Does an infinite asset universe imply a vanishing equity risk premium even without invoking risk aversion?
Does an infinite asset universe imply a vanishing equity risk premium even without invoking risk aversion?
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External question — Quantitative Finance Stack Exchange
Author: T123
Original post: https://quant.stackexchange.com/questions/85846
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
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I'm exploring a theoretical idea for several days now and would appreciate any thoughts or feedback on whether this reasoning is flawed, already known in the literature, or related to existing equilibrium results.
My starting point is the classical CAPM/mean-variance framework together with Roll's critique regarding the unobservability of the true market portfolio.
Rather than focusing on investors' risk aversion, I am wondering whether part (or all) of the observed equity risk premium could be interpreted as a consequence of the finiteness of the investable asset universe.
The intuition is the following (as far as i got until today):
In a finite market, there is only a limited number of tradable assets (say n=N). Therefore, diversification opportunities are necessarily incomplete. Even if investors continuously search for arbitrage opportunities or superior risk-adjusted portfolios, they ultimately operate within a constrained asset space.
Of course infinitely many assets don't imply as many risk factors, but why should a common risk factor still exist in such an universe?
Now consider a thought experiment where the number of available assets tends to infinity.
In such a market new assets are always available.
Long-short constructions can be expanded across an arbitrarily large universe.
Capital trying to exploit a pricing inefficiency does not necessarily concentrate on a small set of assets, because it can continuously spread across a growing universe.
The analogy I have in mind is Hilbert's Hotel: whenever one "room" becomes crowded, everyone shifts one room further and space is created again. Similarly, arbitrage capital would never be forced to crowd into a finite number of securities.
My question is whether, in this limit, the economically stable equilibrium would be one in which all non-risk-free excess returns disappear.
In other words:
In a finite market, a positive market risk premium exists. The "risk-premium" here can be explained without risk aversion in this economy and serves as measure of the tightness of investment opportunities, which is necessarily positive given real markets, thus market return is larger than risk free returns.
As the asset universe expands, diversification becomes increasingly powerful. In the limit of infinitely many assets, all remaining priced risks may become diversifiable. If every risk can be diversified away, the only arbitrage-free expected return is the risk-free rate, thus the solution to such an infinite asset-market to be in equilibrium is that all covariances are zero (or, more general the average of covariances approaches zero as n goes to infinity).
Under that interpretation, the equity risk premium would not fundamentally arise from risk aversion but from the fact that the asset universe is finite and therefore incomplete.
The resulting conjecture would be:
The market risk premium could be interpreted as a measure of the "constrainedness" or finiteness of the investable opportunity set rather than purely as compensation for risk aversion.
This leads me to several related questions:
Is there any established result showing that an infinite investable asset universe causes all priced risks to disappear?
Are there equilibrium models where the risk premium is generated primarily by market incompleteness or finiteness of the asset space rather than investor risk aversion?
Is there any connection between this idea and Roll's critique, in the sense that every empirical market portfolio proxy necessarily contains only a finite subset of the theoretical market portfolio?
If such a limit existed, would the efficient frontier collapse toward the risk-free asset, making the classical risk-return tradeoff disappear?
Has this type of argument appeared in the CAPM, APT, general equilibrium, or arbitrage-pricing literature?
I am specifically interested in answers staying within asset-pricing theory and portfolio theory. I would prefer to avoid consumption-based explanations and focus purely on the implications of an increasingly large investable asset universe.
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Quoted from Forex.com.bd-Editorial External question — Quantitative Finance Stack Exchange Author: T123 Source score (net votes, not local likes): 0 Original post: https://quant.stackexchange.com/questions/85846 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I'm exploring a theoretical idea for several days now and would appreciate any thoughts or feedback on whether this reasoning is flawed, already known in the literature, or related to existing equilibrium results. My starting point is the classical CAPM/mean-variance framework together with Roll's critique regarding the unobservability of the true market portfolio. Rather than focusing on investors' risk aversion, I am wondering whether part (or all) of the observed equity risk premium could be interpreted as a consequence of the finiteness of the investable asset universe. The intuition is the following (as far as i got until today): In a finite market, there is only a limited number of tradable assets (say n=N). Therefore, diversification opportunities are necessarily incomplete. Even if investors continuously search for arbitrage opportunities or superior risk-adjusted portfolios, they ultimately operate within a constrained asset space. Of course infinitely many assets don't imply as many risk factors, but why should a common risk factor still exist in such an universe? Now consider a thought experiment where the number of available assets tends to infinity. In such a market new assets are always available. Long-short constructions can be expanded across an arbitrarily large universe. Capital trying to exploit a pricing inefficiency does not necessarily concentrate on a small set of assets, because it can continuously spread across a growing universe. The analogy I have in mind is Hilbert's Hotel: whenever one "room" becomes crowded, everyone shifts one room further and space is created again. Similarly, arbitrage capital would never be forced to crowd into a finite number of securities. My question is whether, in this limit, the economically stable equilibrium would be one in which all non-risk-free excess returns disappear. In other words: In a finite market, a positive market risk premium exists. The "risk-premium" here can be explained without risk aversion in this economy and serves as measure of the tightness of investment opportunities, which is necessarily positive given real markets, thus market return is larger than risk free returns. As the asset universe expands, diversification becomes increasingly powerful. In the limit of infinitely many assets, all remaining priced risks may become diversifiable. If every risk can be diversified away, the only arbitrage-free expected return is the risk-free rate, thus the solution to such an infinite asset-market to be in equilibrium is that all covariances are zero (or, more general the average of covariances approaches zero as n goes to infinity). Under that interpretation, the equity risk premium would not fundamentally arise from risk aversion but from the fact that the asset universe is finite and therefore incomplete. The resulting conjecture would be: The market risk premium could be interpreted as a measure of the "constrainedness" or finiteness of the investable opportunity set rather than purely as compensation for risk aversion. This leads me to several related questions: Is there any established result showing that an infinite investable asset universe causes all priced risks to disappear? Are there equilibrium models where the risk premium is generated primarily by market incompleteness or finiteness of the asset space rather than investor risk aversion? Is there any connection between this idea and Roll's critique, in the sense that every empirical market portfolio proxy necessarily contains only a finite subset of the theoretical market portfolio? If such a limit existed, would the efficient frontier collapse toward the risk-free asset, making the classical risk-return tradeoff disappear? Has this type of argument appeared in the CAPM, APT, general equilibrium, or arbitrage-pricing literature? I am specifically interested in answers staying within asset-pricing theory and portfolio theory. I would prefer to avoid consumption-based explanations and focus purely on the implications of an increasingly large investable asset universe.
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