Limits...
Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model.

Shinzato T - PLoS ONE (2015)

Bottom Line: In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk.Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets.We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return.

View Article: PubMed Central - PubMed

Affiliation: Mori Arinori Center for Higher Education and Global Mobility, Hitotsubashi University, Kunitachi, Tokyo, Japan.

ABSTRACT
In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always result in the best rate of return on assets. Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets. We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return. We compare the results from our method with the results obtained by the operations research approach and with those obtained by a numerical simulation using the optimal portfolio. The results of our method and the numerical simulation are in agreement, but they differ from that of the operations research approach.

No MeSH data available.


The investment risk ɛ and the concentrated investment level qw are shown for the case in which the return rate xkμ is independently and identically distributed with a standard normal distribution.The horizontal axis indicates the scenario ratio α = p/N, and the vertical axis shows the investment risk and the concentrated investment level qw. The two solid lines (results obtained by our proposed approach) and the two dotted lines (results obtained by the operations research approach) are theoretical results. The markers with error bars are the numerical results evaluated using the optimal solution according to a return rate which was randomly assigned. In the simulation, the number of investment outlets N was 103, and we averaged 100 return rate matrices . This figure shows that the results obtained by our proposed approach (solid lines) and the numerical results (markers with error bars) are in agreement. On the other hand, the results obtained by the operations research approach (dotted lines) do not coincide with the others. Thus, unfortunately, the approach based on maximizing the expected utility cannot propose an optimal investment strategy.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4520490&req=5

pone.0133846.g001: The investment risk ɛ and the concentrated investment level qw are shown for the case in which the return rate xkμ is independently and identically distributed with a standard normal distribution.The horizontal axis indicates the scenario ratio α = p/N, and the vertical axis shows the investment risk and the concentrated investment level qw. The two solid lines (results obtained by our proposed approach) and the two dotted lines (results obtained by the operations research approach) are theoretical results. The markers with error bars are the numerical results evaluated using the optimal solution according to a return rate which was randomly assigned. In the simulation, the number of investment outlets N was 103, and we averaged 100 return rate matrices . This figure shows that the results obtained by our proposed approach (solid lines) and the numerical results (markers with error bars) are in agreement. On the other hand, the results obtained by the operations research approach (dotted lines) do not coincide with the others. Thus, unfortunately, the approach based on maximizing the expected utility cannot propose an optimal investment strategy.

Mentions: In Fig 1, three minimal investment risks per asset and three concentrated investment levels are shown. The horizontal axis indicates the scenario ratio α = p/N, and the vertical axis shows the two indicators. The results of our proposed approach are indicated by solid lines, the numerical results are indicated by markers with error bars, and the results of the operations research approach are indicated by dotted lines. The results of our method (solid lines) and the numerical results (markers with error bars) are in agreement. For this numerical simulation, we considered the case in which we have a priori knowledge of the return rates. Thus, it turns out that our proposed approach can precisely assess the potential of an investment system. On the other hand, the dotted lines are based on a scenario in which the expected utility is maximized, and these results do not coincide with the others. Unfortunately, this indicates that the approach based on maximizing the expected utility is unable to determine the optimal investment strategy and may instead provide a misleading portfolio which is not guaranteed to be optimal with respect to particular set of return rates.


Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model.

Shinzato T - PLoS ONE (2015)

The investment risk ɛ and the concentrated investment level qw are shown for the case in which the return rate xkμ is independently and identically distributed with a standard normal distribution.The horizontal axis indicates the scenario ratio α = p/N, and the vertical axis shows the investment risk and the concentrated investment level qw. The two solid lines (results obtained by our proposed approach) and the two dotted lines (results obtained by the operations research approach) are theoretical results. The markers with error bars are the numerical results evaluated using the optimal solution according to a return rate which was randomly assigned. In the simulation, the number of investment outlets N was 103, and we averaged 100 return rate matrices . This figure shows that the results obtained by our proposed approach (solid lines) and the numerical results (markers with error bars) are in agreement. On the other hand, the results obtained by the operations research approach (dotted lines) do not coincide with the others. Thus, unfortunately, the approach based on maximizing the expected utility cannot propose an optimal investment strategy.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4520490&req=5

pone.0133846.g001: The investment risk ɛ and the concentrated investment level qw are shown for the case in which the return rate xkμ is independently and identically distributed with a standard normal distribution.The horizontal axis indicates the scenario ratio α = p/N, and the vertical axis shows the investment risk and the concentrated investment level qw. The two solid lines (results obtained by our proposed approach) and the two dotted lines (results obtained by the operations research approach) are theoretical results. The markers with error bars are the numerical results evaluated using the optimal solution according to a return rate which was randomly assigned. In the simulation, the number of investment outlets N was 103, and we averaged 100 return rate matrices . This figure shows that the results obtained by our proposed approach (solid lines) and the numerical results (markers with error bars) are in agreement. On the other hand, the results obtained by the operations research approach (dotted lines) do not coincide with the others. Thus, unfortunately, the approach based on maximizing the expected utility cannot propose an optimal investment strategy.
Mentions: In Fig 1, three minimal investment risks per asset and three concentrated investment levels are shown. The horizontal axis indicates the scenario ratio α = p/N, and the vertical axis shows the two indicators. The results of our proposed approach are indicated by solid lines, the numerical results are indicated by markers with error bars, and the results of the operations research approach are indicated by dotted lines. The results of our method (solid lines) and the numerical results (markers with error bars) are in agreement. For this numerical simulation, we considered the case in which we have a priori knowledge of the return rates. Thus, it turns out that our proposed approach can precisely assess the potential of an investment system. On the other hand, the dotted lines are based on a scenario in which the expected utility is maximized, and these results do not coincide with the others. Unfortunately, this indicates that the approach based on maximizing the expected utility is unable to determine the optimal investment strategy and may instead provide a misleading portfolio which is not guaranteed to be optimal with respect to particular set of return rates.

Bottom Line: In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk.Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets.We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return.

View Article: PubMed Central - PubMed

Affiliation: Mori Arinori Center for Higher Education and Global Mobility, Hitotsubashi University, Kunitachi, Tokyo, Japan.

ABSTRACT
In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always result in the best rate of return on assets. Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets. We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return. We compare the results from our method with the results obtained by the operations research approach and with those obtained by a numerical simulation using the optimal portfolio. The results of our method and the numerical simulation are in agreement, but they differ from that of the operations research approach.

No MeSH data available.