Altruism: "Acting against the maximisation of one's self-interest for the sake of another or others and/or to satisfy a moral or ethical ideal".
Morality: "Principles concerning the distinction between right and wrong or good and bad behaviour".
Self-interest: "That which a person deems to be of value to themselves".
Selfishness: "Lack of consideration for others".
Virtue: "Goodness of action or attribute. That which should be admired" (Admittedly, virtue seems to imply morality. This seems to make the question circular, unless the definition of 'morality' shifts from something like the definition above to something more like 'valuable', as it eventually does here.
Initial 'intuitive' assumptions
A) If our self-interest aligns perfectly with particular sets of moral and ethical standards, then we are simultaneously moral, ethical and self-interested. To behave morally and ethically in such a circumstance therefore never requires that we act against the maximisation of self-interest.
B) If our self-interest conflicts with particular moral and ethical standards, then - if we are to act morally/ethically - we must act against our self-interest in order achieve moral and ethical ideals.
C) If our self-interest conflicts with the interests of another or others, and if our moral and/or ethical principles identify a circumstance in which we must prioritise the interests of others over our own, then we must act altruistically.
Altruism, as defined above, does not seem to exist. It seems to entail a contradiction:
If we subscribe to a particular set of moral and/or ethical principles, then they are by definition manifestations of our self-interest.
So, if we deprive ourselves of something (act against aspects of our self-interest) in order to satisfy these principles, we still seem to be acting in a way designed to maximise our self-interest, because we value the principle more than the thing of which we deprive ourselves.
For example, if a veteran returns to the battlefield for another tour because he knows his experience may well save the lives of other soldiers, and because he believes that helping to save the lives of his fellow soldiers is the morally and ethically right thing to do, and if he does this against his self-interest of minimising the risk to his life:
The soldier's maximal self-interest is simply not equivalent to the minimisation of the risk to his life. He clearly values acting in this 'selfless' way more than he values remaining as safe as possible, remaining at home with his family, and persisting with new job committments (an illustrative hypothetical only. I absolutely cast no adverse moral or ethical judgement upon anyone in this circumstance).
Therefore, he is not acting altruistically if altruistically means, "Acting against the maximisation of one's self-interest for the sake of another or others and/or to satisfy a moral or ethical ideal", because he is merely prioritising his principles over his safety. His maximal expression of self interest in this context is precisely that; to act despite the potential consequences to his safety. He has concluded that it is better for him to make the physical 'sacrifice' than to not make the physical sacrifice, and is therefore clearly acting in the interests of what he deems to be most important.
In this way, however we act, regardless of whether or not we are acting in ways which damage aspects of our self-interest (such as decreasing wealth when we donate, or going without food to feed our children), we always act ultimately accordance in a way which accords with our maximal self-interest. (Therefore, Assumption B seems contradictory).
Even if our ethics somehow compete with a morality that we believe is imposed by some ultimate 'external' or 'objective' source, the decisions we make seem always to reflect a desire to maximise our self-interest; ie. in adhering to the principles of whichever moral/ethical source we value most (Therefore, Assumption C seems contradictory).
Assumption A seems to suggest that no particular virtue can be associated with acting perfectly morally and/or ethically, because if we do so, we do it in accordance with the principle of maximising our self-interest, in which case self-interest and moral/ethical virtue become almost indistinguishable. (Note: This is not to claim that acting in accordance with a particular moral and/or ethical framework cannot be far more valuable (in personal/social/environmental terms etc) than another).
Assumption B seems similarly flawed, in that it seems we do not ever ultimately act against the maximisation of our self-interest, even when acting in accordance with certain ideals which seem to conflict with aspects of our self-interest.
Assumption C seems impossible too, because there seems no way altruism (as defined here) can exist. This in turn seems to refer us back to Assumption A; that acting morally/ethically is either something which aligns with the maximisation of our self-interest or does not.
Whether or not a morality is deemed to exist somehow independently of our minds, or as a subjective human construct, if we are persuaded by morality do we not therefore act morally because we are persuaded by it and because it accords with our self-interest? How can we ever act in accordance with such a morality and yet against the maximisation of our own self-interest? In other words:
How might we attach virtue (as opposed to mere value) to acting 'morally'?
(Even if we decide to act in accordance with that which is deemed 'moral'; is this decision itself virtuous if it stems from self-interest, or is it merely valuable insofar as the morality concerned provides positive outcomes to the person and/or others/the environment?).
Do we conclude that a person is virtuous because their self-interest happens to coincide with what is deemed moral?
For a very simplistic example: If self-interest leads a person to walk into a burning building to save a child, are they more virtuous than the person who doesn't enter the building, if both acting and not acting arise from self interest? (This example requires that consequences other than risk to the rescuer - such as consequences for his family and friends for example - are ignored.)
It might be that a person decides what is of interest to them and that they decide to do what is virtuous because it they deem it to be virtuous. But in such a case, being virtuous still comes down to doing what is in one's interests; to the fact that for such a person to be 'unvirtuous' would be to act against their interests.
Altruism: Psychological egoism