEAPS and zero coupon bonds, so the harvesting mentality was definitely internalized for him.

Enjoyed that very much.  Thanks for posting.

What did HB say about LEAPS?

Before he settled on index funds he was hunting for more volatile stock funds. He proposed things like "aggressive growth" funds and using long dated LEAPS for equity exposure. The idea was to have something with a lot of volatility, which would work with the other volatile assets as part of the portfolio.

I think he settled on index funds because they are so practical.

[MachineGhost]

It is interesting how the more I dig into the surface level areas of quantitative finance the more I come to appreciate the PP. I don't know if Mr. Browne was a genius, lucky, or both. He wrote a lot about explicitly seeking volatility in the markets using LEAPS and zero coupon bonds, so the harvesting mentality was definitely internalized for him.

No kidding.  And it looks more and more that it was a huge mistake for HB to stop recommending high beta mutual funds.

I'm still reading, but the paper is fascinating (esp on coin flipping generating a positive growth rate).  Besides pseudo-mean reversion in randomness, it is all but claiming that the rebalancing effect comes from exploiting the same cognitive biases that inhibit achieving above average performance.  That's certainly a new perspective on the how.  I'm not sure I buy it but I'll keep reading.

[melveyr]

I did my own simulation using the rand() function on google docs. This shows how rebalancing between 3 coin flip games with zero expected return can produce gains. The coin flip game works by doubling your money if you get heads, and halving it if you get tails.



If it works properly it should update every once in awhile with a new simulation 

[MachineGhost]

I believe this chart will update every minute or so with a new simulation

Lets not get carried away.  You need to at least add in .39% transanction costs per trade just as Vegas takes its vig, otherwise everyone would get rich from playing roulette.

Edit: And taxes!  See my new thread on that subject.

[melveyr]

I believe this chart will update every minute or so with a new simulation

Lets not get carried away.  You need to at least add in .39% transanction costs per trade just as Vegas takes its vig, otherwise everyone would get rich from playing roulette.

Hah, well I will keep this simulation friction-less for now, but yes transaction costs are very important in the real world. That is why I like the wide 15/35 bands that Browne recommended (not too mention the small momentum affect which I am happy to participate in).

[sophie]

I did my own simulation using the rand() function on google docs. This shows how rebalancing between 3 coin flip games with zero expected return can produce gains.

Brilliant!!!  Thank you melveyr!!

There is a lot to digest in this paper.  One topic that really caught my attention:  A buy and hold strategy suffers a penalty on returns equal to one half the variance of the asset.  This is a topic that Craig and MediumTex touched on in their book, but with this framework you can say a lot more.  The conventional wisdom that holding a portfolio concentrated 90%+ in a single asset is in fact costly to the investor because of this drag effect - which gets bigger the more volatile the asset.  Yet, this is exactly what most retirement plans have you doing, with stocks!  So the idea that a 50/50 mix of stocks and bonds is more "conservative" and would produce lower growth than 100% stocks, may be exactly wrong.

The rebalancing premium may also explain why actively managed funds underperform index funds more than half the time.  Index funds are mainly about staying balanced, in order to follow the specific index, so they are maximizing their chances of getting the rebalancing premium.  Whereas actively managed funds probably spend more time being out of balance.  Thus an active manager's bets may pay off half or even more of the time, but because of drag from the variance and less of a rebalancing premium, the fund ends up losing out to the index.

It truly amazes me, how the PP is so perfectly designed.  And remember this next time you have to go buy something you think will do poorly.

[MachineGhost]

There is a lot to digest in this paper.  One topic that really caught my attention:  A buy and hold strategy suffers a penalty on returns equal to one half the variance of the asset.

But does anyone truly do a buy and pray strategy except maybe those old fuddy duddies that collect hundreds of divided-paying stocks?  Either way, you may find the below formula for converting average annual return (AAR) that Wall Street loves to parrot out to the more real worldy compound annual growth rate (CAGR) interesting in light of the above:

(1+AAR)^2 - (Standard Deviation)^2 = (1 + CAGR)^2

So essentially, AAR is only equal to CAGR when the standard deviation is zero.  Hence, the difference beween CAGR and AAR is the penalty of the volatility drag!  Ouch.

Whereas actively managed funds probably spend more time being out of balance.  Thus an active manager's bets may pay off half or even more of the time, but because of drag from the variance and less of a rebalancing premium, the fund ends up losing out to the index

The vast majority of active managers are penalized if they have high tracking error, so they cannot be out of balance for more than a quarter.  And yet, managers cannot generate any alpha unless they diverge from an index.  When it is your job on the line instead of a vocation, what do you think human nature defaults to?  Especially if you're getting paid six figures to rip the stupid muppet's faces off?  Passive index funds almost always replicate market-cap weighted indexes that do not rebalance by inherent design.  The advantages of passive indexing comes largely from the quantification, not the return penalty of the subpar index that is being replicated.

It truly amazes me, how the PP is so perfectly designed.  And remember this next time you have to go buy something you think will do poorly.

I wouldn't go that far.  The PP evolved over time via intentional simplicity.  It was just a coincidence that simple equal weighting beats market cap weighting, but it does not beat other weighting schemes that would be hard for the non-tech savvy to implement.  The effect is more noticeable at the asset class level than the portfolio level, though.  And it still does not belie the fact that the PP is risk overweighted to the most risky asset of gold just as risk parity is overweighted to bonds.  A truly risk neutral portfolio would not be equal weight.

[sophie]

But does anyone truly do a buy and pray strategy except maybe those old fuddy duddies that collect hundreds of dividend-paying stocks? 

Love that phrase...I may borrow that.  Some of the fuddy duddies may be reading this though.  A value portfolio producing a stream of qualified dividends isn't the worst strategy for retirement.

It truly amazes me, how the PP is so perfectly designed.  And remember this next time you have to go buy something you think will do poorly.

I wouldn't go that far.  The PP evolved over time via intentional simplicity.  It was just a coincidence that simple equal weighting beats market cap weighting.

I read somewhere that HB didn't just guess at the 25% allocations.  He borrowed some time on a supercomputer (which probably had about the power of a modern ipad) and ran simulations.  It may be that the "optimum" weighting was not precisely 25%, but was close enough to it.  I found it interesting that the rebalance premium is maximal at about the point of equal weighting, i.e. it's a symmetric parabola with zeros at 0%/100%.  Another consideration, of course, is that risk parity depends on back testing and predictions may not pan out going forward.

The one area in the PP that I wanted to tinker with was the bonds:  they're not volatile enough to match stocks and gold.  The spread on zeros is still high compared to nominal bonds, but they're not terrible when spread out over 10 years.  I wonder if HB would advocate buying zeros for the PP now, at least in tax advantaged accounts, especially with EDV to make things really easy.  I bought a couple of zeros and got to compare the bump in value on Friday with the nominal bonds I own with the same maturity date:  4.0% vs 2.38%.  Wow.

[Pointedstick]

The one area in the PP that I wanted to tinker with was the bonds:  they're not volatile enough to match stocks and gold.  The spread on zeros is still high compared to nominal bonds, but they're not terrible when spread out over 10 years.  I wonder if HB would advocate buying zeros for the PP now, at least in tax advantaged accounts, especially with EDV to make things really easy.  I bought a couple of zeros and got to compare the bump in value on Friday with the nominal bonds I own with the same maturity date:  4.0% vs 2.38%.  Wow.

Yeah, it's pretty nuts; my EDV did the same. A PP with Zeroes instead of 30-year treasuries and a small-cap value index fund instead of a total stock index fund would be quite a beast .

[melveyr]

Another kind of silly hyper-leveraged PP could involve EDV, SLV, and VWO. You would weight them at 1/vol of the the last 3 years of daily moves. All of those components act kind of like leverage components of TLT, GLD, and VTI respectively. I will probably stick with the vanilla PP however 

Sophie, whenever I run the numbers I notice that LTT, gold, and TSM have had roughly equivalent volatility for the last 3 years. Even if I was trying to do a quant risk parity I would still end up really close to a HBPP... Perhaps you were looking at window of time farther back? I don't think the PP has always been as balanced as it has been lately.

[sophie]

...whenever I run the numbers I notice that LTT, gold, and TSM have had roughly equivalent volatility for the last 3 years. Even if I was trying to do a quant risk parity I would still end up really close to a HBPP... Perhaps you were looking at window of time farther back? I don't think the PP has always been as balanced as it has been lately.

Yes, going back to 2005 you find stocks (SPY) have volatility of 21%, GLD is 21%, and bonds (TLT) are 14%.  Over the same period, EDV is 28%.  Just for kicks I also checked IJR (small cap index):  26%.  Obviously such measurements depend very much on the economic conditions in the time period of the test.

This is not to say bonds will be less volatile going forward, but I think it makes perfect sense to add some zeroes/EDV to the mix without departing from the PP's framework.  HB was clearly tempted by zeroes (see discussion in his 1987 book), but steered clear because of the large spread at the time and likely also because of the tax issue.

Anyway I didn't mean to hijack this thread, but I'd thought about zeroes in the past along the lines of matching risk, and the implications of maximizing volatility in this paper has revived my interest.

[melveyr]

...whenever I run the numbers I notice that LTT, gold, and TSM have had roughly equivalent volatility for the last 3 years. Even if I was trying to do a quant risk parity I would still end up really close to a HBPP... Perhaps you were looking at window of time farther back? I don't think the PP has always been as balanced as it has been lately.

Yes, going back to 2005 you find stocks (SPY) have volatility of 21%, GLD is 21%, and bonds (TLT) are 14%.  Over the same period, EDV is 28%.  Just for kicks I also checked IJR (small cap index):  26%.  Obviously such measurements depend very much on the economic conditions in the time period of the test.

This is not to say bonds will be less volatile going forward, but I think it makes perfect sense to add some zeroes/EDV to the mix without departing from the PP's framework.  HB was clearly tempted by zeroes (see discussion in his 1987 book), but steered clear because of the large spread at the time and likely also because of the tax issue.

Anyway I didn't mean to hijack this thread, but I'd thought about zeroes in the past along the lines of matching risk, and the implications of maximizing volatility in this paper has revived my interest.

Pardon my ignorance, and/or if this has been answered before, but how exactly does one go about calculating the volatility of an asset?

Get a series of daily, weekly, monthly, or yearly % returns in a spreadsheet. Then use the STDEV.P() formula on that series to arrive at the "standard deviation" or volatility of the investment. Its a measurement of how much the returns vary versus the mean return of the investment. So if an investment returned exactly 5% every single year, always, the standard deviation of yearly returns would be 0.

You can also transform the returns of the securities into the natural log returns if you want to get nerdy about it 

[BearBones]

Does this paper shed more light on the relative merits of a barbell vs bullet bond/cash holding? Seems that it would support a barbell.

[dualstow]

Just read the paper. Great stuff!
I admire the successful hunters, but I guess I'm a lazy harvester,and a content one.

EDIT: I should mention that "read" above is past tense, /RED/. Ho letto il paper.
I wasn't telling BearBones or anyone else to go read the paper. 

[MachineGhost]

I read somewhere that HB didn't just guess at the 25% allocations.  He borrowed some time on a supercomputer (which probably had about the power of a modern ipad) and ran simulations.  It may be that the "optimum" weighting was not precisely 25%, but was close enough to it.  I found it interesting that the rebalance premium is maximal at about the point of equal weighting, i.e. it's a symmetric parabola with zeros at 0%/100%.  Another consideration, of course, is that risk parity depends on back testing and predictions may not pan out going forward.

The supercomputer backtesting was for coming up with the PRPFX portfolio.  The 4x25 was a muppet simplification done for a book almost a decade later.  So if PRPFX turned out to be too biased to stagflationary assets, I argue the PP has a similar weakness as well.  Gold alone contributes a whopping 67% of the portfolio's historical risk exposure.  So all those skeptics weren't wrong, they just didn't elucidate it quantitatively.

What investors (and Wall Street) don't seem to understand about risk is that if you go back in history far enough, you will eventually measure the maximal amount of risk you would never expect to suffer in your natural lifetime, but if you unfortunately do, you have wisely factored it into the portfolio weight ahead of time before the damage occurs.  If it comes down to portfolio overexposure to the riskiest asset because of a heuristic rule of thumb for the muppets (i.e. the equal weight PP) vs actual market history, I will opt to go with the latter.  It seems to me that it is far better to be surprised to the upside in the future than to have your expectations and your capital crushed from short sighted rationalizing and ignorance of risk.

Anyone care to wager how many people will jump ship the next time the PP hits a 25% maximum drawdown?  And the number may even be larger in the future because debt deflation potential is trillions of times larger than in 1980.  Hiding behind a cult of equal weight is not adequate risk control.  No one can take a hit to their net worth of 25% unless they're emotionally dead or completely delusional.

[dualstow]

Anyone care to wager how many people will jump ship the next time the PP hits a 25% maximum drawdown?  And the number may even be larger in the future because debt deflation potential is trillions of times larger than in 1980.  Hiding behind a cult of equal weight is not adequate risk control.  No one can take a hit to their net worth of 25% unless they're emotionally dead or completely delusional.

I'll be emotional, but I can take the hit. In fact, I *have* taken quite a large hit from when I was in stocks and very little else.

[dualstow]

I agree it's true that most stock-heavy investors, if they've done step 1 of investing research, expect more severe downturns. But expecting it/ talking about it are very different from going through it. In other words, expecting it or knowing of the possibility didn't cushion the blow that much.

I get your point, though- many of us have come to the pp because of losses, temporary or otherwise, in supposedly riskier portfolios. I'll certainly be disappointed if I lose more than 20% in a single year. But, I guess I'm in what MG called the cult. We'll see how it works out.

One thing that might help: "rebalancing" from the vp (if it's up) into the pp!

[melveyr]

Regarding the "cult of equal weight" I don't think that the PP is crazily unbalanced or anything like that. When I do backtests from the 1978-2012 period I found that the equal risk contribution portfolio for the risky PP assets is
(defining equal risk contribution by using Mr. Roncalli's method http://www.thierry-roncalli.com/download/erc-slides.pdf )

38% 30 Year Treasury
34% stocks
28% gold

That was the perfect equal risk contribution portfolio. The fact that the perfect quantitative solution ex-post isn't very far from the ex-ante prescription of Mr. Browne indicates to me that the 3 way split was pretty darn good in the past. So why overly complicate future allocations?

[MachineGhost]

That was the perfect equal risk contribution portfolio. The fact that the perfect quantitative solution ex-post isn't very far from the ex-ante prescription of Mr. Browne indicates to me that the 3 way split was pretty darn good in the past. So why overly complicate future allocations?

I think the real point here is equal weight and equal risk contribution rank near the bottom of possible approaches.  Putting lipstick on a pig may make it look a little prettier, but it is still a pig.

Code: Select all

Equal Weight 3x33			8.60%	-29.84%
Equal Risk Contribution (34,38,28)	8.70%	-27.94%

Has the ERC method been discussed over in the Engineering thread?

[melveyr]

That was the perfect equal risk contribution portfolio. The fact that the perfect quantitative solution ex-post isn't very far from the ex-ante prescription of Mr. Browne indicates to me that the 3 way split was pretty darn good in the past. So why overly complicate future allocations?

I think the real point here is equal weight and equal risk contribution rank near the bottom of possible approaches.  Putting lipstick on a pig may make it look a little prettier, but it is still a pig.

Code: Select all

Equal Weight 3x33			8.60%	-29.84%
Equal Risk Contribution (34,38,28)	8.70%	-27.94%

Has the ERC method been discussed over in the Engineering thread?

Hmm I actually don't think so. It is very similar to the 1/vol method except that it also takes into correlation coefficients, it offers a purer definition of price risk in the context of your portfolio but is highly dependent on correlation (which we all know is painfully unstable). I think 1/vol would be better for generating allocations over short term time windows because correlation is so unstable but I like using the ERC formulas to look back on a portfolio to see where the risks came from over a long period of time.