Is there a cap on stats gained from bonding?

Do horses have a cap on the stats that they can reach from bonding?

I can buy horses from the stable that have better stats than my current horse. Do the horses have a maximum 'level' that they can reach through bonding?

Could my starting horse be trained to have the highest stats of any horse, or am I going to reach a cap on this horse and need to buy one with a higher maximum?

There is a maximum to how much stats will increase from bonding. The exact numbers are 3 for speed, and 2 for acceleration. Health and stamina is not exactly specified, unfortunately.

You cannot get higher bonuses from bonding, so a horse with higher base stats will always be better than your current horse, when fully bonded.

Note that like all horses, bonding can increase your horses base speed by 3 points, and acceleration by 2 points, as well as increasing health and stamina.

https://www.ign.com/wikis/red-dead-redemption-2/Arabian_Horse