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?