The style was invented for polo. It was designed to keep the saddle in place better than a Y or hunting breastplate. Some people swear by them. You can try tightening it and you can buy a detachable neck strap for it to help keep it up.
Heres a picture of where its supposed to sit. Yours is sitting on the chest muscles which is too low. Yours would be a tiny bit looser and a tiny bit lower because it is not elastic and cannot be fitted as snugly but it would still be pretty close to the reference picture