The risk-return tradeoff: A COGARCH analysis of Merton's hypothesis

Abstract

We analysed daily returns of the CRSP value weighted and equally weighted indices over 1953–2007 in order to test for Merton's theorised relationship between risk and return. Like someprevious studies we used a GARCH stochastic volatility approach, employing not only traditionaldiscrete time GARCH models but also using a COGARCH — a newly developed continuous-timeGARCH model which allows for a rigorous analysis of unequally spaced data.When a risk–returnrelationship symmetric to positive or negative returns is postulated, a significant risk premium ofthe order of 7–8% p.a., consistent with previously published estimates, is obtained. When themodel includes an asymmetry effect, the estimated risk premium, still around 7% p.a., becomesinsignificant. These results are robust to the use of a value weighted or equally weighted index.The COGARCH model properly allows for unequally spaced time series data. As a sidelight, themodel estimates that, during the period from 1953 to 2007, the weekend is equivalent, involatility terms, to about 0.3–0.5 regular trading days.