Where the analysis ends: historical description and forward-looking estimation

The boundary

The topic series “Volatilität im Portfoliokontext” deals with risk, not return. Historical risk metrics can be recalculated. How risk and return will develop in the future, by contrast, remains uncertain. Whether the expected return of digital assets adequately compensates for their risk depends on assumptions, investment horizon and valuation model. A single metric does not answer this question. This page names the boundary instead of glossing over it.

It presents no new empirical analysis but places the values of episodes 1 and 2 in context. It accompanies episode 4 of the topic series in the format “21Nexus | Portfoliofragen” (video in German) and can be read without the video.

Description and estimation

The difference lies not in whether something can be calculated but in what the calculation rests on. The table contrasts historical description with forward-looking estimation.

What can be described historically

A historical risk metric is the application of a defined calculation rule to an observed data series. It, too, rests on decisions, for example on period, window, annualisation and definition. Anyone using the same series and the same conventions obtains the same value. In this topic series these are volatility and the count of extreme days (episode 1) and the correlation with the S&P 500 (episode 2). All values are calculated from daily closing prices, and the conventions are disclosed.

Reproducible does not mean stable. The table shows, for four of these metrics, the lowest and the highest value they have taken over their respective history.

All four values are reproducible, and yet none is a reliable predictor. The annual volatility of Bitcoin ranged between 41.9% and 148.9%, the correlation with the S&P 500 between −0.11 and +0.57. The calculation describes what was. Which value applies next, it does not say. Historical risk metrics are therefore also not a reliable predictor of future risk.

What depends on assumptions looking forward

Expected return and expected risk are not observations but estimates. Expected return depends on three important decisions, and each is an assumption.

Assumptions. Which development of usage, market structure and framework conditions is assumed influences the expectation. Different, equally justifiable assumptions lead to different results. They do not follow from the price series alone and are to be disclosed.

Investment horizon. Expected return and its relationship to risk depend on the period over which one considers it. The same investment can be valued differently over short and long horizons.

Valuation model. For equities and bonds, ongoing payments support the valuation. For Bitcoin they are absent, and for many other digital assets they are only partly comparable. Valuation models therefore draw on other variables, such as usage, scarcity or network effects, and can arrive at widely diverging results.

Estimates of future risk are also model-dependent. Forecasts of volatility and correlation rest on models, estimation windows and an assumption about how far the past carries forward. Realised, implied and forecast volatility are different concepts that do not measure the same thing. Risk forecasts are a discipline of financial analysis in their own right and not a result that can be read off a historical metric.

Whether the expected return adequately compensates for the risk can only be answered with these decisions, and the answer holds only under them. A single metric does not answer this question.

Historical returns and assessment

Historical returns can inform the assessment of expected return but do not replace it. A historical return is the result of a particular period, a particular market environment and a particular starting level. It says what was under those conditions, not what is to be expected under others. This page evaluates no returns and states no return expectation.

Why this topic series ends here

The topic series places volatility and dependence in context and marks where the analysis of return would have to begin. This defines the scope of the topic series: a statement on return requires its own assumptions and its own evidence, and neither is supplied here. Anyone assessing a position has thereby described only part of the investment’s risk profile, not the entire decision. Liquidity, custody and operational risks, for example, remain open.

With episode 4 the topic “Volatilität im Portfoliokontext” is complete, but not the format. “21Nexus | Portfoliofragen” will continue with further questions from the portfolio context, and accompanying articles will continue to appear on this page for the episodes.

Limits of the conclusion

The table on the stability of the metrics is a selection. Three points matter for the interpretation.

Selection of metrics. Four metrics from episodes 1 and 2 are shown. Other metrics such as loss measures or drawdowns are not evaluated, and the reference to their variability is therefore not exhaustive.

Ranges are not forecasts. Lowest and highest value describe only the range of the calendar years or trading days observed. They are not a forecast range, and future values may lie outside it.

No statement on return. This page makes no statement on whether the return of digital assets compensates for their risk. It names what the answer depends on and does not supply it.

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Legal notice

This publication serves solely for general information and professional commentary. It constitutes neither investment advice nor an investment recommendation, financial analysis or an offer to buy or sell financial instruments. Individual investment objectives, financial circumstances or the risk tolerance of individual investors are not taken into account. Information on historical performance and metrics permits no conclusions about future developments. The data used originate from sources that we consider reliable; no guarantee is given for accuracy or completeness. The information reflects the position at the date of publication; there is no obligation to update. Publisher: 21Nexus Capital GmbH, Neuer Wall 54, Hamburg.