Question $12$

Sea$-$Trefoil is a multinational bank with a strong presence in the bond and equity markets. The bank is currently active in these markets and has a trading portfolio comprised of a $2\mathrm{.}5$ million long position in equities and a $3$ million long position in bonds. The two markets are negatively correlated with their correlation coefficient at $-0\mathrm{.}44,$ while their monthly volatility is $2\mathrm{.}12\%$ for the bond market and $4\mathrm{.}69\%$ for the equity market. Using the internal model approach, and assuming $21$ trading days per month, the bank wants to calculate the following:

a$)$ The monthly portfolio value at risk at the $95\%$ and $99\%$ confidence level.

$(10$ marks$)$

b$)$ The daily portfolio value at risk at the $95\%$ and $99\%$ confidence level.

$(10$ marks$)$

c$)$ The monthly portfolio component value at risk at the $95\%$ confidence interval $(15$ marks$)$

Note: The $95\%$ and $99\%$ confidence level have one$-$tailed normal distribution values of $1\mathrm{.}645$ and $2\mathrm{.}326$ standard deviations respectively.