An Investor's Business Daily article discusses why GBTC's value does not match the value of the Bitcoins held in the fund.
It says that GBTC is not an ETF - it is a grantor trust.
It is not registered with the SEC [...] and it doesn't trade on an exchange. It trades on the over-the-counter market, which has less stringent participation rules than exchanges. And unlike most ETFs, GBTC charges a high annual fee of 2% of assets."
It uses a recent day as an example of how GBTC trades at a substantial premium relative to the value of the Bitcoins held by the fund:
At the Jan. 29 closing price, Bitcoin was $11,233.95. That would make the NAV for a share of GBTC (11,233.95 x 0.00100733) $11.31. However, shares of GBTC closed at $19.14, a 69% premium to the NAV. So investors would have to pay 69% more per share than the underlying asset is worth.
It explains the premium by noting there has been a high demand for GBTC and a small supply of shares:
Instead of an ETF, people should think of GBTC as a closed-end fund. These typically trade at a premium or discount to its NAV. The reason for GBTC's premium is the high demand for the small supply of shares. It has only 176 million shares outstanding. [...] "If GBTC was more liquid and larger, and Bitcoin had wider acceptance, then there would be closer correlation between the price of GBTC and the price of the underlying asset," said David Foster, a securities fraud litigator in Farmington Hills, Mich.
Michael Sonnenshein, managing director of Grayscale Investments, basically said the same thing in the article:
"Since the shares began quotation on the OTCQX market in early 2015, they have traded at a premium valuation to the NAV," said Sonnenshein. "While we cannot pinpoint a singular reason for the premium, we can surmise several factors. Firstly, there are fewer shares available on the market than there is demand. Secondly, it is the only U.S.-based investment vehicle that provides direct exposure to Bitcoin through the purchase of a security."
The article then mentions how the recent GBTC stock split has increased the supply and lowered the premium:
Grayscale recently declared a 91-for-1 stock split for the trust for shareholders of record on Jan. 22. They received 90 additional shares on Jan. 26. This lowered GBTC's share price and increased the supply adding more shares to meet demand, thus increasing liquidity. The premium of share price over NAV has fallen but is still a whopping 47%.
Another thing the article mentioned is that the amount of Bitcoins held in the fund will fluctuate significantly as people buy and sell GBTC, so that would probably explain the frequent daily discrepancies that I've seen:
GBTC held 177,037 Bitcoins as of Jan. 29. The number of coins held by the trust fluctuates substantially as investors move money in and out of GBTC.