Thought Bubbles from the Deep

[peter2]

The expectancy is as stated and the problem is that LTI is investing too much on each coin toss.

The Kelly Criterion shows the optimum bet size for this proposal is to "invest" no more than 20% on each toss.

K% = 0.6 - [0.4 / AW/AL] = 0.6 - 0.4 = 0.2 = 20%

In practice the Kelly calculation can produce large draw downs, even using the correct position size, but as LTI sets off metal detectors at airports he will be able to handle that and profit handsomely if he is allowed to invest more wisely.

 

[barney]

- actually I'm just make most of this **** up so its probably all wrong)

(give or take a bourbon or two)

LOL .............. now you're speaking a language I can understand

Good thread DeepS

 

[craft]

The expectancy is as stated

Yep in theory but in real life only if the bet size is the same dollar amount each time. As soon as you start talking fractional size of a portfolio for position sizing or any dynamic position size for that matter you better start thinking geometric rather than arithmetic or the expectancy calculation isn't going to tell you diddly squat about real life. Individual size, and sequence of every win/loss skews the real life expectancy from theory. (as the extreme analogy demonstrates)

Keeping the bet size small will at least stop the misconceptions about expectancy hurting you too much in real life.

If the LTI was allowed to change the rules and ask for a constant bet size small enough that he would effectively have no chance of ruin then he could have had a shot at the theoretical 18% expectancy - except 240 occurrences is not enough to mean much given a 60/40 win rate. Position size should be a synthesisation of your acceptable drawdown tolerance based on the probable string of losses that can arise given your win rate and the correlation of your positions if you have multiple positions.


Ps

Habakkuk – You weren’t my high school maths teacher were you?

 

[satanoperca]

Hi,

Been playing with individual position size (1% of capital), portfolio position size, portfolio heat at any time in the market (% amount at risk at anyone time regardless of the number of positions based on stops and an error factor for slippage/gap downs) and win/loss ratio while counting for a large run of loses in a row and size of potential draw down.

It would be great if anyone could elaborate on how they calculate how much is at risk if there is a wipe out day and stops at hit. What % of capital.

Another question is if the bet was :

LTI had a win loss ratio of 50%, coin toss
LTI was paid 100% of his capital for each win
The man only 50% of LTI's capital a win

Would LTI be better off?

 

[craft]

The expectancy is as stated and the problem is that LTI is investing too much on each coin toss.

The Kelly Criterion shows the optimum bet size for this proposal is to "invest" no more than 20% on each toss.

K% = 0.6 - [0.4 / AW/AL] = 0.6 - 0.4 = 0.2 = 20%

In practice the Kelly calculation can produce large draw downs, even using the correct position size, but as LTI sets off metal detectors at airports he will be able to handle that and profit handsomely if he is allowed to invest more wisely.

If you are talking 20% of cumulative balance that will keep you in the game but the variance in the equity curves are insane, the importance of the 18% theoretical expectancy is absolutely dwarfed by the real world impact of sequence of wins and losses.

4 different random simulations with same variables: 60% win rate; 90%win amount; 90% loss amount; 20% of current balance as bet amount.



Run 1 final balance of $18,009,347 – 62% max drawdown
Run 2 final balance of $1,409,357 – 84% max draw down
Run 3 final balance of $2,896 – 99% max drawdown
Run 4 final balance of $17,873 – 97% max drawdown.

If you are talking fixed dollar amount based on initial account size, 20% is far too high a risk of ruin.



Anyrate enough dribble from me apparently I should be showing more interest in going shopping - yay Joy.

 

[cynic]

Hi,

Been playing with individual position size (1% of capital), portfolio position size, portfolio heat at any time in the market (% amount at risk at anyone time regardless of the number of positions based on stops and an error factor for slippage/gap downs) and win/loss ratio while counting for a large run of loses in a row and size of potential draw down.

It would be great if anyone could elaborate on how they calculate how much is at risk if there is a wipe out day and stops at hit. What % of capital.

Another question is if the bet was :

LTI had a win loss ratio of 50%, coin toss
LTI was paid 100% of his capital for each win
The man only 50% of LTI's capital a win

Would LTI be better off?

Lti would break even after a typical succession of coin tosses. I.e. 0.5 X 2 = 1.

1^n will always equal 1.

 

[DeepState]

.....24 minutes later, the last coin toss is made. LTI is in too much shock to notice what the outcome was. After all, a number next to zero multiplied by 1.9 or 0.1 is still pretty much still next to zero.

LTI: What the deep fried sushi?? I've just toasted my entire portfolio!!! That's BS, you're farking with me!!!

Man: My pants are still on, Gaijin. It is your y-fronts which are stretched over your back, over your face and tucked under your chin.

LTI: (Muffled) How can this be? The coins did toss up a 60% hit rate. The payments were as specified. The trade by trade outcome has an expectancy of 18%. Like Buffett. Dammit, I have read his annual reports and never take more than 5 seconds to conduct a DCF. How can this be??? (shock turning to table thumping)

Man: Not quite so straight forward is it LTI.

LTI: How did your fiendish sleight of hand work? TELL ME!!

Man: On any given trade, the exected return is 18%. Compounding these is a whole other thing. Any positive expectancy has to be great enough to allow for recovery of losses. The more extreme the potential outcomes, the harder it is to achieve.

LTI: But with positive expectancy and a long term horizon, I should make money and am right to be impervious to drawdowns.

Man: Get this through your head - Apparently not. Do the math. Alternatively, ask someone who can. Apparently there are Australian equity chat sites that have such people. The compound return here was about -21%. A pretty far cry from the expectancy you have heroicially generated and based so much of your confidence on. Here, have a sake. On the house.

LTI: What if I had implemented a stop loss and skipped two rounds or more if I had taken three losses in a row? What if I waited for a three win set-up to position?

Man: There is no combination of these things that would have changed this outcome except for not taking up the challenge in the first place or effectively sitting out so much of it that there was essentially no play. These coins have no memory of what the last outcome was.

LTI: What if I diversified? What if we ran the coins on two original parts of my portfolio instead?

Man: As it turns out, you aren't the only LTI we've been fuelling our foreign reserves with. You are the 1000th this month. Each one ended up like you. Busted despite 18% expectancy, lots of stop loss and sit out programs, steel body parts. Some had big accounts, some had small accounts. And everything in between. Put them all together and you have the equilvant of a buy-hold, diversified, portfolio of stocks with 18% period to period return expectations and return outcomes that we had decribed. That combined portfolio also went to the BOJ balance sheet.

LTI: Misery loves company.

Man: Wouldn't know.

LTI: Although somewhat extreme, the set up is kind of like that for the kinds of stocks most talked about on HC. Other very smart people on an excellent site that I have come across and provide general advice on, ASF, have also made such observations too. Analysis of the turnover of the commentators who are the most frequent traders and hot and heavy on high-spec stocks like we have been modeling shows they don't last!

Man: Pure coincidence no doubt.

----

As the sun rises, the man and LTI are still at the bar.

LTI: What if....blah blah

Man: Busted...

..

LTI: (Through bleary eyes) What if I had split my portfolio into 100 equal parts and, at each turn, had 100 of those coins rolled independently. One coin for each portion of the porftfolio. No matter what happened, I would re-divide the portfolio into 100 equal parts and do this again in the subsequent rounds. What if I had done that for 240 rounds???

Man: LTI, may I call you Joe? Joe, the BOJ is pleased to stake you for USD $1bn. Here is a honeypot for your right arm (attractive arm candy arrives). Out in the world are millions of people who will take the other side of your trade. Your job is to take them down, but not so fast that newcomers with big eyes are discouraged from arriving in droves to replace the prior generation of hopefuls. Some will really have positive expectancy, steel body parts, long term investment horizons and perceptions of being impervious to drawdowns. Dack 'em anyway.

There will also be some who will not take the other side. Nod with respect. Also, it's probably a good idea to remember that coins and markets share similarities, but are not the same.


Please feel free to insert observations on money management that may be helpful to readers.

 

[qldfrog]

Thanks DS for your nice lesson in stats, risks and expectancies.Any feeling as tho the market general situation?
While not close yet at the time of this post, Wall Street still going downward, bringing the AUD along.
Oil and gold +- even when seen in AUD.
a needed drawdown or a more profund issue with the debt related to oil (and for Oz gas investment)
Does the "oil debt"and ramifications worries you?; I have no real idea which banks are exposed (here and O/S) and that info looks hard to get: exposure of banks to oil?
Please note that at this price i am actually bullish mid term for oil: I expect serious issues in S.A. coming from within and oil will not stay where it is when RIAD is in flamme, especially as I see probable a conflict with Iran triggered by the royals in S.A. to create internal diversions for their populace when things turn ugly.
Oil at 33$ today just need to go to $50 which is still quite low to create a 50% gain, I can wait 5 years for that and my return would be quite decent overall, so I see my risk more in the actual instrument I use (oil index OOO)
HAve a nice week end

 

[DeepState]

Thanks DS for your nice lesson in stats, risks and expectancies.Any feeling as tho the market general situation?
While not close yet at the time of this post, Wall Street still going downward, bringing the AUD along.
Oil and gold +- even when seen in AUD.
a needed drawdown or a more profund issue with the debt related to oil (and for Oz gas investment)
Does the "oil debt"and ramifications worries you?; I have no real idea which banks are exposed (here and O/S) and that info looks hard to get: exposure of banks to oil?
Please note that at this price i am actually bullish mid term for oil: I expect serious issues in S.A. coming from within and oil will not stay where it is when RIAD is in flamme, especially as I see probable a conflict with Iran triggered by the royals in S.A. to create internal diversions for their populace when things turn ugly.
Oil at 33$ today just need to go to $50 which is still quite low to create a 50% gain, I can wait 5 years for that and my return would be quite decent overall, so I see my risk more in the actual instrument I use (oil index OOO)
HAve a nice week end

HNY QF

Not following markets to any great detail at present. Brain dump:

Economics looks alright in big picture summary terms so this sell-off appears sentiment driven. Big falls in LatAm accompanying China. Must be something more to it given the commodities are also moving. Can't all be a supply side issue for all I am guessing. Risk spreads continue to increase in the debt market with CDS spreads continuing to widen. Perhaps the equity market is catching up to risk being priced in again. All fine if that is all that it is and the process is orderly. Key risk is that financial conditions in EM tighten a lot. Can't tell if this is going on already on a big scale. No analysis done. Someone out there prob has a Goldman Sachs Financial Conditions index to hand and can share it.

Usual risk aversion trades are going on. Cannot fully comprehend why China equity tail would wag global dog in a direct sense. Can understand if contagion takes hold. That's hard to predict but you can imply the pricing from movements, sort of, under a bunch of tenuous assumptions. Too much movement to be consistent with the bond market pricing of risk assets - again on a quick look basis only. Could argue that this is an equity valuation correction which was just looking for an excuse. That is valid, in my view, for the US. Craft has outlined the calculations under XAO Bull. Do this for the US and you get a different answer. Just BTW, that thread might want to consider the imbalance between the shape of the Australian economy and the earnings in the index before drawing tight outcomes from the analysis and macro settings like GDP/Capita etc. Need to allow for resource demand not being Aust sourced and additional capital requirements for banks etc. Might already be obvious to them.

Not shifting anything major in my portfolio. Downside equity moves have been largely offset by bond yields coming in and AUD weakness in my case. Still taking some limited losses given the long bias, but not cutting my holiday short. No movements made on protection levels. Easy not to be stressed when not looking and frequently inebriated. Interesting, actually, to compare this to the last round in terms of emotional involvement. I think there may be optimal alcohol levels for investment. Not zero.

Major efforts recently are to find an improved departure point for my Australian equity portfolio. That is, what should my equity portfolio look like if I conducted absolutely zero fundamental analysis or otherwise had no directional view on any stock. It isn't the index.

No forecast on oil. You can forecast it, but the information content is questionable given it is a price between inelastic consumers and suppliers in the near to medium term. Small changes in the real economy lead to large price movements. 1% supply increase has large consequences. The geopolitical elements are games on top of games. I am an interested observer. Interesting that Saudi Aramco might list. Tells you something about Saudi government finances. Think they will provide greater transparency to the market and help stamp out any corruption that might or might not exist???

China devaluation was in line with my earlier statements and expectations given ongoing reserve drain and underlying PPP deflation. If Europe and Japan can do it, why not peg yourself against them as well and do it too. Makes it harder for the world to get going....and this is also a reason why developed markets might fall, but there is more to that argument and it is late.

I think we have seen this movie before. I can't tell if it will have the same ending.

 

[qldfrog]

Appreciated and indeed HNY DS

 

[DeepState]

Was interested in all the recent machinations of the onshore and offshore renminbi markets. Was curious as to how it all operates given it is clearly seen to be pivotal to stabilising financial markets more broadly and the exchange rate more specifically. Offshore interest rates were absolutely soaring recently as Chinese authorities soaked up the offshore supply to support the currency in the offshore market. In the process it was trying to shake out shorts and limit the arbitrage between the on and offshore rates. It seems like the type of thing that happens when some emerging market economy is running out of reserves and getting into the last gasp of defending its currency. China probably isn't a good parallel to that. Maybe.

Research consisted of typing a few terms into Google search and reading the very first article that came up. "The difference between the confusing onshore and offshore renminbi market" from Business Insider in 2013

http://www.businessinsider.com.au/difference-between-onshore-and-offshore-renminbi-2013-2

Some phrases of interest:

+ The crucial thing about the offshore renminbi is...free of Beijing's control

+ Borrowing costs are much cheaper in the CNH bond market

+ The expectation that the renminbi would appreciate has been a key factor driving demand for CNH

How things change.

 

[DeepState]

FT reports that we are at peak gold supply for the current cycle.

 

[sinner]

FT reports that we are at peak gold supply for the current cycle.

So much mining capacity (not just for gold, I guess) has been brought online during the commodity boom, as you well know it requires a lot of capital investment and relatively long lead times for that capacity to come online. So I guess it is hardly surprising we are at peak supply.

I think the peak will fall off rapidly as projects get mothballed, especially if there is financial sector contagion "we can't find your only-just viable gold mine because we are liquidating twenty completely unviable CSG and tight oil projects".

I guess I am one of only a few on the forum who even consider it interesting that we are at "peak gold supply" from mining and yet the inventory of physical gold has been drained from the bullion banking system (of which LBMA and GLD make up easily to two largest reserves) nonstop for 4 years. What does it mean when we are at "peak gold supply" and they still need to drain LBMA to meet demand?



I can already hear the clackety-clack of people replying (don't bother, this is a one off visit) "but, sinner, the inventory drain is merely because the price of gold went down!"...um...I guess that is why SLV is still carrying the same ~10,000 tons it has been carrying since 2011 when the USD price of an ounce of silver was ~$50 and now its ~$13.

 

[DeepState]

I learned tonight that you trade more speculatively when hungry than when feeling satiated. (During dinner with an expert on obesity of all things - though neither of us could be said to be carrying any extra)

Evolutionarily, when you are needing nourishment in a big way, I suppose it would be better to take risk to get a kill rather than die of 'risk-free' starvation. This effect is visible in the kinds of gambles that people choose to take when hungry.

FYI:

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0011090

I suppose it is important to keep in a good state of internal equilibrium when investing/trading. Staying glued to a screen without adequate attention to basic needs is hazardous to your wealth and health.

 

[qldfrog]

Thanks DS, a good rational excuse for that additional chocolate bar!
But it makes sense: hunger (both physical or wealth) is not a good advisor;
see how people under financial stress are the ones often making the riskiest investment and losing the lot;
Some people may then wonder cause or consequence:
Are you under financial stress because you make stupid riskier financial decisions in the first place?
In any case, more lasagna for me tonight..maybe

 

[DeepState]

The BoJ recently announced a foray into NIRP, Negative Interest Rate Policy. This follows the actions of other central banks, notably the ECB but also including Denmark and Sweden.

In April 2013, Kuroda (Bank of Japan Governor) introduced the so called QQE. A major monetary stimulus which was, proportionately, more significant than those of the ECB and Fed. At the time, the BoJ expected that a 'virtuous cycle' would emerge which would lift inflation back to 2% per annum (all items excluding food) in "about two years". This was designed to shake off the deflationary mindset which has beset Japan for over a decade.

The target date has been pushed out further with time despite increasingly aggressive actions. Most recently, the expectation is for the inflation rate to reach the target level in the "first half of 2017"...but only if oil prices rise moderately from here. Interesting that the BoJ has to take a punt on the future of oil prices to find a way to meet their targets. Clearly a stretch argument, albeit plausible.


In more recent times, the ECB has indicated that more stimulus seems to be called for. The tightening bias in the BoE has been withdrawn. The US market is pricing in a single tightening in 2016 of 0.25%, relative to the Fed member expectations for four tightening steps in 2016.

Is it looking like monetary stimulus has run its course? Or is this some temporary thing caused by the fall in oil and slowing in the emerging markets...partly caused by a fall in oil revenue?

The monetary authorities have largely been the prime force holding up the economy and keeping financial burdens in check. Enormous faith has been placed in them. What if it isn't justified? Alternatively, what if it is justified, but they've now exhausted their credible tool set*? Yet the markets continue to react as if there is still juice in this strategy. Hmmm.


* More stuff like buying direct assets, financing infrastructure directly etc. have been proposed....can you imagine the RBA building, say, the East-West Link in Melbourne?? That's the sort of thing being discussed. Never say never I guess.

 

[So_Cynical]

I guess I am one of only a few on the forum who even consider it interesting that we are at "peak gold supply" from mining and yet the inventory of physical gold has been drained from the bullion banking system (of which LBMA and GLD make up easily to two largest reserves) nonstop for 4 years.

One of the few, peak Gold and yet the POG holds up, i've been on the peak gold band wagon for a while.

 

[DeepState]

What portfolio should you hold if you want a basic exposure to the Australian market as a source of equity risk premium?

The benchmark indices are arbitrary in the sense that a large bank is held at large weight simply because it is big. Had a major buyer come in and taken a strategic chunk, reducing the float available in the bank, free-float adjusted exposures would fall. Nothing changed in the operating environment. The benchmark indices are an indication of aggregate holdings available to public investors who do not take strategic chunks of companies. It will produce returns better than the average of such investors due to the presence of frictions. An odds on strategy to be above the money-weighted average of investors is simply not to try to beat the rest. Add tax considerations to this and, depending on the rate and whether you are a trader/investor, these frictions become very meaningful, although a few percent can seem trivial to many on this site...it isn't over time and considerably raises the bar to argue against a pure index approach. Nonetheless, is there a better starting point?

Risk parity is a concept which was brought into popularity by Ray Dalio of Bridgewater Associates, the world's largest hedge fund manager. The idea has evolved to, kinda sorta, build a portfolio whose main components had equal risk contributions (proportion of overall volatility). This was a set and forget technique which required no further judgment about the future performance other than volatility and correlations. That is, no specific return forecasts are made. Dalio's idea was to apply this to a trust for his family after he had passed away...hence no forward looking judgment on returns, beyond estimation of risk.

By doing this, the portfolio is well balanced in terms of risk contributions. Each stock in the portfolio contributes the same amount to the volatility of the portfolio. Risk parity. This takes into account volatilities and correlations, which have been demonstrated to be much more stable in estimation than for return forecasts for such things.

If all banks are essentially the same, adding another bank to the portfolio will see the exposures redistributed amongst all the banks, not an addition to the overall weight. That seems pretty sensible.

In other words, the risk parity portfolio does the best it can with the stocks available to build a widely diversified portfolio. One whose exposures are as widely spread as possible given risk estimates. The very diversified nature of the portfolio helps to protect against estimation errors. It takes into account things like a bank's performance tends to be rather similar to the environment for discretionary consumer behaviour.

Based on data to late last year, the risk parity portfolio for Australian equities vs the ASX 200 index had the following GICS exposures (I have broken up Financials into finer definitions given their dominance in the Australian market):




It has much less exposure to banks, preferring to spread the exposure more towards consumer discretionary stocks and other cyclical sectors (eg. IT and Industrials). The more stable nature of healthcare stocks (in general) sees them being given more weight. Interestingly, the exposure to materials remains fairly in line. I think it is clear that this portfolio is more diverse and possibly a more sensible way to gain exposure to the Australian market components.

The portfolio spreads its exposures differently from simply equally weighting the components. However, the broad exposures do produce a significant bias away from the largest companies. Although the exposure to small capitalisation companies is much larger than for the index, the diversification produced by this portfolio reduces the overall expected volatility relative to the index. By dramatically reducing the exposure to large capitalisation stocks, company specific blow-ups are less impactful and pretty much no company specific event is going to hurt that much.

I believe this concept is a useful consideration in determining a suitable departure point for a portfolio. The expected range of performance of this portfolio relative to the index is +/-2.6% on a 1-std devn basis (ie. within this range two-thirds of the time over a year). This means that variation in physical exposure via the use of index futures is viable. There are also some rebalancing benefits which can be expected. If you think that all stocks in the index are expected to have the same geometric return (if you started them all at $1, they will just wiggle around like dust in the air, which has a small breeze, as the prices evolve. None is particularly destined to shoot away to either extreme), the RP portfolio is expected to produce about 1.4%per annum more from rebalancing effects (it won't get this due to frictions, but an edge will remain).

 

[skc]

The monetary authorities have largely been the prime force holding up the economy and keeping financial burdens in check. Enormous faith has been placed in them. What if it isn't justified? Alternatively, what if it is justified, but they've now exhausted their credible tool set*? Yet the markets continue to react as if there is still juice in this strategy. Hmmm.

What is most interesting to me is that, few people acknowledge the fact that, economics is only an emerging area of study/science. Economics only really received much prominence since the great depression in the 30's... so while it's a field of some 80-90 years old, it's also a field that has a very slow feedback loop and is the subject of so many external factors. So we barely know which, if any, of the economic theories are correct and able to stand the test of time.

Most of the actions by Central Banks these days are untested. They have not been done before and they certainly have not been proven to work in the current economic environment (whatever that means in terms of our demographics, stage of technological advancement and stage of the natural resources). It will have unintended consequences and it may work for a while until some equilibrium is tipped somewhere else in the system.

I personally have zero faith in the action of monetary authorities. If they achieve what they set out to achieve, it could be pure fluke as much as anything else. It is truely a bit scary that billions of people's livelihood are being determined / influenced by a bunch of people in Central Banks based on untested theories.

Strange times we live in.

 

[sinner]

Risk parity is a concept which was brought into popularity by Ray Dalio of Bridgewater Associates, the world's largest hedge fund manager. The idea has evolved to, kinda sorta, build a portfolio whose main components had equal risk contributions (proportion of overall volatility).

Regardless, here is the counterveiling view from Warren Buffett, the world's most successful fund manager (as measured by longevity weighted returns):

Stock prices will always be far more volatile than cash-equivalent holdings. Over the long term, however, currency-denominated instruments are riskier investments — far riskier investments — than widely-diversified stock portfolios that are bought over time and that are owned in a manner invoking only token fees and commissions. That lesson has not customarily been taught in business schools, where volatility is almost universally used as a proxy for risk. Though this pedagogic assumption makes for easy teaching, it is dead wrong: Volatility is far from synonymous with risk. Popular formulas that equate the two terms lead students, investors and CEOs astray.

...

It is true, of course, that owning equities for a day or a week or a year is far riskier (in both nominal and purchasing-power terms) than leaving funds in cash-equivalents. That is relevant to certain investors — say, investment banks — whose viability can be threatened by declines in asset prices and which might be forced to sell securities during depressed markets. Additionally, any party that might have meaningful near-term needs for funds should keep appropriate sums in Treasuries or insured bank deposits.

For the great majority of investors, however, who can — and should — invest with a multi-decade horizon, quotational declines are unimportant. Their focus should remain fixed on attaining significant gains in purchasing power over their investing lifetime. For them, a diversified equity portfolio, bought over time, will prove far less risky than dollar-based securities.

(from http://www.berkshirehathaway.com/letters/2014ltr.pdf)

There are 3 major categories of risk:
1. Systemic risk.
2. Systematic risk
3. Idiosyncratic risk

My is only to point out that neither the approach of Berkshire or Bridgewater evaluate and cover all three, although I would submit that Berkshire comes closer than Bridgewater. Even funds like Talebs Empirica that went to great pains to ensure their counterparties would be able to pay on vol explosions, always placed their feet squarely on a foundation that "cash is king". Concepts like a major reserve currency crisis were simply not included in their assumption set.

Disclaimer: Submitted as someone who tracks volatility across different stocks and asset classes and believes it to be a useful quantitative tool for investment decisions.