The Arbitrage Pricing Theory provides a theory to quantify risk and the reward for taking it. While the theory itself is sound from most perspectives, its empirical version is connected with several shortcomings. One extremely delicate problem arises because the set of observable asset returns rarely has a history of complete observations. Traditionally, this problem has been solved by simply excluding assets without a complete set of observations from the analysis. Unfortunately, such a methodology may be shown to (i) lead for any fixed time period to selection bias in that only the largest companies will remain and (ii) lead to an asymptotically empty set containing no observations at all. This paper discusses some possible solutions to this problem and also provides a case study containing Swedish OMX data for demonstration.

This paper concerns the problem of estimating the Mahalanobis distance when the dimension of the data matrix is comparable to the sample size. Two different ridge-shrinkage estimators are considered and estimators of related risk functions are derived. The properties of these point estimators are investigated in terms of excess risk and bias relative to the traditional estimator.

This article treats the problem of linking the relation between excess return and risk of financial assets when the returns follow a factor structure. The authors propose three different estimators and their consistencies are established in cases when the number of assets in the cross-section (n) and the number of observations over time (T) are of comparable size. An empirical investigation is conducted on the Stockholm stock exchange market where the mean-standard deviation ratio is calculated for small- mid- and large cap segments, respectively.