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2022 | OriginalPaper | Buchkapitel

9. Risk Factors in Digital Assets

verfasst von : Tobias Glas

Erschienen in: Asset Pricing and Investment Styles in Digital Assets

Verlag: Springer International Publishing

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Abstract

Following on from the previous chapter, the search for risk factors in digital assets is extended by several means. First, statistical tools such as principal component analysis are used to condense the information contained in the digital asset dataset. After investigating the principal components more deeply, it emerges that this first approach yields no statistically significant results. Therefore, as a second step fundamental as well as other data is considered to intensify the search for risk factors. As that approach still results in rather disappointing outcomes, I turn to the characteristics versus covariances story as a last step. By doing so, three characteristics that tend to explain digital asset returns are identified while being priced significantly in the underlying data.

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Vorheriges Kapitel Investment Styles in Digital Assets

Nächstes Kapitel How to Incorporate Characteristics into the Portfolio Construction Process

See “Total market capitalization,” https://www.coinmarketcap.com/charts, accessed on June 10, 2018.

See “Full list,” https://deadcoins.com/, accessed on June 10, 2018.

See “Total market capitalization,” https://www.coinmarketcap.com/charts, accessed on July 8, 2020.

See “Full list,” https://deadcoins.com/, accessed on July 8, 2020.

The data used is described in Chap. 5, and in Sect. 9.4.3.

A new approach (Kelly et al. 2019), allowing for latent factors and time-varying loadings, might solve several issues connected to the principal component analysis described in this chapter. Thus, the reported results could serve as a “benchmark” for the instrumented principal component analysis, which I leave for future research.

That number might also be available for other coins associated with their own blockchain, but I stuck to the same data as used by Wheatley et al. (2018) to ensure comparable results.

Time-series regressions on prices are especially prone to an effect called “spurious regressions.” This is mostly due to non-stationary (in)dependent variables. This means the regression result will show a linear relationship where normally no relationship exists. That is also the case for variables moving in trends. Therefore, regressions on returns usually circumvent the problem of non-stationarity. The residuals of a regression of returns on, e.g., monthly changes of the independent variable should additionally be checked for autocorrelation by using the Durbin–Watson test. For more information regarding spurious regressions, see Granger and Newbold (1974).

Asset pricing models for other (traditional) asset classes achieve clearly higher values. Fama and French (1993), for example, reported R² of about 90% on average. Carhart (1997) arrived at R² between 78% and 97%. Similar R² values are reported by Lustig et al. (2011) for FX markets.

Most of the equations in this section are reproduced in slightly adjusted form from Rebonato and Jaeckel (2000).

Obtaining the covariance matrix would require the multiplication of \(\hat {\mathbf {M}}\) by the respective standard errors.

See Chap. 2 for more details.

The steps described below are reproduced in a slightly adjusted form from Poddig et al. (2015).

The calculation of F would not work if Z contains missing values. Therefore, I replaced all missing values of Z with 0, since Z was already de-meaned.

The equations related to PLS are reproduced in slightly adjusted form from Abdi (2010).

For more details please refer to the algorithm section in Abdi (2010), or see the description below.

For more information, see Fung and Hsieh (2001).

See “Methodology – (1) Price (Market Pair),” https://coinmarketcap.com/methodology/, accessed on November 15, 2018.

That approach does not change the results at all, since the analyses in this chapter are based on the returns of digital assets and not their prices. I also ran all analyses with USD-denominated prices and the results did not change materially (see Appendix H).

See Chap. 8 for more details. Due to the slightly different dataset in this chapter, the values in Table 9.2 diverge from Table 8.2. Although this chapter utilizes BTC-denominated prices, the differences between Chaps. 8 and this chapter are relatively small. This is due to the formation of hedge portfolios. In particular, in Chap. 8 the long part of the hedge portfolio is intrinsically long the BTC/USD exchange rate. The short portfolio, on the other hand, would be short BTC/USD and thus cancel each other out. Therefore, the results of both chapters are an indication of comparably robust results, since the dataset used in this chapter is somewhat smaller in size (i.e., the number of assets under consideration).

Panels C and D mostly feature non-stationary data.

See “Hedge Fund Data Library,” http://faculty.fuqua.duke.edu/~dah7/DataLibrary/TF-FAC.xls, accessed on June 18, 2018.

See “FRED Economic Data,” https://fred.stlouisfed.org/series/DGS10 and https://fred.stlouisfed.org/series/DBAA, accessed on July 2, 2018.

These numbers were chosen intentionally. The number of portfolios (30) times the number of assets within each portfolio (50) is fairly close to the overall number of assets in the dataset used. Thus, each digital asset should be included in a randomly picked portfolio at least once per simulation. The assets within the portfolios are equally weighted. For more information regarding Monte Carlo simulation see Cochrane (2001).

For more information regarding principal component analysis see Jolliffe (2002) and Abdi and Williams (2010), or refer to the previous sections.

See Sect. 9.3 for further details.

The asset pricing literature usually considers a timeframe of 36–60 months. Due to the short digital asset data I needed to deviate from this number to be able to conduct a reasonable analysis.

Of course, an out-of-sample analysis would be more appropriate at this point. The in-sample analysis, however, already includes all available data and should yield the “correct” principal components.

Only the PLS factor values cannot be interpreted as returns.

Which might also be due to the relatively short dataset.

Choosing a higher number at this point would not necessarily yield better results, but would dramatically increase the computation time.

Using two-way cluster-robust standard errors at this point could lead to less reliable results. Two-way standard errors could lead to non-positive-semidefinite covariance matrices which would need to be corrected by using spectral decomposition. Doing so very often might distort the results and make them less reliable. That would also significantly increase the computation time.

Due to basically no significant outcomes covariance results are not included in Appendix I.

In different multivariate models. Results are reported in Appendix I.

I calculated the VIFs as the diagonal of the inverse of the correlation matrix.

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Titel: Risk Factors in Digital Assets
verfasst von: Tobias Glas
Verlag: Springer International Publishing
Buch: Asset Pricing and Investment Styles in Digital Assets
Print ISBN: 978-3-030-95694-3

Electronic ISBN: 978-3-030-95695-0

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-030-95695-0_9