Lisa Goldberg, Barra Inc.
Total risk
The importance of diversification and risk management was
recognized by a few visionaries in the early days of investing. Only in the 1950's,
however, did these concepts become central. Since then, increasingly
sophisticated mathematical and statistical tools have been brought to
bear on the problem of estimating the aggregate risk of a portfolio.
This risk depends crucially on the covariances of the returns of the
individual components of the portfolio. Unfortunately, in practical
situations, so many covariances come into play that it is impossible to
obtain estimates directly from historical data. This difficulty has
been addressed successfully through factor models, which substantially
reduce the number of covariances that are needed.
We shall review the recent history of quantitative risk management and
explain how factor risk models work. We then discuss a mathematical
issue that arises in connection with building a `total risk' factor
model: one that spans many different markets and asset classes.