This paper presents an exact finite‐sample statistical procedure for testing hypotheses about the weights of mean‐variance efficient portfolios. The estimation and inference procedures on efficient portfolio weights are performed in the same way as for the coefficients in an OLS regression. 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. Using 20 years of data on 11 country stock indexes, we find that the sampling error in estimates of the weights of a global efficient portfolio is large.

This paper presents an exact finite‐sample statistical procedure for testing hypotheses about the weights of mean‐variance efficient portfolios. The estimation and inference procedures on efficient portfolio weights are performed in the same way as for the coefficients in an OLS regression. 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. Using 20 years of data on 11 country stock indexes, we find that the sampling error in estimates of the weights of a global efficient portfolio is large.

Value-at-risk methods which employ a linear (“delta only”) approximation to the relation between instrument values and the underlying risk factors are unlikely to be robust when applied to portfolios containing non-linear contracts such as options. The most widely used alternative to the delta-only approach involves revaluing each contract for a large number of simulated values of the underlying factors. In this paper we explore an alternative approach which uses a quadratic approximation to the relation between asset values and the risk factors. This method (i) is likely to be better adapted than the linear method to the problem of assessing risk in portfolios containing non-linear assets, (ii) is less computationally intensive than simulation using full-revaluation and (iii) in common with the delta-only method, operates at the level of portfolio characteristics (deltas and gammas) rather than individual instruments.

This paper characterizes all continuous price processes that are consistent with current option prices. This extends Derman and Kani (1994) , Dupire (1994 , 1997 ), and Rubinstein (1994) , who only consider processes with deterministic volatility. Our characterization implies a volatility forecast that does not require a specific model, only current option prices. We show how arbitrary volatility processes can be adjusted to fit current option prices exactly, just as interest rate processes can be adjusted to fit bond prices exactly. The procedure works with many volatility models, is fast to calibrate, and can price exotic options efficiently using familiar lattice techniques.