X has set up a commodity portfolio with two holdings: a holding in gold of 100m,

and a holding in silver of 120m. The annual volatilities of gold and silver are 40%

and 25% respectively. The correlation between gold and silver is 0.55. What would

be the individual and portfolio total value at risk over a six-month period from the two

commodities? The confidence limit is 1.96 standard deviations.

X wishes to add a third commodity to this portfolio, and you plan to introduce one that

you hope will reduce the risk of the portfolio. He invests 90m in coffee. Coffee has

an annual volatility of 10%, and again the time horizon is six months and the

confidence limit is 1.96.

What is the coffee value at risk, and what is the value at risk for the whole portfolio,

given that the correlation between coffee and gold is -0.40, and between coffee and

silver is -0.30?