a$)$ What are mortgage backed securities$?$ It was believed that the instrument would help reduce the bank$$s maturity mismatch and hence the possibility of banking crisis. Explain the logic behind the argument. $(5$ marks$)($b$)$ However, because of the principal$-$agent problem, mortgage backed securities turned out to be a toxic asset and an important cause of the financial tsunami in $2008-09.$ Explain the principal$-$agent problem here. Who is the agent? Who are the principals? $(5$ marks$)($c$)$ In addition to the principals, insurance companies were also severely hurt during the financial tsunami. Why? Before the financial tsunami, would it be possible for an investor to indentify the risk by checking the balance sheet of the insurance companies? $(5$ marks$)($d$)$ Explain why the mark$-$to$-$market rule has contributed to the deepening of the financial tsunami even if the holders of the toxic assets could hold the asset until the crisis is over. $(5$ marks$)($e$)$ In $2011$Q$3,$ the share price of the Bank of America dropped substantially because of the put$-$back risk. What is the put$-$back risk? $(5$ marks$)$