Managed portfolio performance and transaction costs

Abstract

In this work the economic value of conditioning information within a multi-asset dynamic portfolio setting is examined. The article innovates by deriving a simple closed-form expression for the optimal portfolio weights in the presence of quadratic transaction costs. An application to US stock and bond data provides an estimate of the maximum transaction cost level that will allow the value of conditioning information to be statistically significant.

Keywords:

• managed portfolio
• conditioning information
• prediction
• transaction costs

JEL Classification:

• C53
• G17

Notes

¹ Consumption wealth income ratios are only available at the annual frequency.

² Unconditional Sharpe ratios are defined as the unconditional mean of excess portfolio returns divided by the unconditional SD of excess portfolio returns, with excess returns defined as portfolio returns minus one-month Treasury bill returns and trading costs. This particular definition coincides with the ‘net’ Sharpe ratio definition used in Gârleanu and Pedersen (2013). These ratios are calculated as follows: optimal portfolio weights are obtained by replacing population moments with sample moments in Equation 6, which are then used to construct portfolio returns upon which the Sharpe ratios are calculated.

³ We further assume that transaction costs are based on a smooth deterministic nonparametric measure of the covariance matrix, such that it is allowed to vary over time as follows:

where vech(A) is the half-vectorization operator, , with K(.) representing a kernel function with bandwidth given by b = 0.25T^−0.4 (cf. Gârleanu and Pedersen, 2013, consider a time-invariant measure of the covariance matrix and thus a time-invariant measure of transaction costs).

⁴ Dividing by 2 reflects the fact that appears in the utility function of the investor under the assumption that τ equal one.

⁵ The nonignorant investor uses Equation 6, while the ignorant investor sets the transaction cost component in Equation 6 to zero. Within the context of Gârleanu and Pedersen’s (2013) Sharpe ratio definitions, this amounts to the ignorant investor maximizing ‘gross’ Sharpe ratios and the nonignorant investor maximizing ‘net’ Sharpe ratios.

⁶ To maintain the correlation structure within subsets of the data, we draw from the same time period across all returns, and from the same time period across all state variables.

⁷ For instance, the maximum Sharpe ratio differences over all conditioning instruments could be considered.