In this latest CIO paper, Russell Thompson examines the relationship between Bitcoin and global liquidity — and why conventional liquidity measures may be misleading investors. While broad indicators such as M2 have continued to rise, Bitcoin has declined sharply since late 2025. This report argues that the key driver is not the absolute level of…
ABSTRACT In this paper, Magnus Holm and Hans-Peter Bermin revisit the foundational Kelly trading strategy in the context of modern financial markets where asset prices can experience discrete jumps—sudden changes in value that are not captured by traditional continuous models. While classical results show that the Kelly strategy (which aims to maximise long-term capital…
A new working paper by Dr Hans-Peter Bermin (Chief Risk Officer, Hilbert Group) and Dr Magnus Holm (Co-Founder, Hilbert Group) shows that the maximum drawdown of a standard asset-price model converges to a Gumbel distribution, meaning extreme losses follow a predictable statistical pattern. This insight provides practical tools for estimating worst-case drawdowns over long horizons and strengthens the quantitative foundations behind Hilbert’s…
ABSTRACT – In this paper we present a geometric approach to portfolio theory, with the aim to explain the geometrical principles behind risk adjusted returns; in particular Jensen’s alpha. We find that while the alpha/beta approach has severe limitations (especially in higher dimensions), only minor conceptual modifications are needed to complete the picture. However, these…
ABSTRACT In this paper we show that risk associated with leverage is fundamentally relative to an arbitrary choice of reference asset or portfolio. We characterize leverage risk as a drawdown risk measure relative to the chosen reference asset. We further prove that the growth optimal Kelly portfolio is the only portfolio for which the relative…
ABSTRACT In this paper we show that a Kelly trader is indifferent to trade the derivative if and only if the no-arbitrage price is uniquely given by the minimal martingale measure no-arbitrage price, thus providing a natural selection mechanism for option pricing in incomplete markets. We also show that the unique Kelly indifference price results…
ABSTRACT We show that the Kelly framework is the natural multi-period extension of the one-period mean-variance model of Markowitz. Any allocation on the instantaneous Kelly efficient frontier can be reached by trading in the bank account and a particular mutual fund consisting of risky assets only. However, different to the mean-variance model there is an…