Fidelity Investments is not a publicly traded company as of January 2015, so it does not have a ticker symbol. Ticker symbols are only used for publicly traded companies.
However, Fidelity Investments does have a shorthand for its name. FMR LLC stands for Fidelity Management and Research, a limited liability company.
Ticker symbols developed when ticker tape machines were used for information on stocks. It was easier to have a shorthand for each company, and ticker symbols are still used on stock exchanges. However, private companies, all of which do not trade on the stock exchange, have no use for them.