It would be hard to find someone at this salary level who can match the tracking performance of Vanguard. If they achieve a tracking error that's 1% higher than that of Vanguard's, that would mean an annual loss of approximately $800k compared to Vanguard (1,000,000,000 * 8% * 1%).
[0] https://institutional.vanguard.com/VGApp/iip/site/institutio...
In the given scenario, you aren't just hiring a guy to buy stocks for the Vanguard expense ratio. You're also buying all their financial and information security processes. You're buying risk mitigations like regular audits and SOX compliance and SP800-53 controls. To safeguard a billion dollars, that overhead is totally worth it.
Most tracking indexes, especially the ones Vanguard uses, do not do that and thus do not allow the markets to front-run them. If you adopt the strategy of "do what Vanguard does" and you do it immediately after Vanguard says they did something, you are already too late to get the prices that Vanguard got and can kiss at least .05% goodbye just based on that. I would expect to under-perform by at least .25%, if not more.
Even at 5 bps on a billion, I think you'd be extremely hard pressed to do everything Vanguard does for you for $500K/yr.
I'm at least a factor of 500 away from having to consider this question, but if you told me it would cost me $500K to have one fewer critically important person on my staff to deal with, that would be a good tradeoff in itself.
"Because Vanguard charges too much" isn't one of them, IMO.
If so, not worth dealing with for a billionaire, but definitely an opportunity for a middle-class robo-advisor.
The likelihood of a single person delivering index tracking performance better than these giants is pretty slim. Better to drop the tranche designated for broad market passive indexing into one of these giants' funds as an institutional holder, then have the one-man office project-manage leading education of younger generations, help the family leader clarify the ongoing family mission the office supports, the accountants' filing tax compliance at the individual and trust/foundation levels (likely in many different jurisdictions), grooming a successor, updating processes and procedures to improve auditability/accountability/anti-fraud detection, assisting with legal compliance, helping out with financing approved moonshots, etc.
[1] https://riabiz.com/a/2018/12/13/vanguards-asset-machine-wobb...
But then you have to trust that guy not to fuck it up, while Vanguard has a stellar reputation and a whole office of people making sure things go as expected.
Honestly a much stronger argument is tax efficiency. If you're buying the individual stocks, then even when the index is flat you'll have some capital gains and losses. You can use both these to improve your tax efficiency - the losses can be harvested to offset realized gains elsewhere, while any appreciated shares can be donated to charity and repurchased with new money, effectively increasing your tax basis.
Still, you're likely better off just hiring people to do the tax planning, estate planning, and philanthropic services. It's essentially setting up a single family office with no control over your investments.
And once you talk about foreign stocks, you have different amounts of withholdings to account for, dividends that are not dividends (return of capital).
1,000,000,000*.0005 = $500,000
For that level of expense, you could instead have a one-man office or other service provider that can buy the individual stocks comprising (or closely approximating) the index, and not have to pay any expenses other than his salary and trading costs. Meanwhile he can provide tax planning/philanthropic services as well.