Exercise Solution 8.11

We define asset vector 1S with


Holdings ω = (200, 6, –2). We define


Next, we need to define 1S as a mapping of the key vector. For this purpose, our treatment of the physical gold position parallels our work in Exercise 8.8. Our treatment of the futures parallels our work of Exercise 8.10. We specify a mapping as


Substituting [s3] into [s2], we define our primary mapping: