Sorting nested documents by nested field

Elastic Stack Elasticsearch
1

I have unit_type documents that have nested rent documents. The rent documents have a price property and an effective_date property. I want to filter unit_types and sort the nested rent documents by their effective date. The rent documents are not stored in sorted order currently. If this cannot be done with a nested data type, can it be done with parent/child?

I am using v1.6
Here is my index mapping:

{
  "unit_types_v1": {
    "aliases": {
      "unit_types": {}
    },
    "mappings": {
      "unit_type": {
        "properties": {
          "id": {
            "type": "long"
          },
          "property_id": {
            "type": "long"
          },
          "rents": {
            "type": "nested",
            "properties": {
              "effective_date": {
                "type": "date",
                "format": "dateOptionalTime"
              },
              "id": {
                "type": "long"
              },
              "price": {
                "type": "double"
              },
              "unit_type_id": {
                "type": "long"
              }
            }
          }
        }
      }
    }
  }
}