A Quantitative Approach to Asset Allocation
Qualitative : Quantitative: Portfolio & Asset Management
Portfolio & Asset Management
A key component of investment management requires the use of intelligent distribution of portfolio assets. No matter the details of this framework in question, the general premise of asset allocation is the balance and optimisation of risk-reward given a number of assets within a portfolio.
In Modern Portfolio Theory (‘MPT’), developed by Harry Markowitz in 1952, this balance is achieved through diversification. Markowitz's theory posits that by combining assets with varying degrees of correlation, investors can construct a portfolio that maximises expected return for a given level of risk. MPT encourages investors to not just focus on individual asset performance but to consider how each asset's performance relates to that of others in the portfolio, thus optimising the overall portfolio performance.
Since MPT, there have been numerous frameworks and mental models in relation to asset allocation. In a quantitative context, each model arrived at their optimal allocation via their respective interpretation of ‘risk’. MPT applied generously the concept that standard deviations and variances of an asset were representative of said risk. Whereas, Post Modern Portfolio Theory sought to represent only downside risk and rejected the notion of using standard deviation and variances as measures for risk.
Regardless of the specific framework, there is a consistent set of variables that asset allocation models utilise:
Expected ReturnExpected LossCovariance and CorrelationVolatility
Macro-Micro Mental Model
Given the systemic variables and structure that we identified, our solution to our asset allocation needs were to think from the top-down:
Investment Objectives > Strategies > Asset Classes > PositionsEvery investment firm operates with the goal of generating outsized returns. While the extent of these returns may vary, the fundamental objective of investing is, naturally, to earn money. Another key aspect is how we generate these returns. A clear purpose will inform your Objective which in turn, informs the level and complexity of the Strategies you employ.
Each Strategies are then segmented into the appropriate asset classes and geographical considerations. Further to that, individual positions in the micro-level are established to deliver those strategies. Each hierarchy informs and cascades down from Macro to Micro, and thereafter, cascades back up to informing our quantitative allocations.
*Naturally, this is a streamlined account of managing a top-down mental model.
Quantitative Balancing
With the systemic variables commonly utilised in asset allocation models, each micro-level position is given Expected Returns, Expected Loss, Volatility and Correlation metrics. These individual positions are evaluated against each other within the micro-level through the mathematical optimisation formulae of your choice. This is repeated throughout, cascading up to Strategies.
With the weighted averages of the micro-level Positions, we can now derive the same variable set for the Asset Classes, cascading upwards. It stands to reason that among each formulated strategy, a multitude of asset classes might be needed to express said strategy. Asset Classes are then similarly evaluated against each other within the Asset Classes level through that same mathematical optimisation formulae.
With the weighted averages of the Asset Classes, Strategies are informed of their Expected Returns, Expected Loss, Volatility and Correlation metrics. And finally, a last mathematical optimisation is done at the Strategy level.
Re-visiting Investment Objectives is important to align mathematical optimisation with your goals. Constraints in particular regards to risk tolerance and investment mandate must be introduced early into the calculation and ideally at the clarification of the Investment Objectives.
*it should be stressed that this is a simplified and streamlined thought model
Limitations in Mathematical Optimisation for Asset Allocation
The critical challenge in achieving genuine optimisation lies in the determination of the variables essential in constructing asset allocation models. These variables are qualitative in nature when we discuss Expected Returns/Loss and Prior Probabilities, this is consistent with our thought process of how the Odds of Positive Expected Return is correlated with our fundamental/qualitative thesis.
The most rigorous models can be constrained and compromised by inadequate estimations of Expected Returns/Loss, Variability, and Prior Probabilities.
Links & References:
Modern Portfolio Theory
https://www.investopedia.com/terms/m/modernportfoliotheory.asp
Post Modern Portfolio Theory
https://www.investopedia.com/terms/p/pmpt.asp
https://moneyterms.co.uk/pmpt/
Asset Allocation
https://www.investopedia.com/investing/6-asset-allocation-strategies-work/
https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Kelly.pdf
http://www.stat.columbia.edu/~gelman/research/published/badbayesmain.pdf
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https://www.ray-kok.com/blog/qualitative-quantitative-approach-investing
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