Log returns do not aggregate across assets. Suppose we take asset A with a simple return of r$$A$$t$+1=0\mathrm{.}1$and asset B with a simple return of r$$B$$t$+1=0\mathrm{.}05.$ What are the log returns of them?$$ If we hold a portfolio of $50\%$ asset A and $50\%$ asset B$,$ what is the log return of this portfolio? Is$$the log return of the portfolio the same with the weighted average of each stock$$s log returns?