By excess returns, I'm referring to the current nominal treasury rate minus the log returns of the security.
I'm working to construct a dynamic CML / CAPM application, but am uncertain how standard deviations on the x-axis of the Capital Market Line (CML) model should be calculated in this circumstance. It seems as though it's a small, but critical point which is broadly overlooked.
Should I compute the standard deviations of CML model securities based on log returns in this circumstance. Note, I'm using variable treasury yields as the RFR subtracted from return period in the CAPM model. Unlike the CAPM model, with it's Betas of each security representing the slope of the excess market(independent variable) regressed against excess stock returns(dependent variable), it seems to follow that I would use excess return standard deviations in the CML model. This practice doesn't seem to be followed.
As Expected Returns are calculated from the regression of both excess return components (i.e., the market security excess against the non-market security excess) in the CAPM model, it seems to follow, that the standard deviations and expected returns derived from the CAPM model should be carried over to the CML model, with a matching 'excess standard deviation' (i.e., 'excess historic volatility'). This small nuance could make a significant difference over time.
Thanks for sharing your thoughts!