An investment company is studying the creation of a financial security that will bear the symbol C and will give right to a payment in one year of $150 in the pessimistic scenario and $260 in the optimistic scenario. The risk-free interest rate is 3%. Consider the two financial stocks A and B whose prices in the absence of a learning opportunity are as follows:

a) Is it possible to replicate C by combining A and B? b) What is the price of C stock if there is no arbitrage opportunity? c) If the probability of realization of the pessimistic scenario is 40% and that of the optimistic scenario is 60%. What is the expected return on the C asset? What is the risk premium? d) If the risk premium of C stock is 0.75%, is there an arbitrage opportunity?

\begin{tabular}{|l|c|c|c|} \multicolumn{1}{c|}{ A B } & \multicolumn{2}{c}{ C } \\ \cline { 2 - 4 } Titles & Market price today & in \$Fow in 1 year according to the scenario in \$ \\ \cline { 2 - 4 } & in $ & Pessimistic & Optimistic \\ \hline A & 55 & 35 & 70 \\ \hline B & 95 & 80 & 120 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|} \multicolumn{1}{c|}{ A B } & \multicolumn{2}{c}{ C } \\ \cline { 2 - 4 } Titles & Market price today & in \$Fow in 1 year according to the scenario in \$ \\ \cline { 2 - 4 } & in $ & Pessimistic & Optimistic \\ \hline A & 55 & 35 & 70 \\ \hline B & 95 & 80 & 120 \\ \hline \end{tabular}