Return Distributions

[DeepState]

Hey RY,

I am really enjoying your contributions to this [the - change by RY] forum, you have already given me enough ideas to research and play around with for a long time. Thank you.

..What are your thoughts on black swan events? A system may have a positive expectancy, but a significant enough chance of a total meltdown. And the longer you run the system, the greater chance of running into one eventually.

Australian market is an interesting example at the moment. A lot of value strategies, at the moment would be almost totally invested in mining services companies. Chance of a catastrophic event for a portfolio is thus significantly higher, as it only needs to happen in one industry.

What are your thoughts on controlling systems to lower this risk, what kind of manual overrides to allow, and how to not let those overrides be abused?

Thanks KnowThePast. Please let me know what comes up and what challenges the theses that I have proposed. They are just lift-outs from published and peer reviewed stuff from the major journals and not original to me anyway. So, if you find something out of place....let's put it out there! Or trade the heck out of it...first.

Black Swans are....painful. Deep jump skews. Depending on how you are positioned, either its a fabulous day or a stunned mullet day. Taleb obviously had a lot to say. I would point you to the Sante Fe institute for research in complexity theory for a really colourful way of thinking about it. They brought together heaps if discliplines to figure out things like why crowds do crazy stuff, how DNA/RNA might have first formed. All of these are Black Swans and it is useful to grab everything you can. One of my favourites is the Sand Castle analogy by the now-deceased Per Bak. You could code it in a few hours and watch it unfurl. And there you have an analogy for the kind of scenario you are metioning and pretty much anything you can imagine.

I also am a believer in Minski whose thesis is another way of saying Black Swan.

Any deeply integrated system which involves people or any positive feedback is susceptible to Black Swans. The bigger that system, the bigger the potential event is. Financial markets and underlying economies, government and populace are all linked and hence this fits squarely into those requirements.

Black Swans dominate your return profile. Everything else hardly matters in the end. That's why stock returns are highly leptokurotic and skewed for short time periods. It's why options trade with skew for near term maturity, including in banks given the credit risk they bear is largely a blow-up risk.

They will happen and, as you say, the longer you go, the greater the likelihood you will encounter one. So what do you do?

Diversify. Hold lots of stuff and, if they are somewhat uncorrelated, then you can survive the bumps. But that's not enough, because correlations jump and effective diversity declines in sharp moves. So here we get closer to something interesting. How can you ensure that diversity will exist in a correction? After all, that's when diversity matters most?

You suggest that value would be loaded into Mining Services and this might be an aggregation of risk. If this is right, you will observe decreasing effective diversification within the Mining Services group of companies. That is, the correlations between the stocks will increase. That's a bloody big warning sign. The same could be said of any sub-group of stocks that you could be concerned about. You now need to adjust your portfolio to increase diversity if this is happening. I wouldn't just use numbers. I would be like you and think about it. The right answer is judgment based. I would not hesitate to put on positions that were not supported by statistical outcomes if I thought it was right. Statistical tests do have error in them and knowing when it is a false negative and likelihood of that being the case is an important judgment. It could also be that you know that the underlying systemic structure is poised in a tense state but simply has not encountered the kind of circumstance that would lead it to be visible in market prices. Use everything you have at your disposal! And even then we'll massively fail to catch a lot of things that go bump in the night.

There is also auto-correlation in volatility. This is harvested by people who use GARCH type time series models or others like it like EWMA etc. You can also spot it in options implied vol. In reality, you need both because neither are particularly dominant over the other and a combo proves the best way forward in general.

After all that, you move to tail risk hedging. Put a floor under you. If you can't hack it, protect it. Lay the risk you cannot bear off to the guy who can...and can back it.

Also...having a long time horizon is one of the best things you can bring to the table. This is longitudinal diversity. Those deep skews and other bad behaviours of stock and other security prices, they largely disappear when horizons lengthen. If you can do that, things look pretty tranquil. Rolling 20 year returns don't look very bumpy do they? Rolling monthly ones look shocking.

How do you stop manual overrides from being abused? One way is to be explicit about why you have the override, the kind of evidence you expect to see if this is true and a time line for removing it in the absence of contrary evidence. I don't have a magic solution. This is the area where people distinguish themselves from each other. It's a judgment and often, those judgments are wrong.

I think the biggest thing is that you have to stay alive to play. There is no certainty about the magnitude of Black Swans, so you need to know your butt is covered and this comes at a cost. Or you can self-insure and hope the big one doesn't collect you before you depart this planet.

 

[McLovin]

Any deeply integrated system which involves people or any positive feedback is susceptible to Black Swans.

My favourite example of the perils of positive feedback.

Yes, it's a bit OT.

 

[DeepState]

My favourite example of the perils of positive feedback.

Yes, it's a bit OT.

My favourite single line description of the potential for systemic collapse where humans are concerned:

A person is smart. People are dumb, panicky, dangerous animals, and you know it.

— Agent K

 

[KnowThePast]

Thanks KnowThePast. Please let me know what comes up and what challenges the theses that I have proposed. They are just lift-outs from published and peer reviewed stuff from the major journals and not original to me anyway. So, if you find something out of place....let's put it out there! Or trade the heck out of it...first.

Black Swans are....painful. Deep jump skews. Depending on how you are positioned, either its a fabulous day or a stunned mullet day. Taleb obviously had a lot to say. I would point you to the Sante Fe institute for research in complexity theory for a really colourful way of thinking about it. They brought together heaps if discliplines to figure out things like why crowds do crazy stuff, how DNA/RNA might have first formed. All of these are Black Swans and it is useful to grab everything you can. One of my favourites is the Sand Castle analogy by the now-deceased Per Bak. You could code it in a few hours and watch it unfurl. And there you have an analogy for the kind of scenario you are metioning and pretty much anything you can imagine.

I also am a believer in Minski whose thesis is another way of saying Black Swan.

Any deeply integrated system which involves people or any positive feedback is susceptible to Black Swans. The bigger that system, the bigger the potential event is. Financial markets and underlying economies, government and populace are all linked and hence this fits squarely into those requirements.

Black Swans dominate your return profile. Everything else hardly matters in the end. That's why stock returns are highly leptokurotic and skewed for short time periods. It's why options trade with skew for near term maturity, including in banks given the credit risk they bear is largely a blow-up risk.

They will happen and, as you say, the longer you go, the greater the likelihood you will encounter one. So what do you do?

Diversify. Hold lots of stuff and, if they are somewhat uncorrelated, then you can survive the bumps. But that's not enough, because correlations jump and effective diversity declines in sharp moves. So here we get closer to something interesting. How can you ensure that diversity will exist in a correction? After all, that's when diversity matters most?

You suggest that value would be loaded into Mining Services and this might be an aggregation of risk. If this is right, you will observe decreasing effective diversification within the Mining Services group of companies. That is, the correlations between the stocks will increase. That's a bloody big warning sign. The same could be said of any sub-group of stocks that you could be concerned about. You now need to adjust your portfolio to increase diversity if this is happening. I wouldn't just use numbers. I would be like you and think about it. The right answer is judgment based. I would not hesitate to put on positions that were not supported by statistical outcomes if I thought it was right. Statistical tests do have error in them and knowing when it is a false negative and likelihood of that being the case is an important judgment. It could also be that you know that the underlying systemic structure is poised in a tense state but simply has not encountered the kind of circumstance that would lead it to be visible in market prices. Use everything you have at your disposal! And even then we'll massively fail to catch a lot of things that go bump in the night.

There is also auto-correlation in volatility. This is harvested by people who use GARCH type time series models or others like it like EWMA etc. You can also spot it in options implied vol. In reality, you need both because neither are particularly dominant over the other and a combo proves the best way forward in general.

After all that, you move to tail risk hedging. Put a floor under you. If you can't hack it, protect it. Lay the risk you cannot bear off to the guy who can...and can back it.

Also...having a long time horizon is one of the best things you can bring to the table. This is longitudinal diversity. Those deep skews and other bad behaviours of stock and other security prices, they largely disappear when horizons lengthen. If you can do that, things look pretty tranquil. Rolling 20 year returns don't look very bumpy do they? Rolling monthly ones look shocking.

How do you stop manual overrides from being abused? One way is to be explicit about why you have the override, the kind of evidence you expect to see if this is true and a time line for removing it in the absence of contrary evidence. I don't have a magic solution. This is the area where people distinguish themselves from each other. It's a judgment and often, those judgments are wrong.

I think the biggest thing is that you have to stay alive to play. There is no certainty about the magnitude of Black Swans, so you need to know your butt is covered and this comes at a cost. Or you can self-insure and hope the big one doesn't collect you before you depart this planet.

An awesome post RY, thank you.

This especially struck a chord with me:

Black Swans dominate your return profile. Everything else hardly matters in the end.

While I wouldn't go to extreme of saying that they dominate, they certainly play a huge part. And as you say, it is staying alive and being ready for them that becomes the priority.

On hedging, there's obviously many different hedges one could have. What would you think of shorts as the main strategy?

Statistically, I do not like shorting. They are riskier than long trades, and I would expect the expected return from them to be worse as well. Having part of your portfolio in short positions, however, should partially protect you from most of the black swans and as an added bonus, have you in a ready position to pick up bargains (via short profits).

This is currently one of my areas of research, and I still haven't reached a conclusion. So I am just talking aloud to keep the discussion going and hopefully learn some more.

 

[DeepState]

1. An awesome post RY, thank you.


2. On hedging, there's obviously many different hedges one could have. What would you think of shorts as the main strategy?

Statistically, I do not like shorting. They are riskier than long trades, and I would expect the expected return from them to be worse as well. Having part of your portfolio in short positions, however, should partially protect you from most of the black swans and as an added bonus, have you in a ready position to pick up bargains (via short profits).

This is currently one of my areas of research, and I still haven't reached a conclusion. So I am just talking aloud to keep the discussion going and hopefully learn some more.

Hi KTP

1. Thanks very much.

2. The tail risk hedge is essentially a short position that kicks in more strongly as things deteriorate. Hence it is a form of shorting and more positions are added as things deteriorate. Because you want to be decreasing your exposure as things deteriorate, something with a put option-like payoff for your main exposures is usually involved, or you can synthetically create them with linear instruments via stops, although this will be more slippery than options due to - slippage.

If you are running long-short strategies, then shorts will already feature. You might have put them on as part of a pair/risk-packet that found good value ideas relative to one another, or it might be just an outright position because you think some company or market sucks within a portfolio of other things you might be holding. But even then there are typically risks that can blow you up. Even market neutral funds have such exposure.

For example, a market neutral fund running tight pairs might have a long exposure to S&P 500 and a short on ASX 200. This position obviously has risk, and the potential for Black Swan. You would 'short / tail risk protect' this position by getting someone to write you an option on the difference via swap. That's totally BS for retail, of course. Alternatively, you would have stops that shut the position down as things deteriorate. These stops must always be on and updated frequently.

The concept is: what is your risk exposure? What can you hack? Protect the exposure that you can't handle via option or synthetic means.

Cheers

 

[KnowThePast]

Hi KTP

1. Thanks very much.

2. The tail risk hedge is essentially a short position that kicks in more strongly as things deteriorate. Hence it is a form of shorting and more positions are added as things deteriorate. Because you want to be decreasing your exposure as things deteriorate, something with a put option-like payoff for your main exposures is usually involved, or you can synthetically create them with linear instruments via stops, although this will be more slippery than options due to - slippage.

If you are running long-short strategies, then shorts will already feature. You might have put them on as part of a pair/risk-packet that found good value ideas relative to one another, or it might be just an outright position because you think some company or market sucks within a portfolio of other things you might be holding. But even then there are typically risks that can blow you up. Even market neutral funds have such exposure.

For example, a market neutral fund running tight pairs might have a long exposure to S&P 500 and a short on ASX 200. This position obviously has risk, and the potential for Black Swan. You would 'short / tail risk protect' this position by getting someone to write you an option on the difference via swap. That's totally BS for retail, of course. Alternatively, you would have stops that shut the position down as things deteriorate. These stops must always be on and updated frequently.

The concept is: what is your risk exposure? What can you hack? Protect the exposure that you can't handle via option or synthetic means.

Cheers

Thank RY, this is extremely helpful for my thought process.

What about this risk of unlimited downside for shorts? Are we swapping one risk for another?

 

[DeepState]

Thank RY, this is extremely helpful for my thought process.

What about this risk of unlimited downside for shorts? Are we swapping one risk for another?

No probs KTP

A naked short has unlimited loss potential. But, really, trees don't grow to the moon.

The shorts used as hedges offset the longs. That's if you are using the same for same. ie. Hedge ASX 200 futures with stops (a stop is a contingent short). You never end up at net negative (unless you design it to, in which case you become exposed to risk again on the short side and may, by symmetry, need to hedge your shorts with contingent longs).

If you have basis risk between your exposure to risk and the hedge instrument, say, hedging portfolio of ASX 20 with the SPI, then there is a theoretical possibility that the SPI can go to the moon as your ASX 20 basket craters. In very broad terms, these tightly correlated trades were what LTCM got up to, hedge something with another thing which should move in tight unison. For the most part, it did. But they couldn't survive the journey because convergence did not happen before they ran out of buffer and were liquidated...the market knew they were in trouble as well, figured out what they were doing, and killed them too by forcing stops to be hit. Being 100x leveraged most certainly did not help.

Estimate basis risk. If you are doing it, it generally means you've run out of alternatives to hedge your risk and have to use proxies. The usual way of doing this is to look at history as a starting point and then make some sort of adjustment. Our Head of Risk globally said: look at the worst drawdown you've encountered and, maybe, double it. However, if your trade is crowded, Black Swan risk exists here too. Strange things do happen. For example, if the Volkswagon issue, which disrupted or at least raised the eyebrow of markets, arose in Australia and the stock was outside the ASX 20 this basis risk could be savage for a little while. Give room on each trade to make sure you can hack that. In combination, if you are aware of risk aggregation, the chances of this blowing a true and permanent hole in your balance sheet moves into the truly remote category. Usually your whole portfolio doesn't hang on concepts like basis risk if you aren't Meriwhether and running 100x leverage.

 

[craft]

The concept is: what is your risk exposure? What can you hack? Protect the exposure that you can't handle via option or synthetic means.Cheers

The best and simplest way to deal with risk you can't handle is to not take it in the first place. To do that you really have to be fully around the first two points and that's where I believe people should focus.

 

[McLovin]

My favourite single line description of the potential for systemic collapse where humans are concerned:

A person is smart. People are dumb, panicky, dangerous animals, and you know it.

”” Agent K

That is very good.

 

[sinner]

What craft said can be empirically proved as true.

The cheapest and most effective "hedge" is to simply go to cash (at least, for long only systems).

Here is a good, recent article from Bronte Capital on the days when your hedging doesn't work and what to do

http://brontecapital.blogspot.com.au/2014/01/when-hedge-doesnt-work.html

Here is a scathing review of Talebs work by Eric Falkenstein, a low volatility proponent who I generally agree with. Not to say there aren't black swans, but that low volatility investing is long term profitable whereas lottery ticket (clipped left tail of the return distribution) investments are not so.

http://falkenblog.blogspot.com.au/2012/11/taleb-mishandles-fragility.html

http://falkenblog.blogspot.com.au/2010/12/nassim-taleb-imitates-kanye-west.html

 

[DeepState]

Eric Falkenstein, a low volatility proponent who I generally agree with. Not to say there aren't black swans, but that low volatility investing is long term profitable whereas lottery ticket (clipped left tail of the return distribution) investments are not so.

+1 and then some.

 

[craft]

What craft said can be empirically proved as true.

The cheapest and most effective "hedge" is to simply go to cash (at least, for long only systems).

Nice to see you back Sinner with your extensive links to resources.


Just to make it clear - I personally don't endorse going to cash as a risk control measure. Don't like cash in the first place and secondly a major risk you face if you are forced to go to cash for risk management is the slippage in actually getting there.

Correlation bombs are what sends most people running for risk cover and liquidity just doesn't exist in those times.

Many think him irrelevant - but once again Buffett has the most relevant quote to summarise what I think is the best risk control.

Only buy something that you'd be perfectly happy to hold if the market shut down for 10 years

Implicit in that quote is that you can justify and hold the investment based on the performance of the business itself and ignore the risks that others face by being reliant on market price to justify their investments.

 

[sinner]

Nice to see you back Sinner with your extensive links to resources.


Just to make it clear - I personally don't endorse going to cash as a risk control measure. Don't like cash in the first place and secondly a major risk you face if you are forced to go to cash for risk management is the slippage in actually getting there.

Correlation bombs are what sends most people running for risk cover and liquidity just doesn't exist in those times.

Hullo craft, thx, I think you will find that my participation is closely correlated to the types of discussion underway on the forum.

Probably your experiences with "going to cash" are a bit different from mine, due to most of my experience being at the "global macro" level of sectors, indices and big liquid asset classes whereas from my understanding you tend to stick to single equity names on the ASX.

Many think him irrelevant - but once again Buffett has the most relevant quote to summarise what I think is the best risk control.

Implicit in that quote is that you can justify and hold the investment based on the performance of the business itself and ignore the risks that others face by being reliant on market price to justify their investments.

I think it's extremely relevant, stocks are and should be viewed as representing the net present value of long term cash flows (just like all other investment securities) and therefore if you're not taking that into account it's likely that you are in fact speculating. The work of John Hussman on the inadequacies of the "Forward Operating PE" highlight this well. Interesting side note is that when it comes to predicting short term returns, valuations are useless. But when it comes to predicting long term returns (3,5,7,10Y), nothing does a better job than valuations.

 

[sinner]

and to highlight my last point, here is a different kind of "Return Distribution" chart, that of the distribution of returns over different starting valuations (in this case using the Q-ratio aka Tobins Q on the SP500)



From a paper by Mark Spitznagel titled "The Dao of Corporate Finance, Q ratios and stock market crashes", from back when he worked at the Taleb Universa fund...

 

[sinner]

and another distribution of (10Y) returns over starting CAPE (SP500)

From the (updated) seminal 2007 Mebane Faber paper "A Quantitative Approach to Tactical Asset Allocation"

you get the idea...

 

[sinner]

and finally if you look here

http://gestaltu.com/2013/08/valuation-based-equity-market-forecasts-q2-2013-update.html

You can see how increasing the investment timeframe increases the explanatory power (r-squared) of almost any given valuation measure - although in the case of the 30Y column everything is less but I think that's because over periods >10-20Y then more variation can be explained by variations in inflation and interest rates etc

 

[DeepState]

Hi Sinner

Great stuff. You have an awesome mental library facility.

How would you reconcile the weaknesses of Price to Operating Earnings comment made by Hussman and the very juicy cross sectional predictability chart based on straight multiples just published above?

Cheers

 

[sinner]

Hi Sinner

Great stuff. You have an awesome mental library facility.

How would you reconcile the weaknesses of Price to Operating Earnings comment made by Hussman and the very juicy cross sectional predictability chart based on straight multiples just published above?

Cheers

The weaknesses highlighted by Hussman are specifically in relation to the "Fed Model" using Forward Operating Earnings to represent the cash flows of the entire lifetime of the security...

"Long-Term Evidence on the Fed Model and Forward Operating P/E Ratios " - http://www.hussmanfunds.com/wmc/wmc070820.htm

If an investor is going to use the current level of earnings to determine the reasonable price to pay for a long-term asset, it had better be true that those earnings represent a normal and sustainable level of profit. You wouldn't buy a lemonade stand by extrapolating the profits it earns in August.

Hussman is a big fan of CAPE and P/Sales, anything that better describes the cashflows of the security over its lifetime.

If you take the so called "Graham Value Stock Portfolio" from Scotts Investments (only just saw this recently) - http://www.scottsinvestments.com/2014/04/15/graham-value-stock-portfolio-update-5/ which is a sample value portfolio you can see using the trailing (rather than forward) OPE as a component of an aggregate value score it works OK in a practical sense and this is confirmed in academic research.

EDIT: Also the multiples above are CAPE as in PE10, not PE1 and Q ratio which is more akin to Price/Book. You can see from the r-squared graph that explanatory power for PE1 is much lower than PE10 for all timeframes.

 

[craft]

and to highlight my last point, here is a different kind of "Return Distribution" chart, that of the distribution of returns over different starting valuations

And another from Crestmont research based on USA data.

20 year rolling market return based on starting P/E.

 

[craft]

This is interesting too.

especially the break-up of the 10 year return into components.