Calculate implied expected returns of your assets / instruments.


Implied returns is a reverse mean-variance optimization methodology. It solves for a set of expected returns for the portfolio's assets under the assumption that the portfolio is on the efficient frontier (optimal).

This can help investors understand the implicit assumptions of maintaining their current portfolio allocations. An investor may choose to rebalance their portfolio if the implied returns are substantially different from the plausible range of expected asset returns.

Analysts may also use this method to contrast against other models of expected returns.


The following describes the function signature for use in Microsoft Excel's formula bar.

=IMPLIEDRETURNS(assetReturns, weights, riskAversion, indexCash, rf, dataPeriodicity)




Required. Time series or matrix of asset returns.


Required. Vector of portfolio weights.


Optional. Risk aversion constant. If not specified, it will default to 1.


Optional. Integer to indicate the column index position of a cash asset in assetReturns. This is used to fix a variable in the system of equations in order to solve the reverse optimization. If not specified, it will default to the column index of the lowest return asset.


Optional. Risk-free rate that would correspond with indexCash. If not specified, it will default to the annualized historical average of the lowest return asset.


Optional. Periodicity of the data, used for annualization. If you do not enter the argument, it defaults to 1. e.g. Daily = 255, Monthly = 12, Yearly = 1, Quarterly = 4.

Name-Value Optional Arguments

Specify optional pairs of arguments where Name is the option argument name and Value is the corresponding input object. Name-value arguments must appear after other input argument(s) above, but the order of these pairs does not matter.


=IMPLIEDRETURNS(___, "Name1", value1, "Name2", value2, ..., "NameN", valueN)


Custom covariance matrix of asset returns. This may differ from historical covariance in order to solve implied returns under different risk models.


Row or column vector of implied expected returns. The output vector orientation follows the same orientation as the input vector weights.


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