###### 1.9.3 Portfolio Theory

Directly or indirectly, regulatory and proprietary value-at-risk measures were influenced by portfolio theory. Markowitz (1952) and Roy (1952) independently published PMMRs to support portfolio optimization. In 1952, processing power was inadequate to support practical use of such schemes, but Markowitz’s ideas spawned work by more theoretically inclined researchers. Papers by Tobin (1958), Treynor (1961), Sharpe (1963, 1964), Lintner (1965) and Mossin (1966) contributed to the emerging portfolio theory.

The PMMRs they employed—primarily variance of simple return and standard deviation of simple return—were best suited for equity portfolios. There were few alternative asset categories, and applying value-at-risk to these would have raised a number of modeling issues. Real estate cannot be marked to market with any frequency, making value-at-risk inapplicable. Applying value-at-risk to either debt instruments or futures contracts entails modeling term structures. Also, debt instruments raise issues of credit spreads. Futures that were traded at the time were primarily for agricultural products, which raise seasonality issues. Schrock (1971) and Dusak (1973) describe simple value-at-risk measures for futures portfolios, but neither addresses term structure or seasonality issues.

Lietaer (1971) describes a practical value-at-risk measure for foreign exchange risk. He wrote during the waning days of fixed exchange rates, when risk manifested itself as currency devaluations. Since World War II, most currencies had devalued at some point; some had done so several times. Governments were secretive about planned devaluations, so corporations maintained ongoing hedges. Lietaer proposes a sophisticated procedure for optimizing such hedges. It incorporates a variance of market value PMMR. It assumes devaluations occur randomly, with the conditional magnitude of a devaluation being normally distributed. Computations are simplified using a modification of Sharpe’s (1963) diagonal model. Lietaer’s work may be the first instance of the Monte Carlo method being employed to value a PMMR.