Yes, though in my opinion, this is one of the dirty secret of the VC world. The GP contribution, after taking into account their fees, is essentially negative.
Let's take a more generous example where the GP contributes 5% of the fund. After 10 years of 2% fees, the GP has put in 5% and taken out 20%, so their net contribution is essentially -15%.
Unless I'm misunderstanding what you're saying, I think you're confusing the carry and the management fee. you can't add/subtract those percentages, because they're not representation the same base quantity (ie, they're percentages of different things).
EDIT: Nevermind, I read "the GP has put in 5% and taken out 20%" as referring to a hypothetical carry of 20%.
Ostensibly, the 2% management fee goes to the firm and is intended to cover operations, business expenses, and overhead, rather than individual compensation for the partners. On the other hand, the money they put in does come from them individually (and the carry goes back to them individually as well). They're not supposed to be using the management fee to compensate themselves personally in the way that -20% + 5% would imply.
I won't pretend that there aren't partners and/or firms who abuse this, but that's not the way it's intended to work. And if they don't use that fee to cover all necessary operations first[0], it constitutes outright fraud and the LPs would sue.
[0] And there are a lot of expenses - running a venture firm may be lucrative in the long run, but in the short run, it's expensive!
When there's no cost to moving them, yes, but that's not the case here: We're talking about the VCs personally, and the money that is in the hands of the firm is not worth the same to the VCs personally. Even if they could take the entire amount with impunity, they'd still be taxed on it as income, meaning that they'd lose as much as a third (depending on their marginal tax rate), so 15% is already incorrect from the start.
But on top of that, they're not able to pocket all of that money, because they have a fiscal responsibility to use it in the interest of the fund's shareholders. The same is not true about their personal bank accounts (which is where the 5% comes from).
Dollars are fungible, but that doesn't mean that $1 in a highly restricted fund is the same as $1 in an unrestricted fund. The former is worth some amount less (the discount determined by the premium associated with the restriction).
If that last paragraph weren't true, by the way, money laundering schemes wouldn't lose any money due to attrition, and corruption would be essentially "free". But thankfully, that's not the case - people who embezzle money have less than 100% yield. (Not always a lot less, but still less).
> management fees aren't just for expenses
If LPs can show that a VC is neglecting necessary expenses and instead pocketing the management fee - as 5%-20% = -15% would imply - then the VC had better figure out how he's going to pay his lawyers, because the LPs have got a great lawsuit on their hands.
I didn't say that they were neglecting expenses, only that they spent some of the management fee on things that were not expenses.
> fiscal responsibility to use it in the interest of the fund's shareholders
I don't think that's true but it's easy to argue that the transaction is in the interests of LPs.
> they could take the entire amount with impunity, they'd still be taxed on it as income
I suspect, like private equity firms, they net the transactions or use some other tricks to avoid taxes. So I could offer you a rebate on management expenses and in return get 5% of the fund.
1/ If the lifetime of a fund is 10 years, partners don't get the management fee for ten years. They get the fee until the fund is fully invested (usually 5-6 years).
2/ Money in is capital, money out is taxable income (unless it's carry, then it's a repayment of capital/capital gains). If the fund returns nothing, you lose your capital.
This creates following situation:
1/ 2% * 5 years is 10%, meaning as a partner you make 5% (probably a lot less, since you need to deduct expenses).
2/ Once we take into account taxes (let's say ~25% on $x), you are not making much, because your 10% becomes 7.5% after taxes.
But GPs can't invest 5% in a fund of a few billion $/€. Then again, you can't raise that kind of money without a track record, so maybe it doesn't matter.
In a way, a lot of these funds are entrepreneurial ventures as well. It's not too hard, for 1-2 people who knows plenty of wealthy individuals, to raise a $25-50M fund. You'd be amazed at how much money is available in the world (pension funds, wealthy families, endowments, etc etc)
So, the math tends to be a 2-20 (management fee / carry).
Let's say this fund returns $100m over a period of 5 years:
Fund size: $50M. Y1-5: Management fee (used for salaries + general expenses), 2%: $1M per annum (- expenses, e.g. secretary, travel, etc). To be divided between two partners. For a small fund, this is probably $200-300k per annum, per partner. Not bad, but not amazing either, given you just spent 1-2 years raising all that money.
When the fund is liquidated, the fund managers receive 20% of the capital gain. They first return the $50m initial capital, and then get 20% of the $50m they made, i.e. $10M (split between both partners).
Partners usually also invest some of their own money. It's rare to see funds where the principals don't have capital invested (this aligns incentives)
Edit: same math applies to private equity funds, where deals tend to be less risky than in VC. (for the fund, not the acquired company)