What Was Probably True
Modal Verbs of Probability - Past
Modal verbs of probability express an opinion based on what a speaker knows about a situation at the moment of speaking. The following forms are used to speak about past situations.
Example:
He must have been aware the endorsement would reflect poorly on the candidate.
They must have been involved in securing the endorsement.
The funds in your account may have been insufficient to cover this purchase.
'Must' plus the perfect form (must have done) expresses the idea that you are almost 100% sure of your opinion about a given situation which took place in the past.
Subject + must + have + past participle + objects
Example:
I must have been confused with the particular policies of that bank branch.
They must have been involved in securing the endorsement.
'Might' or 'could' plus the perfect form of the verb (could / might have done) expresses an opinion that you think was probably true at a past moment in time.
Subject + might / could + have + past participle + objects
Example:
The funds in your account may have been insufficient to cover this purchase.
He could have had overdraft protection with the account.
'Can't' plus the perfect form of the verb (can't have done) expresses the idea that you are almost 100% sure that something was not true at a past moment in time. Note that the form is 'can't have done' NOT 'couldn't have done'.
Subject + can't + have + past participle + objects
Example:
That can't have been a bear market because I made a lot of money
A commercial loan can't have been given to that builder.