You should read the actual letter, you can't replicate their portfolio, much of it is privately held assets.

That’s why I said “rouglhy”, the vast majority of the portfolio is publicly traded companies and half of it is Apple. Is exposure to those few private assets worth 50%?

"vast majority" isn't right though. The market cap of the company is $700 bill. The equities are worth around $350 bill. So people who spend all day figuring the value of Berkshire think the other assets make up 50% of the value. The book value of those private assets (worth about $350 billion) isn't especially meaningful. Amazon book value is $100 bill or something, the company is valued at $1.5T or so. Apple is less than 100 bill book value, market cap 2.5 trill or so.

One could effectively arb out the 350 bill of equities, and they'd be paying 350 bill for a set of assets which have a book value of 100-150 bill. So what? It says nothing.

Aren’t the private assets held at book value (historical purchase price less goodwill and depreciation) and so likely dramatically understate market value?

Yup, the book value is almost certainly understating what the assets are worth. But that isn't always the case. So, it basically means nothing. Folks have to do the analysis, and in this case they have.

The private assets provide the cash to buy the public assets, maybe?

Many of the public assets also provide cash.

Even if they only hold stock positions that you could replicate, you would be buying when Berskshire is already done buying and selling when they are done selling. For example, the recent Bershire's position in Activision was disclosed when Microsoft already made the acquisition offer, so it was too late to replicate it.

The transition plan has been in place for years. At the risk of sounding like a wsb meme, it's priced in.

You seem to be confused that Berkshire is some kind of a mutual fund or an ETF. It is not.

they have a huge cash position and when where they chose to invest it will create a halo effect causing it to get bigger .... also they can and will do stock buy backs if they cant a better investment.