Understanding Capital Markets
When studying markets, it is necessary to explore and understand their basic workings. These notes are based on ideas which were collected while learning about finances and investing. A focus is applied to the Efficient Market Hypothesis and underlying relationship between risk and return. Other points are discussed, such as the irrationality of selecting individual securities or trying to time the market based on forecasts due to the arithmetic of active management. The underlying research was recognized and uncovered with contributions from Louis Bachelier, Paul Samuelson, William Sharpe, and Eugene Fama with many additions from other proponents. As initially observed by Louis Bachelier in 1900, "past, present, and even discounted future events are reflected in market prices, but often show no apparent relation to price changes" (as would be expected if the current price of a security is related to currently available information and changes in the current price of the security are only related to the unexpected outcomes of future events).
Efficient Market Hypothesis
As defined, the Efficient Market Hypothesis states that all of the available information is always fully reflected in the current prices of securities. This also implies that expectations or predictions of future information are also reflected in the current prices of securities. As a result, once future information is realized, any changes in the current prices of securities must be unexpected and resemble randomness or random-walk behaviour, especially in the short-term, since there is no reason for uniformity in the distribution of possible unpredictable outcomes. The uncertainty around this information is said to be reflected in the current prices of securities based on a discount rate, as the current price of a security can be seen as the present value of expected future cash flows which is equal to the ratio of the sum of expected future cash flows and discount rate of those cash flows relative to the time horizons of those cash flows - higher expected future cash flows increase the price, while higher discount rates decrease the price. So, the discount rate represents a risk being reflected in the current price of a security and only future information affects the discount rate and expected future cash flows for a security once it is realized. It should be acknowledged that it is difficult to test the Efficient Market Hypothesis, as any test of the Efficient Market Hypothesis is jointly a test of the asset pricing model used for the test - in other words, anomalies may result from the asset pricing model and not necessarily the actual market.
As an illustration of the Efficient Market Hypothesis, suppose a piece of information about the value of a security is widely available to investors. If the current price of the security does not already reflect this information, then investors will subsequently compete to trade on this information for their own self-interest and, thereby, change the current price of the security to reflect this information. In other words, if participants in a market think a security is undervalued at its current price based on available information, then they will buy it and increase the price until it reaches a fair price and, if participants in a market think a security is overvalued at its current price based on available information, then they will sell it and decrease the price until it reaches a fair price. This creates an equilibrium between supply and demand.
This also leads to securities having a price which is the best guess or aggregate of the accepted price by all of the participants in the market, where prices will efficiently adjust to equalize the supply and demand from the participants in the market. In a sense, the current price of a security becomes a mechanism to collect disperse bits of information about fundamental values and expectations from all of the participants in the market to provide accurate signals for capital allocation. This information is dispersed as it is not possible for any individual participant in the market to have access to all of the available information, but the cumulative decisions of all of the participants in the market must include all of the available information (otherwise the information is not available, since no participants in the market have access to it), such that the current price of a security is the result of all of the available information. Thus, the current price of a security should only rationally change once future information which is unexpected is introduced into the market, such that the accepted price by all of the participants in the market proportionally reacts to this future information.
There are different forms of the Efficient Market Hypothesis which are associated with the degree to which information can be reflected in current prices. As the most efficient, the strong form states that all of the public and private information is reflected in current prices (with there being no type of information which can give a participant in the market an advantage). The semi-strong form states that all of the public information is reflected in current prices but private information is restricted to insiders (who are unable to act on this information due to regulation). As the least efficient, the weak form states that only historical prices, returns, and trading volumes are reflected in current prices without any future outlooks (with the existence of undervalued and overvalued securities). Factors which make a market less efficient are behavioural characteristics and cognitive biases, such as overconfidence, overreaction, representative bias, information bias, and errors in human reasoning. In reality, it is very likely that real markets very closely approach the semi-strong form from the side of the weak form, especially with the advancements of technology, quicker execution of trades, reduction in transaction costs, faster distribution of information, fair regulations around announcements, decentralized operations, independent actions, diversity of opinions, and lower reliance on personal intuition or anecdotes.
It is often misunderstood that the outcomes of the Efficient Market Hypothesis imply that the prices of securities are objectively correct. However, this is not necessarily the case even if a market was ideally efficient. Instead, the outcomes of the Efficient Market Hypothesis only imply that any mispricing of securities is unbiased. Thus, it is still acceptable for there to be mispricing of securities, but this mispricing is effectively random without an identifiable preference for being overvalued or undervalued (although participants in the market may still have individual preferences, but these are equalized through the wisdom of crowds). This can be understood by considering the limits to arbitrage, where a mispricing related to an arbitrage opportunity may remain and give the illusion of an inefficiency. This is an illusion of an inefficiency, because it is necessary to also account for the additional information presented by attempting to take advantage of the arbitrage opportunity, as this attempt will in itself have a cost to conduct in a transaction. If the cost of the attempt is lower than the potential compensation, then it can only be seen as efficient for this mispricing to remain as rational, as the marginal benefits of acting on the information of this mispricing cease to exceed the marginal costs, such that it is not biased and cannot be exploited from or does not show a preference for either side of a transaction once all of the information is actually considered (in other words, it is not an inefficiency once the effective price is calculated with all of the costs).
These ideas are applicable to almost all of the securities which trade in financial markets, including equities which are shared ownership in a business or bonds which are contributions to capital lent to stakeholders. For interest, these ideas can also be taken further to consider other things outside financial markets. The fundamental concept can be applied to most situations in which the outcome is driven by a competitive relationship between supply and demand with potential compensation for success, such as jobs, insurance, traffic, tourism, websites, cost of living, and prices of goods and services. Again, it is unrealistic to expect ideal efficiency in any of these situations and there will be short-term volatility as information is incorporated into decisions, but this efficiency will tend to increase based on the simplicity, number of participants, opportunity for compensation, and liquidity characterizing the situations. In financial markets, the scale of transaction is such that an average of $775,000,000,000 was traded each day in 2021.
Risk Considerations
The idea of risk forms a crucial part of the Efficient Market Hypothesis, but it can be difficult to define and even more difficult to measure. Broadly, the risk in a decision from a participant in the market can be reasonably defined as the uncertainty about the future consumption related to that decision (more things can happen than will happen as risk increases). This is based on the assumption that the participant in the market plans or anticipates to use their wealth in the future for this consumption, such that it subsequently implies that risk may vary based on characteristics like location, regulations, taxes, costs, time horizon, available investments, risk capacity, current capital, projected income or human capital, expected returns, sequence of returns through multiple periods, sensitivity to economic events, sensitivity to recessions, and overall goals of consumption. It is also assumed that the participants in the market are risk averse and rationally prefer the lowest uncertainty, likelihood of failure, potential for loss, variance, and co-variance with other preferences for a level of expected return (or, equivalently, rationally prefer the highest expected return for a level of uncertainty, likelihood of failure, potential for loss, variance, or and co-variance with other preferences). So, given 2 portfolios with the same expected returns, participants in the market will prefer the portfolio with lesser risk (or, equivalently, given 2 portfolios with the same risk, participants in the market will prefer the portfolio with greater expected returns). It should be noted that these participants in the market may be children, college graduates, working professionals, retirees, institutions, endowments, and many other classifications with different characteristics, while the decisions may be related to discretionary spending, charitable donations, legacy gifts, and many other classifications with different characteristics.
The risk in a decision can be illustrated through a simple example of needing to have $10,000 in 30 years. In this decision, the only option with no risk would be finding an investment which is absolutely guaranteed to deliver $10,000 in 30 years. For example, if the interest rate on a loan of 30 years was 2.5% to a borrower who was assured to avoid defaulting, then the required current capital would be $4,767.42 in order to satisfy this decision with no risk. Any other option which did not have the absolute guarantee of delivering $10,000 in 30 years encompasses some form of risk for this decision and, because of this lack of absolute guarantee, a participant in the market should demand a higher expected return to compensate by the degree of uncertainty by which the option varies from an absolute guarantee. In this case, the security was a loan, but it can be any other security which has a return and associated degree of uncertainty by which this return varies from an absolute guarantee. Importantly, this shows that risk can vary based on the decision and the risk-free rate for one decision may be different to the risk-free rate for another decision. This risk can then be aggregated for all of the decision from the participant in the market to obtain the overall risk for a unique situation based on their lifetime consumption and, for the underlying relationships of the market, further aggregated for all of the participants in the market and their own unique situations to obtain the overall risk of the market.
Unfortunately, the aggregated risk of all of the participants in the market cannot be known, as their individual ability, willingness, and need to take risk cannot be discerned from the information which is available. It must still be present in the underlying relationships of the market, as all of the participants in the market will make decisions based on their own risk or at least their perception of their own risk - it is just that this information is not available for a unified calculation. This does create an initial paradox, as the participants would need to know the risk of securities in order to actually make decisions in the market about those securities and their unique situations. For this reason, a proxy for risk is often used as an estimated indicator, such as the volatility, variability, or maximum drawdown, but these proxies are ultimately a substituted approximation of the actual risk. In this manner, the risk-free rate is often assumed to be a predictable short-term bond from a reliable government with a negligible chance of defaulting, such that this is approximated as the aggregated risk of all of the participants in the market of the overall risk of the market. It is vital to maintain a holistic perspective.
It is often assumed that the relationship between risk and return needs to be linear, such that it is not possible to obtain higher risk-adjusted returns. Although adjusting returns relative to risk may be difficult without using a proxy for risk, it is difficult to understand why a linear relationship would need to be the case. It seems more rational to acknowledge that this relationship will almost always have a positive gradient, but the value of that gradient may vary as long as it remains positive (although any variation would likely be slow within the domain of possible risk). This somewhat resembles the efficient frontier, which is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return for a given standard deviation of return (optimal combination of securities based on their expected returns and co-variances which results in the highest possible expected return at each level of variance - interestingly, the Two Mutual Fund Theorem states that any portfolio on the efficient frontier can be generated by holding a combination of any two other portfolios on the efficient frontier). In this case, the tangency portfolio will have optimal mean-variance characteristics. However, a limitation of the efficient frontier may be the reliance on standard deviation as a proxy for risk. Other proxies for risk may be the safe withdrawal rate, perpetual withdrawal rate, start date sensitivity, longest drawdown, or ulcer index, although a combination of substitutes is probably more appropriate in reality.
From a generalized viewpoint, it is possible to rank asset classes based on their perceived conventional risk in most historical situations. To emphasize, this does not necessarily correlate to the actual risk in unique situations, but it can be seen as estimated indicators of the possible distribution of outcomes. It should also be kept in mind that there are other preferences (formally referred to as state variables) besides growth with regard to return which could be categorized as influential, such as future expectations, liquidity, investability, inflation protection, skewness, smoothing, tax treatment, environmental impact, social governance, and simplicity - aggregation over all of these components should form their equivalent return for comparisons. For example, cash tends to have less risk than bonds; bonds tend to have less risk than equities; short-term bonds tend to have less risk than long-term bonds; government bonds tend to have less risk than corporate bonds; investment-grade bonds tend to have less risk than high-yield bonds; large equities tend to have less risk than small equities; growth equities tend to have less risk than value equities; and developed equities tend to have less risk than emerging market equities. If robust, these characteristics become indicators of risk.
Average Investor
Together, all of the investors must collectively hold the global market portfolio of all of the equities, bonds, and other securities, as every asset in a market must be owned by a participant in the market at every point in time. Thus, if weighted by the value of investments, the average investor must hold the global market portfolio when aggregated for all of the investors. Because of this, it is a rational idea for any investor to start with a global market portfolio and then deviate from this portfolio based on how their unique situation deviates from the situation of the average investor. This deviation may be based on various characteristics of risk in terms of their ability, willingness, and need to take risk, like location, regulations, taxes, costs, time horizon, available investments, risk capacity, current capital, projected income or human capital, expected returns, sequence of returns through multiple periods, sensitivity to economic events, sensitivity to recessions, and overall goals of consumption. However, this deviation should be applied cautiously, as a precise analytical solution to a complicated and poorly-defined problem with variable uncertainty is likely to be futile and unreliable - in a sense, the optimal portfolio for any individual other than the average investor is and always will be unknowable in the present and can only be identified with future information (can only be estimated in the present based on past information under the assumption that these trends are robust and will tend to be consistent in the future).
Unfortunately and to their detriment, this is not often realized and it is irrationally believed that, instead of considering the global market portfolio, it is possible to select individual securities or time the market based on forecasts to easily obtain greater risk-adjusted returns than the global market portfolio. This dramatic deviation from the global market portfolio would be reasonable if there was bias in inefficiencies and they could be exploited on a significant scale with a reliable strategy (although the continued use of this strategy would likely eliminate the inefficiencies). However, there are still two sides to every transaction, as every asset in a market must be owned by a participant in the market at every point in time. This leads to the situation in which, since it is the average, the global market portfolio must replicate the average return of the market, but the average of all of the portfolios which deviate from the global market portfolio must also replicate the average return of the market. This is the arithmetic of active management and is a categorical fact.
Formally, the arithmetic of active management states that, when properly defined and measured, the average active investor must underperform the global market portfolio once fees are taken into account. This global market portfolio can simply be passively reproduced with a proportional slice of all of the equities, bonds, and other securities with practically negligible fees, so it can be stated that the average active investor must underperform the average passive investor once fees are taken into account. The fees for the average active investor must be greater than the fees for the average passive investor, as the active investor will incur higher management fees, transaction costs, and other expenses due to research and trading compared to a passive investor who does not trade. Thus, logically and irrefutably, the average expected return from active management as a group must be lesser than the average expected return from passive management as a group over every instant and under all of the scenarios.
Another way to think of this is that every investor starts off with the global market portfolio. Subsequently, some investors decide to overweight, underweight, or hedge certain securities based on their preferences (even with weights possibly going negative when shorting). But considering securities with equivalent risk, if one investor decides to overweight or underweight a certain security, another investor must be deciding to underweight or overweight that same security, because everyone must still hold the global market portfolio on average. These deviations can be seen as bets leading to a zero-sum game before fees or negative-sum game after fees, as one side of the transaction will beat the average while the other side of the transaction will lose to the average. They are labelled as bets, as, assuming the participants in the market are rational, there is no reason to favour one side of the transaction over the other side of the transaction given equivalent risk, as both sides are claiming that the current price is incorrect even though the current price is the accepted price by the other participants in the market who hold or avoid holding the security - no participant in the market will ever rationally own or avoid owning a security which they believe to be a bad deal.
It should be noted that a distinction should be made between types of active management. There will always be the need to make active decisions for any portfolio, such as the method to replicate the global market portfolio and managing asset allocation and risk - even choosing the global market portfolio is arguably an active decision, as is choosing a risk-based deviation from the global market portfolio. However, these active decisions should be rule-based with credible evidence, relation to risks and returns, and without spontaneous actions. This may still be referred to as active management, although it still has a passive nature due to the imposed limitations, but, nevertheless, it is completely different to the irrational active management perpetuated by funds which arbitrarily and overconfidently select individual securities or try to time the market based on unreliable forecasts. This irrational active management is uninformed, does not conform to asset pricing models depicting current understandings of markets, and will produce results in line with randomness and based on luck rather than skill - it will always be a negative-sum game after fees.
Active Management
If a market is ideally efficient, it is only possible to consistently outperform the market by taking more risk than the global market portfolio, as, as mentioned, any changes in the current prices of securities are random and any mispricing of securities is unbiased. In other words, all of the outcomes are based on risk and variations of different portfolios are only due to the differences in risk between these portfolios (which will always involve uncertainty, as portfolios have to be constructed ex-ante and actual risk is only realized once future information becomes available). Without considering risk, the implementation of irrational active management is essentially choosing an arbitrary level of risk which is uncontrolled, such that this level of risk and resulting expected returns are based on randomness and luck. Instead, by trying to control risk, the most effective portfolio can be constructed for a given equivalent risk, where low-cost diversified funds with low turnover are almost always the most sensible approach. To emphasize, this implies that active management, through selecting individual securities or trying to time the market based on forecasts, cannot produce excess returns and will only produce returns in line with risk (before accounting for the usual higher fees, higher turnover, and additional uncompensated risk due to lower diversification which then reduce returns), as the alternative would imply that these managers were able to predict the randomness of future information (which is not possible).
However, even if a market is not ideally efficient, it is still most reasonable to treat it as if it is ideally efficient. This is because the state of a market at any instant will be the result of all of the participants in the market who actively trade. These participants in the market are the funds which implement active management, so, as a consequence, selecting a low-cost diversified fund with low turnover is the same as selecting a proportional slice of the net result of the funds which implement active management. However, by selecting a single fund which implements active management, a bet is being placed on the biases, preferences, and abilities of an arbitrary manager with no rational expectation for excess returns compared to every other manager. The primary challenges an arbitrary manager faces are that they are unable to interact with the market in isolation if they do have new information (must compete with others who also have this new information at the same time), they are unable to know about the new information which other participants in the market may be bringing to the market at the same time (if they have new information which others do not have, it is just as likely that others have new information which they do not have), and they do not necessarily know how other participants in the market are going to interpret any new information relative to their own interpretation.
As a real market can only approach ideal efficiency, the success of active management in the market can be evaluated to empirically test the degree to which a market approaches efficiency. This evaluation should be based on the ability of active management to consistently outperform the market without taking additional risk and after costs. In an attempt to attribute active management to luck or skill, S&P releases an annual scorecard which details the persistence of performance of actively managed funds over the past 5 years, where skill would be likely to persist but luck would be based on randomness. For equities in the United States, only 2.17% of funds which were in the top quartile in 2019 remained in the top quartile at the end of 2021 and only 1.66% of funds which were in the top quartile in 2017 remained in the top quartile at the end of 2021. For equities in Europe, only 21.2% of funds which were in the top quartile in 2019 remained in the top quartile at the end of 2021 and only 2.77% of funds which were in the top quartile in 2017 remained in the top quartile at the end of 2021. For equities in the United Kingdom, only 24.4% of funds which were in the top quartile in 2019 remained in the top quartile at the end of 2021 and only 3.57% of funds which were in the top quartile in 2017 remained in the top quartile at the end of 2021. Similar results are seen for other regions as well.
| Country | Starting 2019 | Starting 2017 |
|---|---|---|
| Australia | 21.4% | 3.8% |
| Brazil | 13.2% | 0% |
| Canada | 6.25% | 0% |
| Chile | 30.0% | 11.1% |
| Emerging Markets (EUR) | 6.25% | 1.30% |
| Europe | 21.2% | 2.77% |
| Global Equity (CAD) | 12.1% | 5.56% |
| Global Equity (EUR) | 12.7% | 4.31% |
| Mexico | 25.0% | 0% |
| United Kingdom | 24.4% | 3.57% |
| United States | 2.17% | 1.66% |
| Country | Starting 2019 | Starting 2017 |
|---|---|---|
| Australia | - | - |
| Brazil | 20.9% | 6.25% |
| Canada | 31.3% | 10.8% |
| Chile | 47.4% | 11.1% |
| Emerging Markets (EUR) | 20.0% | 5.19% |
| Europe | 32.9% | 10.5% |
| Global Equity (CAD) | 35.3% | 17.8% |
| Global Equity (EUR) | 32.7% | 14.5% |
| Mexico | 43.5% | 9.52% |
| United Kingdom | 35.4% | 9.52% |
| United States | 22.9% | 14.8% |
These results clearly indicate the lack of persistence and role of luck in active management. If choosing a fund in the top quartile, the odds of the fund maintaining its performance are extremely low and likely a losing bet. However, if the outcome was solely based on luck in an ideally efficient market, it would be expected for the odds of randomly remaining in the top quartile consecutively for the next 4 years to be calculated as 0.39% (odds of randomly remaining in the top half consecutively for the next 4 years to be calculated as 6.25%). Strictly (although there may be influences from noise and uncertainty from closures and mergers while only a single sample period is considered), the results are marginally better than would have been expected if they were solely based on luck in an ideally efficient market, but this may indicate an extreme lack of skill among the funds in the lower quartiles rather than the presence of actual skill among the funds in the top quartile (in other words, funds destroy wealth rather than creating it). Instead of comparing these funds against their peers, it may be more appropriate to compare them against an equivalent benchmark on a risk-adjusted basis.
S&P also releases an annual scorecard which details the performance of funds against a passive index as an appropriate benchmark. These findings have also been risk-adjusted to account for the possibility of a fund using an inappropriate benchmark relative to the risk it is taking. For equities in the United States, 92.7% of funds underperformed the risk-adjusted benchmark over the 10 years proceeding the end of 2021 and 95.4% of funds underperformed the risk-adjusted benchmark over the 20 years proceeding the end of 2021. For equities in Europe, 84.3% of funds underperformed the risk-adjusted benchmark over the 10 years proceeding the end of 2021. For equities in the United Kingdom, 69.9% of funds underperformed the risk-adjusted benchmark over the 10 years proceeding the end of 2021. Similar results are seen for other regions as well, even without adjustments for risk. Again, this is a losing bet with poor odds.
| Country | 5 Years | 10 Years | 20 Years |
|---|---|---|---|
| Australia | 75.2% | 80.7% | - |
| Emerging Markets (EUR) | 87.8% | 95.7% | - |
| Emerging Markets (GBP) | 76.7% | 89.8% | - |
| Emerging Markets (JPY) | 98.8% | 100% | - |
| Europe | 75.8% | 84.3% | - |
| Global Equity (EUR) | 83.8% | 97.7% | - |
| Global Equity (GBP) | 78.5% | 95.6% | - |
| Global Equity (JPY) | 76.7% | 93.7% | - |
| Global Equity (ZAR) | 92.2% | 100% | - |
| India | 72.6% | 67.6% | - |
| Japan | 61.2% | 72.8% | - |
| South Africa | 92.7% | 89.3% | - |
| United Kingdom | 52.3% | 69.9% | - |
| United States | 80.9% | 92.7% | 95.4% |
For interest, suppose that the expected outperformance of a manager is 5% per year after fees and other expenses. If their fund has a volatility of 20% per year, which is inline with expectations for equities, it is possible to calculate the time before it can be confidently inferred with a t-statistic of at least 2.2 that their outperformance is reliable. In this case, it would take almost 64 years which is about 2 or 3 times the length of a normal career. It takes this much time due to the high volatility which can give the illusion of outperformance due to skill (when the actual outperformance is due to luck from the distribution of outcomes) for extended periods of time, such that the length of time needed to eliminate this illusion will proportionally increase as the volatility increases - in other words, at this point, it can be claimed with confidence of 95% that the result is not due to luck (at any point before this, the confidence will be less than 95%). Based on this and findings from research into the role of luck versus skill in the cross-section of returns from funds, there is no way to cleanly divide managers into positive-skill, no-skill, and negative-skill cohorts based on performance during any reasonable time horizon. The winning strategy is to simply avoid playing the game of active management.
Portfolio Diversification
The level of diversification, given equivalent risk, is related to the amount of securities with regard to and within different sectors, countries, and asset classes. Increasing diversification leads to a narrower range of possible outcomes or lower dispersion, while decreasing diversification leads to a wider range of possible outcomes or higher dispersion, while also introducing a disproportionally large probability of a negative outcome. This is because there are forms of risk which are compensated and other forms of risk which are uncompensated. As mentioned, it is expected for a higher return for taking a compensated risk, but there is no expectation for a difference in return for taking an uncompensated risk. In other words, by decreasing diversification, additional risk is being taken, but there is no expectation for compensation for taking this risk and, thus, there is a disproportionally large probability of a negative outcome.
Essentially, compensated risks are related to risks which cannot be diversified away, where these risks are inherent to the structure of the portfolio and produce the expected return. The dispersion (size of the range of possible outcomes) of this portfolio must be lower due to the reliability in the construction of the portfolio without idiosyncratic characteristics. Conversely, uncompensated risks are related to risks which can be diversified away, where these risks are inherent to the concentrated securities within the portfolio. The dispersion (size of the range of possible outcomes) of this portfolio must be higher due to the unreliability in the construction of the portfolio with idiosyncratic characteristics. It should be noted that dispersion is related to how unlikely it is for the actual result to be inline with the expected result. In addition, it should be noted that idiosyncratic characteristics are related to the specific or unique challenges faced by the individual securities which are included the portfolio (cannot be mitigated by the opposite specific or unique challenges usually faced by other securities which are not included in the portfolio due to the lack of diversification). This is in contrast to the systematic characteristics which are only related directly to the actual structure of the portfolio.
By definition, if the market is ideally efficient, the global market portfolio must be the most diversified portfolio with no uncompensated risk for the average investor. Due to the deviations from the global market portfolio, active management must intentionally under-diversify relative to the global market portfolio. Thus, active management must automatically have lower diversification than the global market portfolio and, correspondingly, a higher dispersion with a lower certainty in the likelihood of the actual result being inline with the expected result given equivalent compensated risk. This is expected, since any portfolio must hold a subset of the global market portfolio, so this subset has the range of possible outcomes of the global market portfolio, as well as the intersecting range of possible outcomes due to its deviation. The degree of this higher dispersion will be directly dependent on the degree to which the active management varies from the global market portfolio, but it will always increase the range of possible outcomes due to uncompensated risk given equivalent compensated risk. To emphasize, this is relative to the average investor - if someone deviates from the situation of the average investor, the definition of the most diversified portfolio also needs to deviate.
Grossman-Stiglitz Paradox
A counter-argument often perpetuated is that, if a market was ideally efficient and there was no one to perform active management, then there would be no price discovery or mechanism to set current prices. This is correct and would ultimately lead to an inefficient market, as prices cannot be corrected if there are no participants in the market who trade. However, from another perspective and revealing a paradox, if a market was ideally efficient, there would be no participants who expend the resources required to make the market ideally efficient, as there would be no inefficiencies (or other participants in the market) to exploit for excess return, but, if a market was not ideally efficient, there would be participants in the market trying to exploit inefficiencies which then makes the market ideally efficient, as their participation reflects information in the current prices of securities. In reality, there will be a balance in the degree of active management needed to make an efficient market. For example, approximately 80% of the global market is still currently actively managed, although around 95% of the trading activity is performed by active management, but it has been estimated that it is actually only necessary for 10% of the global market to be actively managed, such that the majority of trading activity is still performed by active management for price discovery.
Regardless, the degree of active management needed to make an efficient market would be self-correcting around an equilibrium. If the degree of active management is too high (as it has been and currently is), then this degree will subsequently decrease, as the majority of managers underperform the market. If the degree of active management is too low, then this degree will subsequently increase, as there will be obvious inefficiencies which managers would be incentivized to exploit in order to outperform (although it will still be a zero-sum game based on the arithmetic of active management). Still, as mentioned and before fees, the expected return from active management, even if the degree of active management is too low, is always equal to the expected return from the global market portfolio and, as a result, it would still be irrational to consider active management, as it is still not possible to identify skilled managers before they realize outperformance. Even though a market cannot be ideally efficient, as it would naturally become inefficient by nature of ideal efficiency, it is still most reasonable to treat it as if it is ideally efficient. In a way, as long as there is active management, every manager is working to make the global market portfolio as efficient as possible (while always expecting an outcome based on luck and lower returns after fees in aggregate).
For a contrasting consideration, an initial decrease in the amount of active management would likely make a market more efficient before it becomes less efficient. This is due to uninformed and misinformed managers who perform the most poorly being the most likely to have their funds liquidated compared to the rest of the managers. Thus, the average of the remaining managers must be more skilled and, as a result, the level of competition within the market would have increased. This increased skill and competition can only make the market more efficient and decrease any inefficiencies within the market. Although it will never be completely realized, this cycle can continue up to the point at which the market becomes ideally efficient, there is no distinguishable skill, and outcomes become based on luck. In addition, costs have decreased with regard to trading and short selling through securities lending, which can also only make a market more efficient, as there are fewer limits to arbitrage and more effective mechanisms for price discovery.
Evaluating Outcomes
A decision should not necessarily be judged solely based on its outcome, but it should rather be judged based on the quality of the decision with regard to the information which was available at the time of the decision. This is due to the possible distribution of outcomes which show that a decision which is fundamentally bad may have a minority of positive outcomes or a decision which is fundamentally good may have a minority of negative outcomes. Thus, considering a single positive or negative outcome does not provide an indication of the actual quality of a decision. An additional consideration in this regard is that chance dominates the realized distribution of outcomes in the short term.
In other words, a realized return can be split into an expected component and unexpected component. However, differences in the cross-section of the expected component are usually marginal relative to the volatility of the unexpected component, so realized returns as the outcome are mostly the result of chance from the unexpected component (often misinterpreted as the result from the expected component). Even over reasonable investment horizons of up to 10 years or 20 years, realized returns are typically dominated by the unexpected component and inferences from realized returns are often false positives. This shows that judging a decision based on its outcome, especially in the short term, is equivalent to basing the judgement on randomness, unless the outcome resulted after many decades of evidence.
As a corollary, it is also absurd to use past performance, which is dominated by the unexpected component, to make decisions, as the expected value of the unexpected component in the future must always be zero, otherwise it would form part of the expected component if this was not the case. So, a decision should only be based on the expected component and can be described as good based on the process used to make the decision if it is known beforehand what risk is being taken, why the risk is being taken, and what the expected outcome is (or what the possible distribution of outcomes is). It is possible to do everything right and still lose - if this was not the case, then there would be a guaranteed outcome and this cannot be possible, as a guarantee would imply that there is no actual risk.
Unconventional Perspective
From a different perspective of thinking, it might be helpful to initially disregard the underlying securities which a portfolio holds. Instead, assuming it is sufficiently diversified, a portfolio can be thought of as an amount of risk with an expected return based on this risk. The only thing which matters is the amount of risk for the expected return - it is simply a system with risk as the input and expected return as the output. The underlying securities are only a way of managing asset allocation and risk to allow for this system to exist, such that they do not actually matter in their individuality if they are sufficiently diversified. As mentioned, there may be other aspects besides growth with regard to return which could be considered important for an individual investor, such that there may be concern for the covariance of their portfolio with other variables outside of growth, such as considerations from the nature of future investment opportunities.
Summarized Conclusions
Simply, investing in a security means purchasing the rights to a portion of the expected future profits from that security. The expected future profits are not guaranteed, so they must be purchased at a discount based on their uncertainty. As a result, the return on an investment in a security is the difference between the expected future profits at the discount when the shares were purchased and actual profits which eventually accrue to the shares owned. In this, the expected return is dictated by the expected future profits and uncertainty around those future profits - it is not dictated by the actual profits, as these are not known and there is no reason to believe that the actual profits will not be in line with the expected future profits (otherwise the expected future profits would automatically change to incorporate these beliefs). Fundamentally, an investor will then only purchase or sell a security at a price which reflects the expected future profits and uncertainty around these future profits. This creates the underlying relationship between risk and return.
The Efficient Market Hypothesis can be summarized from a simple point of logic, where every security in a market has to be owned by a participant in the market at every point in time and no individual participant in the market will rationally own a security which they believe to be a bad deal. Ultimately, it is impossible to definitively prove or disprove the Efficient Market Hypothesis, as any test of the Efficient Market Hypothesis is jointly a test of the asset pricing model used for the test. However, the vast majority of evidence shows that it is very likely that real markets very closely approach the semi-strong form from the side of the weak form, such that it is often most reasonable to treat these markets as if they are ideally efficient. Clearly, active management is a negative-sum game after fees by definition and, based on the lack of persistence of performance of actively managed funds, outcomes are almost completely determined due to luck rather than skill in the majority of cases. A low-cost, globally-diversified, value-weighted, and passive fund will get almost everyone anywhere they need to be with a simple asset allocation between equities and bonds based on risk.
As a final comment around active management, there are undoubtably a small handful of skilled managers. As is the case in competitive environments with the potential for compensation, there will be a distribution of skill but only the extreme outliers will have actual skill which is marginally beneficial enough to be compensated for it. This is similar to sports with Rafael Nadal, Cristiano Ronaldo, Tiger Woods, and Michael Jordan; science with Albert Einstein, Isaac Newton, Nikola Tesla, and Richard Feynman; or music with John Lennon, Paul McCartney, George Harrison, and Ringo Starr. However, because of their skill, it is only rational for them to demand a high fee as personal compensation and, as a consequence, this would likely negate the net result from any slight advantage provided by their skill, as any outperformance provided by their skill would accrue to themselves through this fee. To keep in mind, information about a manager being skilled is also information which would be expected to be reflected in the market, such that the market reacts appropriately to diminish any potential future outperformance. This does not provide any applicable insights though, as it is unlikely for an average investor to even be able to access a skilled manager, since these skilled managers will likely already be at private firms like Renaissance Technologies or Bridgewater Associates. From the pool of available managers, choosing a manager is akin to choosing a hobbyist or recreational player who will be dominated by an actual professional - it is a losing deal.