Britten-Jones gives an exact finite-sample procedure for testing hypotheses about the weights of a mean-variance efficient portfolio. The key observation is that estimation and inference on efficient portfolio weights can be carried out exactly as in an ordinary least squares (OLS) regression: regressing a vector of ones on the assets' excess returns yields OLS coefficients proportional to the tangency-portfolio weights, so standard t- and F-statistics test hypotheses on the weights and, when returns are multivariate normal, have exact t and F distributions in finite samples. Applied to 20 years of data on 11 country stock indexes, the sampling error in the estimated weights of a global efficient portfolio is found to be large.
"This paper presents an exact finite-sample statistical procedure for testing hypotheses about the weights of mean-variance efficient portfolios … OLS t- and F-statistics can be used for tests on efficient weights, and when returns are multivariate normal, these statistics have exact t and F distributions in a finite sample."
A small, elegant result with a big practical payoff: by recognising that efficient portfolio weights are just regression coefficients, Britten-Jones hands practitioners the entire OLS inference toolkit — standard errors, t-tests, F-tests, and exact distributions — for objects that had previously seemed to require bespoke asymptotics. The empirical punchline is the one that stuck: global efficient-portfolio weights are estimated so imprecisely that most are statistically indistinguishable from zero, which is the quantitative case for everything downstream — estimation-risk corrections, the Black-Litterman shrinkage toward equilibrium, robust and sparse portfolios. The exactness leans on the multivariate-normal IID assumption, so fat tails and time-varying moments loosen the finite-sample guarantee, but the qualitative message — weights are wildly uncertain — is if anything stronger under realistic return dynamics.