Question

Value at Risk (VaR) is an attempt to provide a single number for senor management summarizing the total risk in a portfolio of financial assets. It has become widely used by corporate treasurers and fund managers as well as by financial institutions.

A company currently has $5 million invested in commodity X and $3 million invested in commodity Y. The daily sigma of commodity X is 1 percent, the daily sigma of commodity Y is 1.5 percent, and the coefficient of correlation between returns from the two commodities is 0.7. What is the total investment’s VaR for the next 10 days with a 99 percent confidence level?

Answer 1

Weight in Commodity X = Investment in Commodity X / (Investment in Commodity X + Investment in Commodity Y)

Weight in Commodity X = $5,000,000 / ($5,000,000 + $3,000,000)

Weight in Commodity X = 62.5%

Weight in Commodity Y = Investment in Commodity Y / (Investment in Commodity X + Investment in Commodity Y)

Weight in Commodity Y = $3,000,000 / ($5,000,000 + $3,000,000)

Weight in Commodity Y = 37.5%

Porfolio Standard Deviation = (Weight in Commodity X * Standard Deviation of Commodity X)² + (Weight in Commodity Y * Standard Deviation of Commodity Y)² + (2 * Weight in Commodity X * Weight in Commodity X * Standard Deviation of Commodity X * ​Standard Deviation of Commodity Y * Correaltion between Commodity X & Commodity Y)

Porfolio Standard Deviation = (62.5% * 1%)² + (37.5% * 1.5%)² + (2 * 62.5% * 37.5% * 1% * 1.5% * 0.7)

Porfolio Standard Deviation = 0.0001199

Porfolio Standard Deviation = 1.0951%

1 day 99% Portfolio VaR = Porfolio Standard Deviation * Z-score for 99% * Total Investment

1 day 99% Portfolio VaR = 1.095% * 2.33 * $8,000,000

1 day 99% Portfolio VaR = $204,124.49

10 day 99% Portfolio VaR = 1 day 99% Portfolio VaR * 10

10 day 99% Portfolio VaR = $204,124.49 * 10

10 day 99% Portfolio VaR = $645,498.32