Asset allocation according to the recent CFA survey is one of the most critical aspects in asset management, but what exactly is asset allocation and what does modern finance theory recommend when allocating capital across the different asset classes available to investors today.
Asset allocation may be defined as an investment strategy that aims to balance risk and reward by apportioning assets in accordance with the investors risk profile, investment horizon, return requirements and other contraints as may be specified in the investors investment policy statement (IPS).
Asset allocation allows the investor to identify the right mix between the asset classes available and then select a passive or active investment strategy within each asset class. An institutional investor may have access to different asset classes than the individual investor because they may be able to gain access to transactions that the individual investor may not. An example of this is Berkshire Hathaway doing deals during the great financial crisis when they could strike deals with Goldman Sachs for example that was lucrative but only available to them and not the general public.
Another example could be hedge fund and LBO fund investments where the minimum entry target committment can be $5m and therefore many individual investors are not able to participate.
The two traditional asset classes are the equity and fixed income markets. The alternative asset classes are real estate, hedge funds (all types), commodities (e.g. gold futures), private equity and venture capital. Most of these are highly illiquid, have large minimum investment size requirements and require the investor to be knowledgeable with expertise in evaluating managers for example.
There is a variety of methods that have been developed over the years to generate asset allocations either taking into account liabilities or not. Here is a summary of the main ones:
1. Mean-Variance Optimization (MVO) - developed in the 1950's by Harry Markowitz, this is perhaps the most common approach to developing an asset allocation. It builds on the key concepts of his modern portfolio theory (MPT) whereby one needs to not only look at the best risk vs reward ratio but also the correlation of the assets in the portfolio as well and thereby look at the risk and reward characteristics of any asset in the context of the overall portfolio.
The MVO uses the objective function as follows:
For example if the investor risk aversion coefficient is 2, expected variance is 20% and the expected return on the asset mix is 10% then the Um = 10% - 0.005 x 2 x 20% = 10%-0.002=9.8%
The formula is used to generate a set of asset classes that will generate the highest utilities from asset allocations. These are typically generated in the form of an efficiency frontier that shows the appropriate allocation for each specific require return and acceptable level of risk. Low acceptable levels of risk typically generate a high cash and fixed income component while high required risk will often allocate greater portions of the portfolio to equities and alternative asset classes. (emerging market equities are considered riskier and therefore have a higher expected return as an asset class compared to developed market equities)
Key criticisms of the MVO model
a) small changes in inputs may lead to large changes in outputs
b) asset allocations tend to be highly concentrated
c) many investors are concerned with not only mean and variance of returns which is the focus of the MVO approach
d) sources of risk may not be diversified even though assets are
e) does not take into account liabilities
f) single period approach which also has no way of dealing with trading costs and taxes
2. Monte Carlo Simulation - this is a method that is typically used to complement the MVO because the MVO is a single period framework which is a disadvantage in real life. The method typically uses simulation software to identify the most optimal asset allocations by applying assumptions about probabilities of vairious outcomes
3. Reverse Optimization - this technique is effective in dealing with the MVO criticisms a) - c)
In the MVO the optimizer uses the returns, variances and correlations to generate an optimal asset allocation. The reverse optimization identifies an optimal asset allocation over some period of time and then uses that allocation to produce implied asset returns that may be used in forward looking optimizations.
4. Black-Litterman Model - developed in the early 1990s. The model effectively uses the reverse optimization model to generate returns and then adjusts them as per the specific investor's views while still working well as an optimizer.
In practice most of these approaches are used via specialized software but the individual investor can learn from the broad approaches. The above are just the asset only asset allocation approaches but the individual or insitutional investor may have liabilities that need to also be taken into account. We will cover that in a separate post.
Asset allocation may be defined as an investment strategy that aims to balance risk and reward by apportioning assets in accordance with the investors risk profile, investment horizon, return requirements and other contraints as may be specified in the investors investment policy statement (IPS).
Asset allocation allows the investor to identify the right mix between the asset classes available and then select a passive or active investment strategy within each asset class. An institutional investor may have access to different asset classes than the individual investor because they may be able to gain access to transactions that the individual investor may not. An example of this is Berkshire Hathaway doing deals during the great financial crisis when they could strike deals with Goldman Sachs for example that was lucrative but only available to them and not the general public.
Another example could be hedge fund and LBO fund investments where the minimum entry target committment can be $5m and therefore many individual investors are not able to participate.
The two traditional asset classes are the equity and fixed income markets. The alternative asset classes are real estate, hedge funds (all types), commodities (e.g. gold futures), private equity and venture capital. Most of these are highly illiquid, have large minimum investment size requirements and require the investor to be knowledgeable with expertise in evaluating managers for example.
There is a variety of methods that have been developed over the years to generate asset allocations either taking into account liabilities or not. Here is a summary of the main ones:
1. Mean-Variance Optimization (MVO) - developed in the 1950's by Harry Markowitz, this is perhaps the most common approach to developing an asset allocation. It builds on the key concepts of his modern portfolio theory (MPT) whereby one needs to not only look at the best risk vs reward ratio but also the correlation of the assets in the portfolio as well and thereby look at the risk and reward characteristics of any asset in the context of the overall portfolio.
The MVO uses the objective function as follows:
Um=E(Rm)−0.005λσ2m
where
Um = the investor’s utility for asset mix (allocation) m
Rm = the return for asset mix m
λ = the investor’s risk aversion coefficient
σ2m = the expected variance of return for asset mix m
For example if the investor risk aversion coefficient is 2, expected variance is 20% and the expected return on the asset mix is 10% then the Um = 10% - 0.005 x 2 x 20% = 10%-0.002=9.8%
The formula is used to generate a set of asset classes that will generate the highest utilities from asset allocations. These are typically generated in the form of an efficiency frontier that shows the appropriate allocation for each specific require return and acceptable level of risk. Low acceptable levels of risk typically generate a high cash and fixed income component while high required risk will often allocate greater portions of the portfolio to equities and alternative asset classes. (emerging market equities are considered riskier and therefore have a higher expected return as an asset class compared to developed market equities)
Key criticisms of the MVO model
a) small changes in inputs may lead to large changes in outputs
b) asset allocations tend to be highly concentrated
c) many investors are concerned with not only mean and variance of returns which is the focus of the MVO approach
d) sources of risk may not be diversified even though assets are
e) does not take into account liabilities
f) single period approach which also has no way of dealing with trading costs and taxes
2. Monte Carlo Simulation - this is a method that is typically used to complement the MVO because the MVO is a single period framework which is a disadvantage in real life. The method typically uses simulation software to identify the most optimal asset allocations by applying assumptions about probabilities of vairious outcomes
3. Reverse Optimization - this technique is effective in dealing with the MVO criticisms a) - c)
In the MVO the optimizer uses the returns, variances and correlations to generate an optimal asset allocation. The reverse optimization identifies an optimal asset allocation over some period of time and then uses that allocation to produce implied asset returns that may be used in forward looking optimizations.
4. Black-Litterman Model - developed in the early 1990s. The model effectively uses the reverse optimization model to generate returns and then adjusts them as per the specific investor's views while still working well as an optimizer.
In practice most of these approaches are used via specialized software but the individual investor can learn from the broad approaches. The above are just the asset only asset allocation approaches but the individual or insitutional investor may have liabilities that need to also be taken into account. We will cover that in a separate post.
there is also resampled MVO which is equivalent to averaging results from several data sets creating a set of allocations on the efficient frontier
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