Exercise Solution 8.8
It is easy to immediately write down a portfolio mapping for this simple portfolio. The solution is indicated in [s3] below. However, lets formally go through the steps of constructing a primary portfolio mapping as describe in Section 8.3. First, we must define assets. As indicated in Section 8.3.1, assets must represent accumulated values. Gold price 1R1 is not an accumulated value, so it cannot be an asset. Accordingly, we define a single asset with 1S1 representing the USD value, accumulated from time 0 to time 1, of an ounce of gold. Holdings ω = 130. We obtain mapping
[s1]
Accumulated value would include the price of gold as well as any expense of storage or income from leasing the gold. Over a day, such expense or income will be trivial, so we choose to ignore it for this example. The accumulated value of gold will simply equal its price. We define the trivial mapping
[s2]
Substituting [s2] into [s1], we obtain our primary mapping:
[s3]
