I am replicating the dynamic strategy of Daniel and Moskowitz(2016) but my supervisor told me the way I am calculating the cumulative return is wrong and I have to use a loop that does the calculation provided above or use log returns since those are additive (don’t forget to “de-log” after calculating the sum).
and also I did not know how to calculate the lambda but his explanation did not help me !
here is the explanation
Lambda is determined ex-post. The approach to find lambda is similar to the scaling approach for CVOL. First, calculate the strategy for an arbitrary lambda (for example, start with lambda = 0.50). Then, calculate the in-sample volatilty of the strategy and adjust lambda. Hint: The ratio that is used to adjust lambda is vice versa compared to the CVOL adjustment.
· For the main part of their study, DM only show results for the ex-post DYN strategy. Then, there is only one regression necessary. Since you are estimating the ex-ante strategy, an expanding window regression is needed (p. 237). In each loop, one month is added to the expanding regression.
I am uploading what I have so far