* Stake adds to Elliott's portfolio in Europe
* Stake comes after Saga profit warning
* Shares rise, trader cites hope of shake-up (Adds quotes, data on short-selling, updates shares)
By Noor Zainab Hussain and Simon Jessop
July 17 (Reuters) - Activist investor Elliott has disclosed a stake in Saga Plc less than a month after the specialist tourism and insurance firm warned discounting was hurting its tours business.
Saga has been trying to shake off its image as only serving "old people" and had begun rebranding after a profit warning in April. The company is also looking for a new chief executive officer after Lance Batchelor announced his departure last month.
Elliott Capital Advisors disclosed a 5.14% stake in Saga as of July 12, a filing showed on Wednesday.
"We have good and open relations with all of our shareholders and expect to be in contact with Elliott shortly," a spokeswoman for Saga said.
Small-cap Saga's shares rose as much as 8.6% following the news. They were up 7.3% by 1021 GMT.
The shares, widely held by retail investors since Saga floated at 185 pence in 2014, have slumped 58% this year and are down 81% from their peak in 2016.
One London-based trader said news of the stake would spur hope of a management shake-up.
Saga has already had a series of senior level departures in the last two years, including those of its chief financial officer and chairman. A source with knowledge of the matter said no further changes were planned at present.
Another source familiar with the situation said Saga was undervalued, but with a well-regarded brand and assets that could be separated, adding that management needed to review all the options.
BlackRock took out a 0.6% short position in the Saga's stock last week, according to data from Britain's markets watchdog.
Short bets involve paying to borrow the shares before selling them on to another investor, hoping to buy them back at a lower price before returning the stock to the original owner.
Saga's profit warning and continued fall in market value have raised concerns about Saga's debt, which the company has been trying to trim.
In April, Saga said bookings were hurt by older Britons cutting back on travel because of uncertainty over Brexit, with profit liable to fall by as much as 75 million pounds this year.
This marked a shift for Saga, whose travel business has been supported by spending from affluent pensioners, protecting it from a consumer spending hit since Britain voted to leave the EU in June 2016.
To help to revive its insurance business, Saga plans to offer home and automotive policies with three-year fixed pricing and cut prices for renewals. Margins at Saga's tours business have also been crimped by competitive discounting.
Russ Mould, investment director at AJ Bell, said given Saga had already announced changes to its insurance business, "Elliott would need a convincing argument to push for further change". He also said Elliott might want a say in the choice of new CEO, but would need a bigger stake to do so.
Elliott's move comes as top 10 U.S. activist investors step up investments in Europe.
Elliott, with assets under management of about $35 billion, has a history of building up minority stakes in takeover targets with a view to securing an improved bid.
New York-based Elliott most recently built up a position in France's Altran Technologies in the wake of a 3.6 billion-euro ($4.03 billion) buyout bid by its bigger rival Capgemini.
Since last year, the fund has acquired stakes in a number of European companies including Pernod Ricard, SAP and Telecom Italia. It also has a stake in Bayer.
Elliott, Paul Singer's hedge fund, committed $3.4 billion in new capital in the first six months of 2019, data compiled by Lazard shows, outpacing Carl Icahn who spent $2.8 billion.
(Reporting by Noor Zainab Hussain in Bengaluru and additional reporting by Thyagaraju Adinarayan and Carolyn Cohn in London and Arno Schuetze in Frankfurt; editing by Patrick Graham/Louise Heavens/Deepa Babington/Jane Merriman)