Bitcoin needs twice the reserve weight to keep pace with added equities once the CNB drops its pre-2020 history. In the Czech National Bank's study, the weight that matches about 15 extra points of equities rises from 2% to 4% when the 2010 to 2020 data is removed. Both windows re-measure the equity yardstick, so the change is relative to equities. The authors describe bitcoin's full series as "heavily skewed by the initial period of explosive growth from near-zero valuation." The paper's abstract pairs its return claim with this warning, and the Bank Board cited the same instability when it kept bitcoin out of official reserves. Yet Figure 8 remains, alongside a conclusion that says "a 4% allocation to bitcoin compares to a 50% allocation to equities."

The question matters for a balance sheet held largely in foreign currency and judged in koruna. Foreign exchange reserves account for about 98% of CNB assets (CZK 3,166 billion at end-2022). They stand at about 50% of GDP, or 61.5% on the IMF's 2022 measure, against Switzerland's 136.6%. About two thirds were purchased during the November 2013 to April 2017 exchange rate commitment. Earnings in CZK must cover the drag from koruna appreciation and the interest the CNB pays on bank deposits.

Part I takes the October 31, 2022 foreign exchange portfolio, with 18% equities, 46% euro and 12 tons of gold, and tests three changes against November 2002 to October 2022 history. Its recommendation is about 20% equities and 100 tons of gold. Part II updates the exercise to the September 2025 book and brings in bitcoin.

Returns in koruna change the answer

Adam, Michl and Škoda use the CNB's internal FX reserves model to simulate historical portfolios. Daily returns come from 34 index series covering money market, government bonds, MBS, equities and gold across EUR, USD, CAD, AUD, GBP, CNY, JPY and SEK. Candidate portfolios combine those sub-portfolios linearly. Starting with the CNB's actual holdings, the authors vary one weight at a time. They calculate daily-rolling 1-year and annualized 5-year returns for each candidate, then report means and standard deviations. The framing is Markowitz, though the weights are read approximately from plotted frontiers rather than solved for. As the authors put it, "The round numbers in the hypotheses are not global optima."

The numéraire changes what looks attractive. The October 2022 portfolio had 6.81% volatility in CZK and 2.74% in reserve currencies. It also changes the direction of the volatility result for euro and gold. Reducing euro from 46% to 40% cuts reserve-currency volatility by 4bp, while CZK volatility rises by 28bp because the euro moves with the koruna. Increasing gold from 12 to 100 tons adds 22bp of reserve-currency volatility. In CZK it cuts volatility by 3bp and adds 30bp of return (Nov 2002 to Oct 2022, 1-year horizon). The Part I mix of about 20% equities and 100 tons of gold produces 3.31% CZK return with 6.79% volatility.

Part II starts from the September 30, 2025 book: 67.2 tons of gold (5.0%), 25.5% equities and the rest in fixed income. It tests bitcoin weights from 0 to 5%, funded from fixed income, over October 2010 to September 2025 and October 2020 to September 2025.

How much survives the shorter bitcoin window?

Some of the return comparison survives. Across the longer window, a 2% bitcoin sleeve matches the expected-return gain from more than 15 additional percentage points of equities, with lower volatility. A 1% sleeve slightly lowers CZK portfolio volatility. For 2020 to 2025, a move from 0% to 4% bitcoin buys roughly the gain from +15pp of equities in foreign-currency terms, or from 400 tons of gold in CZK terms. Each point of bitcoin weight buys about half as much relative to equities.

The volatility case is more sensitive to the period. From January 2020, bitcoin's volatility over five years was about 60%, versus roughly 20% for equities, 16% for gold and 6% for bonds. Its full-sample monthly correlation is 0.07 with the S&P and 0.01 with gold, while its 1-year rolling correlation with equities reaches 0.6 after the pandemic. A 1% sleeve can lower CZK volatility only if bitcoin barely co-moves with the rest of the book when measured in CZK. Those quoted correlations are local-currency figures. The paper says the low co-movement needed for the result belongs mostly to the pre-2020 period.

"Temporal instability is a defining feature of bitcoin." The authors also warn that cherry-picking risk is significantly higher than for traditional assets. They present the exercise as illustrative, and it works on those terms. The conclusion makes a harder-to-read comparison by switching to total equity weights. In the results, 4% bitcoin matches +15pp of equities added to a 25.5% base, or about 40.5%. The conclusion pairs that same 4% with "a 50% allocation to equities." Anyone taking an allocation from Figure 8 must choose which comparison to use.

The experiments differ

Part I rescales weights left untouched by a change in proportion to the starting portfolio. Part II funds every addition from fixed income. Its gold curves therefore answer a different financing question from those in Part I.

Gold is entered in tons, and its portfolio weight moves with price. At 2022 prices, 100 tons is about 4.5% of reserves; at 2025 prices, about 7.5%. The starting stock is reported as 12 tons in Part I and 9 tons in Part II. Part I uses daily data. We did not find the return frequency restated for the Part II portfolio runs: the full-sample bitcoin correlations are monthly, and the paper says only that it follows the Part I methodology.

The return windows overlap daily. A 20-year sample contains about four non-overlapping 5-year blocks. We did not find a significance test for differences as small as the -3bp gold volatility effect. The authors flag the gold result's dependence on the chosen period too. Over Nov 2012 to Oct 2017, adding gold reduced returns in both numéraires. Over the last five years, 100 tons delivers +33bp CZK return and +20bp volatility.

We could not reproduce any of this. Our data lacks a CZK exchange-rate series and return series for the foreign sovereign, agency and money-market holdings. Our price history begins around 2010, eight years after the paper's main window opens. US-listed ETFs would alter the exposures and remove the koruna mechanism behind the euro and gold findings, so they cannot serve as a valid substitute.

Gold was bought; bitcoin remains a pilot

I read the decisions as consistent with the records available for each asset. Gold's CZK result has 20 years behind it; bitcoin's roughly 15 years are heavily skewed. Across 2002 to 2022, raising gold to 100 tons lowered CZK volatility by 3bp (16bp on 5-year returns) and added 30bp of return. The Board set a 100-ton target over five years in 2022, and holdings reached 71.6 tons by end-2025. The paper calls the remaining move from 67.2 tons "modest".

Bitcoin instead received a USD 1 million test portfolio outside official reserves. The holdings are bitcoin, a dollar stablecoin and a tokenized dollar deposit; the two-to-three-year pilot concerns custody and operations. I would take the allocation case seriously if a post-2020 window, with equity correlation near 0.6, still showed CZK volatility falling at a 1% weight. The text makes that 1% volatility claim only for the longer window. For 2020 to 2025 in CZK, it says only that bitcoin behaves like added gold.