By S. P. Kothari
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Panel B of Figure 7 shows how this allocation translates into an overall portfolio composition. 5 percent for the first set of assets. The high residual risks of the individual spread positions are substantially reduced by diversifying across spreads, making it possible to exploit the high alphas more efficiently than with the single-spread tilts examined in the “Optimal Portfolio Tilts” section. In general, when short selling is not restricted, we can show algebraically that increasing c leaves the active portfolio unchanged, although, naturally, the weight on the active portfolio is lowered.
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Academic work on portfolio optimization has increasingly applied Bayesian methods; the study by Pastor (2000) is the most closely related to the issues considered here. In Bayesian analysis, initial beliefs about return parameters are represented in terms of prior probability distributions. For convenience, one assumes normal distributions for priors, as well as returns. Using a basic law of conditional probability known as Bayes’ rule, one combines the data with one’s initial beliefs to form an updated posterior probability distribution that reflects the learning that has occurred from observing the data.
Anomalies and Efficient Portfolio Formation by S. P. Kothari