Journal of Investment Strategies

Implementing mean–variance spanning tests with short-sales constraints

Farid AitSahlia, Thomas Doellman and Sabuhi Sardarli

  • Mean-variance spanning can be used to decide on asset inclusion in or exclusion from portfolios.
  • Under short-sales constraints the associated Wald tests are prone to numerical instability.
  • We show that this issue can be avoided in the presence of a risk-free asset.
  • We also show how these tests are incorrectly applied in the context of U.S. retirement plans.

A set of assets is said to span the mean–variance space if the efficient frontier it generates cannot be improved upon with additional assets. Mean–variance spanning is used to determine empirically whether or not particular assets should be included in a given portfolio. Because of typical issues relating to parameter estimation in mean–variance optimization, the results of this empirical approach may differ from those of optimization, which assumes known parameters. In this paper, we show that the Wald tests used to account for short sales are prone to numerical instability. To address this, we exploit the uniqueness of the stochastic discount factor in the presence of a risk-free rate, leading to more robust tests.We also show that the purported Wald tests that have appeared in the literature on retirement plans in the United States do not correspond to mean–variance optimality and that their proper implementation leads to significantly different results.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here