Intelligent Asset Management by Frank Xing & Erik Cambria & Roy Welsch

Author:Frank Xing & Erik Cambria & Roy Welsch
Language: eng
Format: epub
ISBN: 9783030302634
Publisher: Springer International Publishing

(5.5)

where R i,−n is the return of asset a i on the n-th past day.

The classical form of the Black-Litterman model [14] relies on investing experts to manually set the confidence matrix Ω based on their own experience. At the worst cases, where the investor has no idea how to derive the confidence matrix, a numerical example provided by [72] pointed out a primary estimation:

(5.6)

We give the explanation for this estimation as follows. Because Σ is by definition a covariance matrix, P(τΣ)P ′ can also be understood as cov(τPΣ, τPΣ), which is a covariance matrix of the expected returns in the views. Note that the mentioning matrix P “filters out” the covariances not relevant to the views. With Definition 5.2, where P is an identity matrix, this estimation is more understandable. Because P(τΣ)P ′ is already diagonal, the latent hypothesis here is that the variance of an absolute view on asset a i is proportional to the volatility of asset a i. This hypothesis shares the same idea as the CAPM: not only the risk premium comes from volatility, but also the confidence of any judgment would decrease the same amount if the return is more volatile. In the example by [72], the estimation of Ω utilizes only the past information of asset price volatilities.

Compared to volatility, the expected return has a more directly perceivable relation to the market sentiment. In contrast to the naive assumption that positive market sentiment leads to positive returns and vice versa, our assumption here is more developed. We believe there exists a strategy that “responds to the market sentiment” and can surf the market and statistically makes profits (generates alpha). However, such a strategy can be complicated. Therefore, we employ machine learning techniques to “learn” this strategy under the framework of the Black-Litterman model. That is, imagine an agent who empirically forms and updates their views using information like the past price series (π t,k) and trading volumes (v t,k). In our extension, these activities further involve a new prior: sentiment time series derived from the alternative data stream obtained from the social media. We denote this new prior by . Now the problem (formally) becomes learning a proper function that maps the expected return estimation to each time period t:

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