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Question 5.6: Verify formula (5.3).

Verify formula (5.3).

e^{k_V }= w_1e^{k_1} + w_2e^{k_2}      (5.3)

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The initial and final values of the portfolio are

V (0) = x_{1}S_{1}(0) + x_{2}S_{2}(0),
V (1) = x_{1}S_{1}(0) + x_{2}S_{2}(0)e^{{k_{2}}}
= V (0e^{k_{1}})(w_{1}e^{k_{1}} + w_{2}e^{k_{2}}).

As a result, the return on the portfolio is

e^{k_V} =\frac{V (1)}{V (0)} = w_{1}e^{k_{1}} + w_{2}e^{k_{2}} .

 

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