The Portfolio MYTH-----Do you need to change your thinking?

[DeepState]

Hi Deepstate --

To my thought, the procedure is pretty clear and pretty much all trading system developers have the requisite domain knowledge.
... Development:
1. Use the data prospector to curate a list of potential candidates.
2. For each candidate, attempt to develop a long / flat trading system using the scientific method. The model is rule-based, uses state signals, marks-to-market daily, is looking for trades that are accurate, frequent, and hold a day or two. If a traditional trading system development platform is being used, an oscillator with a fast cycle works. Pick any one, since at that rate, all are equivalent. Or some other indicator of your choice that will give about 50 signals per year.
3. Also attempt to develop short / flat systems, but there will be lower success.
... Trading:
1. Bring data up to date and evaluate all the systems daily, computing safe-f and CAR25. If the one with the highest CAR25 has a score higher than a risk free account, take a position using safe-f portion of the account.
2. As the jingle says -- rinse and repeat daily.

Still one system at a time, one day at a time.

Volatility was one of the characteristics examined by the prospector. When he or she passed it originally, volatility was acceptable. If it increases at a later time, dynamic position sizing will identify that and lower safe-f and the CAR25 score, moving it down the list of those available to be traded.

If AmiBroker is being used, I have published several models that work.

If Python / machine learning is being used, I have published one decision tree model showing that it replicates the traditional platform. Also examples of about ten alternative models that can be applied with little change to anything. And suggestions for additional predictive variables.

Modeling experience and skill become more important here. The magic sauce, whose recipe developers of machine learning trading systems will hold close, is which additional predictor variables are useful, what steps are taken to create stationary data, and what data preparation is used.

Best regards, Howard

Howard, it's not the broad process mechanics that I am questioning. Though, thanks for writing it out again, and in more depth, to shed more light.

Ultimately, this is another process framework with a range of parameters upon which the success and failure of an effort will rest. In broad terms, I agree with the concepts used in risk deployment. There is merit in checking for performance in a recent period in the belief that regime rigidity is a feature and might help with prediction in that environment. CAR25 is a selection criteria and is a reasonable one.

None of these will save you from throwing garbage at it. And, if the skill of the operator is what differentiates the winners from losers, it was so before this approach was conceived and remains so.

The main question I have relates to portfolio construction. This is a thread where a strong statement about 2 stock portfolios was raised. In my view and in my experience of seeing and participating deeply in professional money management of the real and hedge variety, this is unsupportable for situations outside of play money. And that's fine if so.

Yet, you came along and seriously expressed support for a 1 stock portfolio. And it is this I wanted to explore. Your proposition is 1 stock at any given time consuming the full risk allocation. You will appreciate that the position is an extreme one, but you are a man of serious intellect where statements seem to have rationale, even if we might reasonably disagree on those merits.

So, I say to you that, even under the framework of CAR25 and safe-f, you would be better off holding more than 1 stock at a time. Yes, your current process only selects the best CAR25 over some horizon using all sorts of permutations along the way as may be codified. End of the day, Howard Bandy: 1 stock...full risk deployment on safe-f.

I do not think I am misunderstanding you when I say:

+ Surely, if you had a million well chosen signals feeding in to a soup of algos over a range of instruments, and their merits, however obtained, were ranked first to last on any given day...that you would feel that only one was valid. Yet, that is what the system does.

+ If signals other than the one ranked one have any merit given the skills of the operator, others with lower rankings also have solid expectations. Let's say that these signals are issuing a BUY on some other instrument so there is no overlap. These are currently not used in the Bandy System.

+ By not using signals which also have solid expectations and allowing for portfolio effects, you will produce worse risk adjusted results than otherwise achievable. If the operator is skilled at selecting candidate signals for ranking, that would be a huge information loss.

+ By putting all weight on the 'best' only, the system actually produces a risk-adjusted outcome which is far from best in a portfolio sense.

Reasons why you would not do this include:

+ A trivial case of where the inputs are known to be garbage and no algo to screen them can convert garbage to alpha without finding a latent factor via the screening alone.

+ You literally believe only one of the candidate signals in the primordial soup truly had positive expectation. This would justify full risk deployment on this one instrument on the one signal on this particular day. Whist things may be non-linear in life and require special techniques to identify the underlying order, this kind of binary, first is right and the rest is junk for today, outcome is wildly unreasonable in my view or a sign of a highly unstable set of candidates where identification of merit would already be highly tenuous.

Comment sought:

1. Do you think that only one signal, that chosen as 'best' by the process for a given day, has merit in terms of positive expectations? That the rest have absolutely no merit at all on the ranking criteria beyond that placed first?

2. If the screening criteria does rank in a way which helps us order the merit of signals and others are also somewhat valid, why should this information not be used and result in these signals combining in to a portfolio setting, given an aggregate safe-r equivalent (adjusted as required for whatever you like to get this estimate) and then deployed in to the market. More than 1 stock at a time.

Regards

DS

 

[howardbandy]

Comment sought:

1. Do you think that only one signal, that chosen as 'best' by the process for a given day, has merit in terms of positive expectations? That the rest have absolutely no merit at all on the ranking criteria beyond that placed first?

2. If the screening criteria does rank in a way which helps us order the merit of signals and others are also somewhat valid, why should this information not be used and result in these signals combining in to a portfolio setting, given an aggregate safe-r equivalent (adjusted as required for whatever you like to get this estimate) and then deployed in to the market. More than 1 stock at a time.

Earlier in your post you suggest there might be a million well chosen signals. My view is different. There might be a dozen or two. The data prospector tests each candidate data series for its inherent risk and profit potential and liquidity. Most fail. A few dozen pass. These are the ones that become candidates to have models applied to them. Assuming that every one of those data series does have persistent and detectable patterns that precede profitable trades, there are still not many of them.

Then to your questions.

1. Assume that there are 20 systems that have passed validation and are being followed each day. CAR25 is the risk-normalized profit potential of each. Immediately remove from consideration for today's trade any that have a CAR25 below risk free. There might be days when none remain, but assume there are two. (The math works for any number.) ABC has CAR25 of 15, XYZ has CAR of 9. Each has its own safe-f -- assume they are both 1.00, meaning that all funds can be used to buy shares. The account has $100,000 available. Our choice is whether to buy $50,000 worth of both ABC and XYZ, or $100,000 worth of ABC. Splitting the funds used drops the CAR25 from 15 to 12 -- 0.5*15 + 0.5*9. Yes, put all the funds into the single best alternative.

Anticipating a followup question. Yes, there will be fluctuations and we have no assurance that the results will match the estimates. Those fluctuations apply to all. If there was some reason to expect that XYZ was the better use of funds, that reason is either: subjective, in which case and all bets are off; or objective, in which case the model should be refit to take the new information into account, possibly raising the CAR25.

2. Does the example I used in responding to question 1 give enough to answer? The CAR25 of any portfolio is the average of the CAR25s of the components.

This process is repeated daily. When conditions change, CAR25 changes. The rankings change. Tomorrow's choice might be different than today's.

Best, Howard

 

[howardbandy]

It would seem that you advocate more frequent trading [shorter signals]. Correct me if this is not the case.

I would argue that for many retail traders, this is simply not the way forward. Intra-day and daily price moves are simply too noisy.

Yes, I definitely recommend frequent trading and short holding periods. The research is compelling. I have written about this extensively. My mantra is: trade frequently, trade accurately, hold a short period, avoid serious losing trades.

I recommend using daily data, using state signals (compare with impulse signals), forecasting one day ahead, and managing daily. Managing daily means mark-to-market daily, measuring equity highs and lows on daily prices, and being willing to change position for the next one-day holding period daily.

Your question suggests perhaps using less frequent management or longer data bars. I have not been able to develop any system that passes validation using weekly, or longer, bars. Those that have come close to passing have much lower CAR values than systems using daily data and holding a few days at most. It is up to the trader whether he or she is willing to ignore intra-trade changes in equity between management activities. I recommend being willing to ignore intra-day changes, but not intra-week changes. Mark-to-market each day at the close, being able and willing to either: continue the same trade for one more day; close out the existing trade and change to a new position for one day; close out the existing position and remain flat for one day. This is the sweet spot of having a life other than trading, but actively managing trading.

I do not necessarily advocate use of intra-day bars and creation of systems that regularly trade more than once per day. Intra-day systems are an order of magnitude more complex than end-of-day systems. Complications include acquiring and managing historical and real-time intra-day data; a greatly increased number of data points when modeling; need to monitor the market during the period a trade is active, perhaps issuing cancel and replace orders; increased cost of commission and slippage. For the intra-day models I have created, two trades per day is the sweet spot.

The model fitting process takes volatility and noise into account. If the volatility is too low, there will not be enough profit potential. If it is too high, there will too much risk. Both of these are reflected in CAR25. The purpose of the model is to detect patterns that precede profitable trades -- the signal among the noise. If there is too much noise or if the signal is too low or changes too rapidly, the system will fail to pass the validation tests and will not be a candidate to trade.

Best, Howard

 

[howardbandy]

+ A trivial case of where the inputs are known to be garbage and no algo to screen them can convert garbage to alpha without finding a latent factor via the screening alone.

Assuming the model is rule-based. If inputs are garbage, then they contain no persistent patterns that precede profitable trades. If there is no signal to find, the model might fit itself to whatever noise is present, but the validation tests will fail and the system will not pass on to trading.

 

[howardbandy]

+ Surely, if you had a million well chosen signals feeding in to a soup of algos over a range of instruments, and their merits, however obtained, were ranked first to last on any given day...that you would feel that only one was valid. Yet, that is what the system does.

Yes, that is what the process does. It is designed to do that. It is the best use of funds. The expected final equity after some period of using this technique is highest.

However many systems there are that have passed validation, even granting that there might be a million, each has its own CAR25 score. Assume any number of them have scores that are higher than the score of risk free use of the funds. Day by day, pick the highest one.

 

[howardbandy]

If signals other than the one ranked one have any merit given the skills of the operator, others with lower rankings also have solid expectations. Let's say that these signals are issuing a BUY on some other instrument so there is no overlap. These are currently not used in the Bandy System.

When the conversation moves from rule-based to subjective, estimates of future performance fade into the unknown. You are correct that they are not used in the procedures I recommend.

If an experienced trader prefers to continue with subjective methods that have worked for him or her, I recommend they do that and ignore me. If a newbie is considering trading system development, and thinks subjective judgement has some value, I recommend beginning with Daniel Kahneman's book, "Thinking, Fast and Slow."

For everyone, please pay attention to the increasing ability of machine learning / artificial intelligence techniques. They have already surpassed humans in almost all fields. They are already being used by the largest trading houses. Systems based on subjective judgement of individuals, particularly individuals without extensive expertise, will have a hard time competing.

 

[DeepState]

When the conversation moves from rule-based to subjective, estimates of future performance fade into the unknown. You are correct that they are not used in the procedures I recommend.


If an experienced trader prefers to continue with subjective methods that have worked for him or her, I recommend they do that and ignore me. If a newbie is considering trading system development, and thinks subjective judgement has some value, I recommend beginning with Daniel Kahneman's book, "Thinking, Fast and Slow."


For everyone, please pay attention to the increasing ability of machine learning / artificial intelligence techniques. They have already surpassed humans in almost all fields. They are already being used by the largest trading houses. Systems based on subjective judgement of individuals, particularly individuals without extensive expertise, will have a hard time competing.

Yes, that is what the process does. It is designed to do that. It is the best use of funds. The expected final equity after some period of using this technique is highest.


However many systems there are that have passed validation, even granting that there might be a million, each has its own CAR25 score. Assume any number of them have scores that are higher than the score of risk free use of the funds. Day by day, pick the highest one.

Howard, I am recombining the two posts because the point I am trying to communicate doesn't seem to be getting through. Having tried the verbal approach, I am now going in to explicit examples and some maths to be as unambiguous as I can. In doing so, I will use techniques no more sophisticated than Markowitz and binomial distributions. These are as close to axioms and the simplest expression of randomness as we are going to find in the world of investments. I will use examples to lead the process heavily in your favour. I aim to demonstrate that the requirements for a one stock portfolio to be optimal are unrealistic.


I am not talking about any qualitative override to the system when in flight. I am questioning the system itself and its recommendations. I particular, I am questioning the primacy of the belief in one stock portfolios.


Let me roll out some background in relation to a clean example for exposition.


Our trader is a genius. He models 2 stocks: A and B. These two stocks are unconditionally distributed as equal likelihood of producing a return of either +1 or -1. The expected return is thus 0 per day with no prediction on timing of these outcomes. The returns between the stocks are completely independent of each other. This is a buy-only strategy. The trader will only position long if he thinks the stock will go up.


The trader, using whatever method, including machine language, produces signals which produce a regime independent predictive ability which is equal for both stocks. The trader sees both stocks equally clearly. This figure is a daily estimate correlation of 0.3. Utterly heroic for a symmetric strategy and sure path of extreme riches. It represents a daily hit rate on a signal stock of 65%. Let's say there are no brokers so I will hand over frictions.


Whatever safe-f is, that allocation will be constant for each of the stocks in isolation. Let's call that figure 100. You can have another 100 in cash earning zero in spare because we can't handle the risk of complete nominal deployment.


The expected return on this a stock signal is:

(Prob right x profit – Prob Wrong x Loss) x Trading days

= (0.65 x 1 – 0.35 x 1) x 252

= 75.6 per annum…vastly better than the buy-hold equivalent of zero. Utter genius, as mentioned earlier,


Risk can be approximated by standard deviation. All other distributions like DD can be inferred from this. This is the true distribution, with no errors in measurement. The unconditional standard deviation for any stock is sqrt([E(X^2) – E(X)^2]xTrading Days) where X is the Stock Return

= sqrt([1 – 0.5^2] x 252)

= 13.74 per annum


However, when you are a genius of this level and there is no doubt about that at all because I have removed doubt in this example, you tilt aggressively towards the risk stats that you actually get because you know the market better than it knows itself. This makes it less risky to invest for our trader than another lesser, buy-hold, mortal. In this case, the stdev drops to: 12.06. Do the same calculation but replace probabilities with the predicted outcome (65% right) as opposed to unconditional probabilities of 50%,


So, before a CAR25 is even calculated, which means we don't even care about the regime, a single stock position will produce 75.6 expected return for 12.06 standard deviation per annum. Forget about buy-hold. Trade like there is no tomorrow.


As all reasonable distributions that feed into a safe-f are going to be proportional functions of this ultra simple binomial model, I will stick to this figure rather than infer drawdowns or any thing else that might be used at the portfolio level. We identify this distribution without error. The risk is identical to both stocks and safe-f works out to $100. Let’s say we left $100 under the mattress because our risk tolerance can’t handle its deployment.


A single stock holding, pick any one and just focus on that, will deliver a return of $100 x 75.6% = $75.6 dollars. Ignoring rebalance effects to keep this ultra simple.


Now, if we stuck both strategies side by side and ran them both with equal risk deployment (think of this as two separate accounts doing their own thing), the expected return for the combination remains 75.6% per annum. However, as Markowitz noted in his Nobel paper in the 1950s, there is diversification to be considered in a portfolio. The portfolio of a 50/50 allocation to the strategies for both stocks is sqrt([w(A)^2 var(A) + w(B)*var(B] x Trading days) where w(x) is the weight to each strategy…0.5 for this purpose. Var(A) is the square of the standard deviation for each individual strategy… = 12.06%^2. The standard deviation of the combined equal weighted portfolio is thus 8.53. Remember that these stocks perform completely independently of each other.


Hence, for the same risk exposure, we can put 12.06 / 8.53 x 100 = $141 to work in the trader’s portfolio. This also earns 75.6% so the aggregate portfolio earns $141 x 7.56 = $106. Once again, I am ignoring rebalance effects….which is even further in favour of a single stock outcome, to be sure.


As would be evident to any student of investment, for any given degree of risk tolerance, a lower risk asset will result in greater nominal assets deployed than a higher risk asset for equivalent returns. Hence, a 50/50 parallel portfolio of Stock A and B strategies running unconditionally on regime and still side by side, allows more capital to be deployed because of diversification benefits.


As a result, portfolio diversification produces better outcomes all else equal.



“(Single Stock Exposure to highest CAR25 Strategy) It is the best use of funds. The expected final equity after some period of using this technique is highest.”


To cover off on a comment you made that the ‘best’ produces the highest equity curve, let us assume that the ‘best’ strategy of the two produced an expected return of 76%. There is no way that a strategy with this ‘best’ return would produce a higher equity curve than the portfolio of the two in an expectations sense. It would produce the highest equity curve of all single stock strategies. But that is inferior to portfolios where you have a genius making good predictions on other things which might warrant a little less merit at any given point in time.


Progressing…


With this base, let us now examine what it takes for a process that can differentiate between the potential future success of strategy A and B to justify moving to a one stock situation as has been recommended.


Let me build an overwhelming case in its favour.


The process of CAR25 or whatever conditioning function is to discriminate between Stock A and Stock B strategies assumes the ability to:

1. Identify regimes

2. Differentiate the probable return for candidate strategies in the presence of the expected regime for the next 24 hours.


There is no need for me to specify this. I will assume that the trader remains an utter genius and can handle non-linear maths, specified Deep Thought and codes at the very highest level. All that and understands investing too.


Further, let me remove immense amounts of uncertainty and tilt this even further to the single-stock case. I hope it is evident to all that these following settings do not exist.


Signal A and Signal B, the predictors previously mentioned which have been vetted at the highest level through any screen that there is to consider, are definitely regime dependent. There is no doubt. There are only two regimes in the market: R1 and R2. The occur cleanly. One or the other, no grey. Any meaningful time period contains these in equal measure. In the event of R1, Signal A has an 80% (more than insider trading by the day) change of success and 50% (no skill) chance in the other regime, balancing out to 65% unconditional accuracy ignoring regime identification. Signal B has the mirror characteristics.


The question is, how good does CAR25 and other smarts have to be to justify moving from a 2-stock portfolio to a single stock portfolio that is expected to produce the same dollar outcome for the same risk? How well does this regime identification have to predict in order to overcome the most limited levels of diversification?


For a single-stock solution to make sense, the system must be able to generate more than $106 on the same safe-f.


It turns out that this regime identification success figure needs to be around a 75% hit rate. You need to have a 75% chance of choosing the true ‘best’ model to get this outcome. All the machinery in the world could not generate a genuine 75% hit rate on regime identification at daily intervals for anything resembling a genuine stock market.


These calculations, and the 75% hit rate that comes from it, are for an absurd example to support the idea of the primacy of a single stock portfolio. It is only a small step from here to move to a scenario of a single stock which is known to always go up faster than everything else in the market every day.


This hurdle to a diversified set of signal implementation by this genius becomes more challenging when there are more stocks being examined and the comparison diversified portfolio which maximises whatever return criteria matters to you become harder to beat with a single stock portfolio for any given safe-f.


I cannot find any reasonable basis to support a proposition that a single stock portfolio based on CAR25 or any regime identification process created by hand, machine or combinations thereof would improve outcomes to the level required to justify a one stock portfolio over a portfolio created by someone who has any skill and produced a set of candidate strategies that made sense before being fed in to the CAR25 or other algo to identify the ‘best strategy’ based on regime identification at a one day interval.


Naturally, if we run enough backtests, and use enough techniques particularly those which seek vast non-linear structure, some will show a better outcome arising from single stock portfolios. However, that’s not the hurdle. The hurdle is: would you reasonably have expected that outcome before running it. And..would you reasonably expect that to happen when you let it loose in the wild…. The above suggests it’s a tall order even if there is merit in regime identification and conditioning the candidate signals for this.


Between the one-stock proposal and Duck’s two-stock proposal, I would choose Duck’s. Of course, the case generalises beyond that.



Thanks.

 

[craft]

Howard, I am recombining the two posts because the point I am trying to communicate doesn't seem to be getting through. Having tried the verbal approach, I am now going in to explicit examples and some maths to be as unambiguous as I can. In doing so, I will use techniques no more sophisticated than Markowitz and binomial distributions. These are as close to axioms and the simplest expression of randomness as we are going to find in the world of investments. I will use examples to lead the process heavily in your favour. I aim to demonstrate that the requirements for a one stock portfolio to be optimal are unrealistic.


I am not talking about any qualitative override to the system when in flight. I am questioning the system itself and its recommendations. I particular, I am questioning the primacy of the belief in one stock portfolios.


Let me roll out some background in relation to a clean example for exposition.


Our trader is a genius. He models 2 stocks: A and B. These two stocks are unconditionally distributed as equal likelihood of producing a return of either +1 or -1. The expected return is thus 0 per day with no prediction on timing of these outcomes. The returns between the stocks are completely independent of each other. This is a buy-only strategy. The trader will only position long if he thinks the stock will go up.


The trader, using whatever method, including machine language, produces signals which produce a regime independent predictive ability which is equal for both stocks. The trader sees both stocks equally clearly. This figure is a daily estimate correlation of 0.3. Utterly heroic for a symmetric strategy and sure path of extreme riches. It represents a daily hit rate on a signal stock of 65%. Let's say there are no brokers so I will hand over frictions.


Whatever safe-f is, that allocation will be constant for each of the stocks in isolation. Let's call that figure 100. You can have another 100 in cash earning zero in spare because we can't handle the risk of complete nominal deployment.


The expected return on this a stock signal is:

(Prob right x profit – Prob Wrong x Loss) x Trading days

= (0.65 x 1 – 0.35 x 1) x 252

= 75.6 per annum…vastly better than the buy-hold equivalent of zero. Utter genius, as mentioned earlier,


Risk can be approximated by standard deviation. All other distributions like DD can be inferred from this. This is the true distribution, with no errors in measurement. The unconditional standard deviation for any stock is sqrt([E(X^2) – E(X)^2]xTrading Days) where X is the Stock Return

= sqrt([1 – 0.5^2] x 252)

= 13.74 per annum


However, when you are a genius of this level and there is no doubt about that at all because I have removed doubt in this example, you tilt aggressively towards the risk stats that you actually get because you know the market better than it knows itself. This makes it less risky to invest for our trader than another lesser, buy-hold, mortal. In this case, the stdev drops to: 12.06. Do the same calculation but replace probabilities with the predicted outcome (65% right) as opposed to unconditional probabilities of 50%,


So, before a CAR25 is even calculated, which means we don't even care about the regime, a single stock position will produce 75.6 expected return for 12.06 standard deviation per annum. Forget about buy-hold. Trade like there is no tomorrow.


As all reasonable distributions that feed into a safe-f are going to be proportional functions of this ultra simple binomial model, I will stick to this figure rather than infer drawdowns or any thing else that might be used at the portfolio level. We identify this distribution without error. The risk is identical to both stocks and safe-f works out to $100. Let’s say we left $100 under the mattress because our risk tolerance can’t handle its deployment.


A single stock holding, pick any one and just focus on that, will deliver a return of $100 x 75.6% = $75.6 dollars. Ignoring rebalance effects to keep this ultra simple.


Now, if we stuck both strategies side by side and ran them both with equal risk deployment (think of this as two separate accounts doing their own thing), the expected return for the combination remains 75.6% per annum. However, as Markowitz noted in his Nobel paper in the 1950s, there is diversification to be considered in a portfolio. The portfolio of a 50/50 allocation to the strategies for both stocks is sqrt([w(A)^2 var(A) + w(B)*var(B] x Trading days) where w(x) is the weight to each strategy…0.5 for this purpose. Var(A) is the square of the standard deviation for each individual strategy… = 12.06%^2. The standard deviation of the combined equal weighted portfolio is thus 8.53. Remember that these stocks perform completely independently of each other.


Hence, for the same risk exposure, we can put 12.06 / 8.53 x 100 = $141 to work in the trader’s portfolio. This also earns 75.6% so the aggregate portfolio earns $141 x 7.56 = $106. Once again, I am ignoring rebalance effects….which is even further in favour of a single stock outcome, to be sure.


As would be evident to any student of investment, for any given degree of risk tolerance, a lower risk asset will result in greater nominal assets deployed than a higher risk asset for equivalent returns. Hence, a 50/50 parallel portfolio of Stock A and B strategies running unconditionally on regime and still side by side, allows more capital to be deployed because of diversification benefits.


As a result, portfolio diversification produces better outcomes all else equal.



“(Single Stock Exposure to highest CAR25 Strategy) It is the best use of funds. The expected final equity after some period of using this technique is highest.”


To cover off on a comment you made that the ‘best’ produces the highest equity curve, let us assume that the ‘best’ strategy of the two produced an expected return of 76%. There is no way that a strategy with this ‘best’ return would produce a higher equity curve than the portfolio of the two in an expectations sense. It would produce the highest equity curve of all single stock strategies. But that is inferior to portfolios where you have a genius making good predictions on other things which might warrant a little less merit at any given point in time.


Progressing…


With this base, let us now examine what it takes for a process that can differentiate between the potential future success of strategy A and B to justify moving to a one stock situation as has been recommended.


Let me build an overwhelming case in its favour.


The process of CAR25 or whatever conditioning function is to discriminate between Stock A and Stock B strategies assumes the ability to:

1. Identify regimes

2. Differentiate the probable return for candidate strategies in the presence of the expected regime for the next 24 hours.


There is no need for me to specify this. I will assume that the trader remains an utter genius and can handle non-linear maths, specified Deep Thought and codes at the very highest level. All that and understands investing too.


Further, let me remove immense amounts of uncertainty and tilt this even further to the single-stock case. I hope it is evident to all that these following settings do not exist.


Signal A and Signal B, the predictors previously mentioned which have been vetted at the highest level through any screen that there is to consider, are definitely regime dependent. There is no doubt. There are only two regimes in the market: R1 and R2. The occur cleanly. One or the other, no grey. Any meaningful time period contains these in equal measure. In the event of R1, Signal A has an 80% (more than insider trading by the day) change of success and 50% (no skill) chance in the other regime, balancing out to 65% unconditional accuracy ignoring regime identification. Signal B has the mirror characteristics.


The question is, how good does CAR25 and other smarts have to be to justify moving from a 2-stock portfolio to a single stock portfolio that is expected to produce the same dollar outcome for the same risk? How well does this regime identification have to predict in order to overcome the most limited levels of diversification?


For a single-stock solution to make sense, the system must be able to generate more than $106 on the same safe-f.


It turns out that this regime identification success figure needs to be around a 75% hit rate. You need to have a 75% chance of choosing the true ‘best’ model to get this outcome. All the machinery in the world could not generate a genuine 75% hit rate on regime identification at daily intervals for anything resembling a genuine stock market.


These calculations, and the 75% hit rate that comes from it, are for an absurd example to support the idea of the primacy of a single stock portfolio. It is only a small step from here to move to a scenario of a single stock which is known to always go up faster than everything else in the market every day.


This hurdle to a diversified set of signal implementation by this genius becomes more challenging when there are more stocks being examined and the comparison diversified portfolio which maximises whatever return criteria matters to you become harder to beat with a single stock portfolio for any given safe-f.


I cannot find any reasonable basis to support a proposition that a single stock portfolio based on CAR25 or any regime identification process created by hand, machine or combinations thereof would improve outcomes to the level required to justify a one stock portfolio over a portfolio created by someone who has any skill and produced a set of candidate strategies that made sense before being fed in to the CAR25 or other algo to identify the ‘best strategy’ based on regime identification at a one day interval.


Naturally, if we run enough backtests, and use enough techniques particularly those which seek vast non-linear structure, some will show a better outcome arising from single stock portfolios. However, that’s not the hurdle. The hurdle is: would you reasonably have expected that outcome before running it. And..would you reasonably expect that to happen when you let it loose in the wild…. The above suggests it’s a tall order even if there is merit in regime identification and conditioning the candidate signals for this.


Between the one-stock proposal and Duck’s two-stock proposal, I would choose Duck’s. Of course, the case generalises beyond that.



Thanks.

Thumbs up from me DS for taking the time to articulate the portfolio position.

I'm also really sceptical that one day persistence of the best historical return system on a single security will in reality overcome frictional cost and gap risk when applied over a statistically significant population. To my last post around this point. Howard reiterated his theory but forgot to provide the ex post evidence requested.

Clearly some of us are not going to be swayed without some hard evidence. But perhaps those that want to believe the secret sauce lies within more complexity and even smarter artificial intelligence don't need evidence just a theory/belief to justify continued effort is enough.

Too cynical again - right.

 

[Value Hunter]

http://www.lazardnet.com/us/docs/sp6/3048/LessIsMore-ACaseForConcentrated_LazardInvestmentFocus.pdf

The above is a link to a study which shows that on average a fund managers top 5 picks outperform their portfolio as a whole.

 

[Value Hunter]

In one of his books Peter Lynch advocated that individual investors should own between 3 and 5 stocks. This was because an individual investor only has the time and expertise to understand and follow a limited number of companies.

As for Buffet advocating index funds he said the majority of investors should use them. However those with skill and ability should concentrate is what he advocates. Even Ben Graham in the intelligent investor classified investors as two groups defensive and enterprising. Defensive would be similar to an index fund investor today using a mix of bonds and stock ETFs.

Buffet at one point had 40% of his partnership in American express. Charlie Munger once said that he had 110% of his net worth in one stock (an oil company from memory).

As for Buffet being diversified in his early years that is because he ran 2 strategies in his portfolio simultaneously:
1) Long term investments such as American Express which were typically big concentrated positions
2) Special situations/arbitrage which needs to be diversified by its very nature. This what caused his portfolios to have a large number of positions.

 

[Value Hunter]

Most people do not have the skill, dedication or temperament to be a concentrated stockpicker. These people can either use a mechanical approach, focus on special situations/arbitrage (not recommended these days do to competing with high firepower computerised hedge funds), or use index funds. Skilled investors should have portfolios which are no more than 10 stocks and preferably 3-5 stocks.

Even Joel Greenblatt advocates most people adopt a well diversified magic formula approach while a skilled minority pick 3-6 (or was it 5-8?) stocks based on careful analysis.

 

[Value Hunter]

To summarise average investors should buy an index fund of some description. Skilled investors should carefully select a small number of stocks (in my stock portfolio I only own 3 stocks, however I own other assets such as property, commodities, etc). In my 3 stock portfolio one stock compromises over 95% and the other two stocks combined make up the other 5%. So far it has worked out well.

 

[Knobby22]

To summarise average investors should buy an index fund of some description. Skilled investors should carefully select a small number of stocks (in my stock portfolio I only own 3 stocks, however I own other assets such as property, commodities, etc). In my 3 stock portfolio one stock compromises over 95% and the other two stocks combined make up the other 5%. So far it has worked out well.

I'm usually around 8 stocks.
I find it too hard if I go anymore.

 

[Value Hunter]

Just FYI for Deep state and anyone else who might suggest my approach might be because I only have play money invested in shares that is not the case even though only part of my total investments are in shares my overall investment (not only shares) portfolio is quite leveraged (no margin loans though) so if my top shareholding went bust my net worth would drop by 80-85% and it would take me many many years to recover.

 

[skc]

The above is a link to a study which shows that on average a fund managers top 5 picks outperform their portfolio as a whole.

The top performers do better than the average... Isn't that kind of true by definition?

 

[minwa]

Why anyone would want to concentrate in any one stock which could end up like a Lehman or Madoff no matter how rosey any analysis seems is beyond my comprehension.

Especially if they are a portfolio manager whose sole/majority income comes from it. Why gamble on one stock who is just one rumour/announcement away from dealing a major drawdown to your account beats my senses.

 

[Value Hunter]

SKC you misunderstood me I meant top 5 positions by weighting in the portfolio. In other words the stocks they (fund managers) invest the most money in (percentage allocation), on average perform the best (compared to other stocks in their own portfolio) because they tend to invest the largest sums of money in their best ideas.

 

[Value Hunter]

Minwa which investor do you think is taking more risk?
Investor A) Has an equally weighted portfolio of 7 stocks: one Iron Ore exploration company, one gold exploration company, one oil exploration company, one start up Australian medical cannabis company (with no current crops or land ownership), one high tech startup like Martin Jetpack, shares in Myer and shares in Qantas.
Investor B) 100% of his money invested in a very strong global brand like Nestle (you could easily substitute a company like Johnson and Johnson or 3M in this example).

I would wager that if investors A and B both went into a coma (let's assume they were both 20 years old when they went into the coma) and then one day after 50 years suddenly woke up investor A would most likely have a portfolio of worthless companies which long ago went bankrupt, whereas investor B would have a portfolio worth many times there initial investment.

 

[Value Hunter]

My point is that what you invest in is just as important if not more important than how diversified you are. A soccer team made up of 14 (let's include three substitutes) crappy players will make a crappy soccer team. Likewise a portfolio of poorly chosen companies will perform poorly.

Another example, let's say two investors both living in Greece are investing in 2007 in the share market. The first Greek investor bought an index fund representing the Greek stock market. The second Greek investor set up a brokerage account that could invest overseas and bought shares in Unilever. We all know who would be better of today.

 

[minwa]

Minwa which investor do you think is taking more risk?
Investor A) Has an equally weighted portfolio of 7 stocks: one Iron Ore exploration company, one gold exploration company, one oil exploration company, one start up Australian medical cannabis company (with no current crops or land ownership), one high tech startup like Martin Jetpack, shares in Myer and shares in Qantas.
Investor B) 100% of his money invested in a very strong global brand like Nestle (you could easily substitute a company like Johnson and Johnson or 3M in this example).

I would wager that if investors A and B both went into a coma (let's assume they were both 20 years old when they went into the coma) and then one day after 50 years suddenly woke up investor A would most likely have a portfolio of worthless companies which long ago went bankrupt, whereas investor B would have a portfolio worth many times there initial investment.

You're using the situation that real world investment have to go into a coma. This is not the case. Most people (hopefully) manage their investments - if they do not, only then is it a coma gamble as you put it.

Investor A with a 25% stop in each stock has much lower risk than investor B with a 25% stop in Nestle. That stop is useless when overnight something happens and Nestle opens up with a drop larger than 25%. In the case of investor A, the most can be lost is 14% (1/7th) vs B all the way up to 100%.