I have a question concerning the idea of consumption in multi period. The following is given
$W_0$ is initial wealth
$x$ is the weight on an asset with price / value $S_t$
$B$ is a zerobond at some riskless rate $1<R<2$
the question: how can it be justified (or can it at all be?) that the agent's only chance to transfer money into the second period is via buying the risky asset $S_1$ and not by buying zerobonds? would it not be much more realistic if one had
$$C_1=W_0-xS_1\pm B$$ $$C_2=xS_2\pm BR$$?
Thanks in advance for any suggestions.