“Under the standard Bayesian framework, the investor is equipped with a prior…This prior captures the investor’s beliefs over the possible evolution of returns. N.B.: This issue would apply to almost all financial contracts in the case of a significant structural change of the macro environment. Even if such estimates are available, they may be useless to investors if the behavior of underlying assets changes over time.” “A central challenge for portfolio allocation… the implementation of mean-variance optimal portfolios…Using historical data to estimate returns and correlations, frequently lead to unattractive, leveraged, and highly unstable portfolios…The limitations of historical data as a determinant of portfolio allocation seem particularly salient in the case of innovative asset classes with limited track record… it is difficult to form reliable estimates of expected returns and covariance matrices needed as inputs for standard portfolio optimization. Emphasis and cursive text have been added. The post ties in with SRSV’s summary lecture on risk management. Empirical evidence for the case of cryptocurrencies suggests that in an environment of uncertain returns MinMax delivers better PnL return-to-drawdown ratios than conventional volatility control.Ĭhassang, Sylvain and Alice Wang (2018), “Managing a Crypto-Currency Portfolio Via Minmax Drawdown Control”. Averaging over a plausible range of aversion parameters gives a model portfolio. Optimal asset allocation depends only on aversion to different types of drawdowns. In the case of one risky and one safe asset, this boils down to managing simultaneously the risks of conventional PnL drawdowns and foregone risk returns. An alternative is ‘MinMax’ drawdown control, which builds on a broad interpretation of drawdowns as maximum actual or opportunity losses from not adjusting a benchmark portfolio to a specific underlying asset. A popular solution is risk-parity with volatility targeting. Alas, short data series or structural changes often render estimates of covariance matrices unreliable. Containment of drawdowns and optimization of performance ratios for multi-asset portfolios is critical for trading strategies.

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