Gemara

(Rav Ula): We can learn the extent of honoring parents from a Nochri, Dama ben Nesinah. Once he could have profited 600,000 gold Dinars from a business deal, but he would have needed to wake his father. He refrained from doing so.

(Rav Dimi): Once, Dama was wearing silk woven with gold, and was seated among the Roman officials. His mother came, tore his garment, hit him on the head and spat in front of him. He did not embarrass her.

31b: R. Tarfon would bend down for his mother to step on him when climbing into or out of her bed.

Rabanan: That is not half as much as is required! Did she throw a wallet in the sea, and you would not embarrass her?

32a (Beraisa - R. Eliezer): The extent of honoring parents is if the parent throws his wallet in the sea, and the child does not embarrass the parent.

Question: If honor of parents is from the parents' money, we must say that it is the father's wallet. If so, why does the child care? (It is not hard to refrain from embarrassing the parent.)

Answer: The case is, the child is destined to inherit the parent.

Rishonim

Rif: The extent of honoring parents is if the parent will throw his wallet in the sea in front of the child, and the child does not embarrass the parent.

Question (Ran DH Lo): According to the opinion that Kivud Av v'Em is from the parents' money, why didn't Dama wake his father?

Answers (Ran): One need not spend his own money to honor his parents, but he must forfeit all his money to avoid embarrassing his parents. Alternatively, one need not spend money to honor them, but he must refrain from a profit if necessary to honor them.

Rambam (Hilchos Mamrim 6:7): The extent of honoring parents is if the child has a wallet of gold coins, and his parent threw it in the sea, and the child does not embarrass the parent, shout or get angry. He accepts Hash-m's decree and is silent. The extent of fearing parents is if the child was wearing choice garments, and was seated at the head of the congregation, and his parent came and tore his garments or hit him on the head and spat in front of him, and he does not embarrass him. He is silent, and fears the King of kings who commanded about this. Had a mortal king commanded something more painful than this, he could not quiver (to show unwillingness), all the more so regarding the command of the One who said and brought the world into being through His will!

Rosh (1:50): The extent of honoring parents is if the parent will throws a wallet in the sea in front of the child, and the child does not embarrass the parent.

Poskim

Shulchan Aruch (YD 240:3): The extent of fearing parents is if the child was wearing choice garments, and was seated at the head of the congregation, and his parent came and tore his garments or hit him on the head and spat in front of him, and he does not embarrass him. He is silent, and fears the King of kings who commanded about this.

Shach (4, and Prishah 15): The son may claim the cost of his garment from his father in Beis Din, like the Rema says below.

Shulchan Aruch (8): The extent of honoring parents is if the child has a wallet of gold coins, and his parent threw it in the sea, and the child does not embarrass the parent, shout or get angry. He accepts the Torah's decree and is silent.

Rema: Some say that if he wants to through the son's money into the sea, he may stop him, for one need not honor with his own money, only with the parent's.

Beis Yosef (DH v'Ad): The Gemara said that according to the opinion that Kivud Av v'Em is from the parents' money, we must say that it is the father's wallet. Since we rule like this, this implies that the child may embarrass a parent who seeks to throw the child's wallet in the sea. The Ri rules like this. However, the Rif and Rambam rule that Kivud Av v'Em is from the parents' money, yet they forbid one to embarrass his parent who seeks to throw the child's wallet in the sea. They must hold that one need not spend his own money to honor his parents, but he must forfeit his money to avoid embarrassing his parents. Alternatively, the Halachah does not require losing money to honor them, but if he did, it is part of the Mitzvah. The words 'this is the extent of fearing parents' are very precise. The one who asked the question did not think that we distinguish like this (rather, the child must pay for Kivud Av). The one who answered could have given this distinction. He preferred to answer according to the questioner's premise.

Rema: We do not distinguish between honoring and paining. If he already threw the money, he may not embarrass him. He may claim from him in Beis Din. This refers only to throwing money into the sea, which is a loss. If the parent wants to prevent the son from profiting, in any case he may not stop him.

Bach (DH v'Ad): The Rif's text explicitly said 'his wallet', i.e. the son's. If Kivud Av v'Em is from the parents' money, the son may claim his loss and will not lose. However, if the father does not have money to pay, the Rif could agree that the son may embarrass the father to prevent a loss. Perhaps the RI holds that one may embarrass the father to avoid the need to go to Beis Din. Perhaps above (Sa'if 3) we discuss when the son cannot prevent the father from tearing his garment, so the Rema did not bring a dissenting opinion. This is better than the Beis Yosef's Perush. The Ri's Perush seems primary.

Radvaz (Hilchos Mamrim 6:7): Rabanan asked R. Tarfon 'did she throw your wallet in the sea, and you did not embarrass her?' (This is unlike the Ri.) Surely, even texts that do not say 'your' agree that they meant this. Why would she have her own wallet?

Lechem Mishneh (Hilchos Mamrim 6:7): The Rambam holds like the Ramah, who permits embarrassing the parent to prevent loss. The Rambam discussed after the wallet was thrown. The Rif can explain similarly. The Rif says 'the extent... the parent will throw his wallet', i.e. the parent's wallet.

Gra (18) The text of the Rif and Rambam said 'embarrassing is different' (to avoid this, the son must spend his money).

Shulchan Aruch (18): A Mamzer is obligated to honor and fear his father. Even if his father is a Rasha, he must honor and fear his father.

Rema: Some say that he need not honor a father who is a Rasha unless he did Teshuvah.

Taz (17): The Ran and Tosfos distinguish between paining parents and honoring them. The Rema (Sa'if 8) does not distinguish:

R. Akiva Eiger: He may not do an act to disgrace him. He need not do an act to spare his father from disgrace (Mishneh l'Melech Hilchos Malveh 4:4).