The correlation between changes in price of a spot asset and futures asset is 99%.The standard deviation of changes in spot prices is $2,and that of futures prices is $3.What is the standard deviation of a position that is long 5 units of the spot asset and is hedged by shorting 4 units of futures?
A)1.5
B)2.0
C)2.5
D)3.0

Question

Quizplus · Accepted Answer

Use the formula provided in the text.The calculations are as follows:
> rho = 0.99
> sigDS = 2
> sigDF = 3
> n=5
> m=4
> vr = n^2*sigDS^2 + m^2*sigDF^2 - 2*rho*m*n*sigDS*sigDF
> vr
[1] 6.4
> sqrt(vr)
[1] 2.529822

The Correlation Between Changes in Price of a Spot Asset