Question $2($a$)$ A confectioner takes a long position on cocoa futures for $100$ metric tons at $$200$ per metric ton. The exchange requires a $10\%$ initial margin. Meanwhile, the maintenance margin is $60\%$ of the initial margin. What would the spot price of cocoa have to be in order to lead to a margin call for that confectioner$$s position? $(2$ marks$)($b$)$ You currently hold a portfolio of Malaysian stocks worth RM$3,000,000.$ You anticipate that in the coming $3$ months there will be volatility in equity markets. As such, you would like to completely hedge your portfolio of stocks. Use the following information to answer the questions. Beta of your portfolio $=1\mathrm{.}1$ Spot index value $($FBM KLCI$)=1,650$ Risk$-$free rate $=4\%$ per annum $3-$month SIF contract $=1,666\mathrm{.}26$ points Expected dividend yield $=0\%$ i$.$ ii$.$ iii. How many SIF contracts should you use to fully hedge your portfolio? $(1$ mark$)$ Outline the hedge strategy and show the resulting portfolio value assuming that the market falls by $5\%$ by futures maturity. $(5$ marks$)$ If you felt that equity markets were going to fall, why not just liquidate your portfolio $($sell all your stocks$)$ and buy them back after the downward trend, instead of hedging your portfolio using derivatives? $(2$ marks$)($c$)$ You are presently managing a portfolio comprising $$40$ million in U$.$S$.$ equities and $$10$ million is U$.$S$.$ Treasury bills $($assumed to be a risk$-$free asset$).$ The U$.$S$.$ stocks have a weighted$-$average beta of $1\mathrm{.}2.$ Assume a spot S&P $500$ Index of $5,900$ and an index multiple of $100.$ i$.$ ii$.$ What is the overall beta of your portfolio? $(1$ mark$)$ You predict that the U$.$S$.$ stock market will decline in the near future. Hence, you would like to reduce the overall beta of your portfolio to $0\mathrm{.}7$ by taking short positions in Stock Index Futures. How many SIFs should you short $($rounded up$,$ if necessary$)?$