How can create the new column in the previous table instead of new one?

Question

The data defination for my table:

 \d  quote
                               Table "public.quote"
 Column |     Type      | Collation | Nullable |              Default              
--------+---------------+-----------+----------+-----------------------------------
 ticker | text          |           |          | 
 date   | date          |           |          | 
 open   | numeric(7,2)  |           |          | 
 high   | numeric(7,2)  |           |          | 
 low    | numeric(7,2)  |           |          | 
 close  | numeric(7,2)  |           |          | 
 volume | numeric(7,2)  |           |          | 
 id     | integer       |           | not null | nextval('quote_id_seq'::regclass)
Indexes:
    "quote_pkey" PRIMARY KEY, btree (id)

I can create new column into a new table:

SELECT *,
   CASE WHEN ROW_NUMBER() OVER (PARTITION BY ticker ORDER BY ticker,date asc) >= 12
        THEN AVG(close) OVER (PARTITION BY ticker ORDER BY ticker ROWS BETWEEN 11 PRECEDING AND CURRENT ROW)
   END AS short_ma INTO new_quote  FROM quote;

Can i add the new column short_ma in the previous table quote,instead of creating new table new_quote with alter command or other way?

The alter command structure maybe something like:

ALTER TABLE quote ADD COLUMN short_ma DECIMAL(7, 2) GENERATED ALWAYS AS () STORED;

My try failed :

ALTER TABLE quote ADD COLUMN short_ma DECIMAL(7, 2) GENERATED ALWAYS AS (
SELECT CASE WHEN ROW_NUMBER() OVER (PARTITION BY ticker ORDER BY ticker,date asc) >= 12
        THEN AVG(close) OVER (PARTITION BY ticker ORDER BY ticker ROWS BETWEEN 11 PRECEDING AND CURRENT ROW)
   END AS short_ma FROM quote) STORED;