June 4 (Reuters) - Shares in Saudi Arabia's Kingdom Holding fell as much as 10 percent on Thursday, wiping out most of the gains made last week on the back of a surge of investor enthusiasm over its stake in Elon Musk's SpaceX, which is due to go public soon.

Kingdom Holding’s stake in the US rocket company could be worth close to six billion dollars once what would be the largest initial public offering in history is completed.

Only a small percentage of Kingdom Holding's shares are traded, which has contributed to the stock's price volatility this week.

Saudi billionaire Prince Alwaleed bin Talal owns a 78 percent majority stake in the company, while the Saudi sovereign wealth fund, the Public Investment Fund, owns about 17 percent.

The stock rose by about 15 percent last week, but its sharp decline today made it one of the biggest losers on the Saudi index.

Kingdom Holding said in a disclosure today that it owns 0.34 percent of SpaceX, valued at $4.47 billion at the end of March.

She added that although the final pricing for the initial public offering and the company's valuation have not yet been confirmed, if SpaceX's valuation reaches Musk's target of $1.75 trillion, Kingdom Holding's stake would be worth approximately $5.67 billion.

SpaceX on Wednesday set a price of $135 per share in its IPO, targeting proceeds of $75 billion.

Market participants had already anticipated significant financial gains from Kingdom Holding's investment in SpaceX. The Saudi company's stock has risen by more than 82 percent since the beginning of the year, compared to a rise of less than 5 percent for the broader Saudi stock index.

Kingdom Holding has a decades-long track record of investing in early-stage, world-leading technology companies. Its past and present investments include Twitter (before Musk's acquisition and rebranding as X), Careem (before Uber's acquisition), Lyft (the ride-hailing service), and Musk's AI startup, XAI.

(US Dollar = 3.7543 Riyals)