Portfolio Risk and Correlation

[riskstudent]

Assume that I hold a $1billion portfolio of US. 30-year bonds.

Now I take a short position in $200 million of US 10-year bonds. These 10-year bonds have a correlation of 0.8 to the 30-year bonds.

What will happen to my portfolio risk, it will increase or decrease? Please explain.

Remember that the new position is a short position.

 

[David Harper CFA FRM]

In case it's helpful, i'll add a mathematical hint:

portfolio variance (A+B) =weight(A)^2*variance(A) + weight(B)^2*variance(B) + 2*weight(A)*weight(B)*correlation(A,B)*volatility(A)*volatility(B)
... and the short position enters as a negative weight; e.g., weight(B) = -$200/(1000 - 200) = -25%