As curious as it may sound, few asset allocation primers describe portfolio models while connecting them to each other. This article does so by describing and contrasting the mechanics of standard asset allocation models, including the utility-based, Markowitz, Kelly, risk parity and fixed allocation approaches. It seeks to accomplish four objectives: First, it develops the mathematics of the models; second, it identifies the precise conditions under which the models are equivalent; third, it discusses the specifics – risk/return characteristics – of each approach; and last, it provides numerical examples that compare allocations to asset classes and return and risk measures for various models.

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The Author

Jamil Baz

Co-head of Client Solutions and Analytics

Helen Guo

Analista de investigación cuantitativa, Análisis de clientes


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Past performance is not a guarantee or a reliable indicator of future results.

No representation is being made that any account, product, or strategy will or is likely to achieve profits, losses, or results similar to those shown. Hypothetical or simulated performance results have several inherent limitations. Unlike an actual performance record, simulated results do not represent actual performance and are generally prepared with the benefit of hindsight. There are frequently sharp differences between simulated performance results and the actual results subsequently achieved by any particular account, product or strategy. In addition, since trades have not actually been executed, simulated results cannot account for the impact of certain market risks such as lack of liquidity. There are numerous other factors related to the markets in general or the implementation of any specific investment strategy, which cannot be fully accounted for in the preparation of simulated results and all of which can adversely affect actual results.

Return assumptions are for illustrative purposes only and are not a prediction or a projection of return. Return assumption is an estimate of what investments may earn on average over a ten year period. Actual returns may be higher or lower than those shown and may vary substantially over shorter time periods.

Investing in the bond market is subject to risks, including market, interest rate, issuer, credit, inflation risk, and liquidity risk. The value of most bonds and bond strategies are impacted by changes in interest rates. Bonds and bond strategies with longer durations tend to be more sensitive and volatile than those with shorter durations; bond prices generally fall as interest rates rise, and the current low interest rate environment increases this risk. Current reductions in bond counterparty capacity may contribute to decreased market liquidity and increased price volatility. Bond investments may be worth more or less than the original cost when redeemed. High-yield, lower-rated, securities involve greater risk than higher-rated securities; portfolios that invest in them may be subject to greater levels of credit and liquidity risk than portfolios that do not. Currency rates may fluctuate significantly over short periods of time and may reduce the returns of a portfolio. Equities may decline in value due to both real and perceived general market, economic, and industry conditions. The use of leverage may cause a portfolio to liquidate positions when it may not be advantageous to do so to satisfy its obligations or to meet segregation requirements. Leverage, including borrowing, may cause a portfolio to be more volatile than if the portfolio had not been leveraged. Derivatives may involve certain costs and risks such as liquidity, interest rate, market, credit, management and the risk that a position could not be closed when most advantageous. Investing in derivatives could lose more than the amount invested.

This material contains the opinions of the authors but not necessarily those of PIMCO and such opinions are subject to change without notice. This material is distributed for informational purposes only and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.

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