YAML equivalent of array of objects in JSON

Great answer above. Another way is to use the great yaml jq wrapper tool, yq at https://github.com/kislyuk/yq

Save your JSON example to a file, say ex.json and then

yq -y '.' ex.json

AAPL:
- shares: -75.088
  date: 11/27/2015
- shares: 75.088
  date: 11/26/2015

To supplement the accepted answer if the tight spacing bothers you, you can also do:

AAPL:
  - 
    shares: -75.088
    date: 11/27/2015
  - 
    shares: 75.088
    date: 11/26/2015

...this is adapted straight from the YAML specification's example 2.4.

TL;DR

You want this:

AAPL:
  - shares: -75.088
    date: 11/27/2015
  - shares: 75.088
    date: 11/26/2015

The YAML equivalent of a JSON object is a mapping, which looks like these:

# flow style
{ foo: 1, bar: 2 }

# block style
foo: 1
bar: 2

Note that the first characters of the keys in a block mapping must be in the same column. To demonstrate:

# OK
   foo: 1
   bar: 2

# Parse error
   foo: 1
    bar: 2

The equivalent of a JSON array in YAML is a sequence, which looks like either of these (which are equivalent):

# flow style
[ foo bar, baz ]

# block style
- foo bar
- baz

In a block sequence the -s must be in the same column.

Let's turn your JSON into YAML. Here's your JSON:

{"AAPL": [
  {
    "shares": -75.088,
    "date": "11/27/2015"
  },
  {
    "shares": 75.088,
    "date": "11/26/2015"
  },
]}

As a point of trivia, YAML is a superset of JSON, so the above is already valid YAML—but let's actually use YAML's features to make this prettier.

Starting from the inside out, we have objects that look like this:

{
  "shares": -75.088,
  "date": "11/27/2015"
}

The equivalent YAML mapping is:

shares: -75.088
date: 11/27/2015

We have two of these in an array (sequence):

- shares: -75.088
  date: 11/27/2015
- shares: 75.088
  date: 11/26/2015

Note how the -s line up and the first characters of the mapping keys line up.

Finally, this sequence is itself a value in a mapping with the key AAPL:

AAPL:
  - shares: -75.088
    date: 11/27/2015
  - shares: 75.088
    date: 11/26/2015

Parsing this and converting it back to JSON yields the expected result:

console.log(jsyaml.load(`
AAPL:
  - shares: -75.088
    date: 11/27/2015
  - shares: 75.088
    date: 11/26/2015
`));

<script src="https://cdnjs.cloudflare.com/ajax/libs/js-yaml/4.1.0/js-yaml.min.js"></script>

You can see it (and edit it interactively) here.