Is it permissible to invest someone else's money, deposited as a trust, in stocks, and if the stocks lose value, is it obligatory to guarantee only the principal, or must the owner of the money be informed of the loss?

It is obligatory for whoever has a trust to preserve and protect it until they return it to its rightful owners, as Allah Almighty says: ﴿Indeed, Allah commands you to render trusts to whom they are due﴾, and as the Prophet, peace and blessings be upon him, said: «Render the trust to the one who entrusted you, and do not betray the one who betrayed you.» Betrayal of a trust is one of the signs of hypocrisy. Disposing of a trust without the owner's permission is a misuse of its preservation and obligates you to guarantee it. If it incurred a loss, you must make up for it from your own money, and you must repent to Allah and seek forgiveness from the owner of the trust.