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 some previous studies we used a GARCH stochastic volatility approach, employing not only traditional discrete time GARCH models but also using a COGARCH -a newly developed continuous-time GARCH model which allows for a rigorous analysis of unequally spaced data. When a risk-return relationship symmetric to positive or negative returns is postulated, a significant risk premium of the order of 7-8% p.a., consistent with previously published estimates, is obtained. When the model includes an asymmetry effect, the estimated risk premium, still around 7% p.a., becomes insignificant. 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, the model estimates that, during the period from 1953 to 2007, the weekend is equivalent, in volatility terms, to about 0.3-0.5 regular trading days.

Re-examining the risk–return relationship in Europe: Linear or non-linear trade-off?

“…Despite the differences among all the models presented, they share a strong linear (monotonic) assumption in the definition of the relationship between return and risk. Recently, Muller et al (2011) use the basic and asymmetric Cointegrated-GARCH (COGARCH) approach to test the Merton's hypothesis. They argue that the asymmetric COGARCH model is not supportive of Merton's hypothesis, while the symmetric version of COGARCH shows a significant positive covariance between the market risk-premia of both the CRSP value weighted and equal-weighted excess market returns and volatilities over the period 1953-2007. However, Merton's model is not the only theoretical approach explaining the risk-return relationship.…”

Melancholia and Japanese stock returns – 2003 to 2012

“…1 See Müller, Durand, and Maller (2011) for a review of literature discussing the relationship of risk and expected return. 2 The TOPIX is a free-float adjusted market capitalization-weighted index that is calculated using all the domestic common stocks listed on the TSE First Section.…”

What Enables a High-Risk Project to Yield High Return from a Construction Contractor’s Perspective?

“…The risk-return tradeoff has been studied much in the financial industry [1,2,[15][16][17][18][19][20] The risk is defined as the degree of exposure to the uncertainty that can have a positive or a negative effect on outcome [21,22]. In the financial investment, the risk is usually divided into interest rate risk, market risk, credit risk, sovereign risk, and operating risk [2,23].…”

“…Many researchers insist that there is a positive relationship between risk and return [15][16][17]. Moreover, many empirical studies prove the principle of "high-risk high-return" and many models such as risk premium and portfolio have been developed based on this principle [18][19][20]. This principle is taken for granted in most industries.…”