Exercise Solution 8.9
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 expressed in the base currency, which is USD. Gold price 1R1 is not an accumulated value, and it is not denominated in USD, 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 expressed in USD. Because 1R1 is denominated in EUR, we define the mapping
[s2]
Substituting [s2] into [s1], we obtain our primary mapping:
[s3]
