I recently bought the SIA shares after the rights issued at a price of 4.40 but realised the theoretical ex-rights price should be around $4.17. What should I do?

Hi. Since you bought the shares after ex rights, you dont have any rights to subscribe. If you meant to purchase the rights on SGX at additional costs on top of the subscription cost of $3/unit, its not worth it cus by then the cost of rights will be about the same as the market price.

E.g. share price $3.50, the rights will cost $0.50 + $3 to subscribe to the rights.