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Finding Alphas: A Quantitative Approach to Building Trading Strategies by Igor Tulchinsky

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12 The Relationship between Alpha and Portfolio Risk

By Ionut Aron

There are many ways to think of what alpha means. Perhaps the most direct way is to think of it as a skill and, by extension, as a yield produced by that skill. Most rational investors seek to obtain the best possible return for a given level of risk. It takes skill to find the optimal strategy to produce that return with high probability and consistency. Alpha reflects the ability of a manager to enhance the returns of a portfolio without increasing its risk.1

PORTFOLIO RISK

The reference to a portfolio in the definition of alpha is not arbitrary. It provides the necessary basis against which alpha is evaluated: we need to know the level of risk and return we started with in order to determine whether the alpha adds value.2 This implies that alpha is highly context dependent: it may add value to a particular portfolio but not to another.

To understand why this is the case, it helps to think of the reference portfolio in terms of the combination of risks it already contains. Every source of return derives from a source of risk, and so any portfolio can be viewed as a combination of risks, with weights on each risk according to the manager’s skill, preferences, and/or constraints.

The difference in performance between two portfolios comes from the number of sources of risk and return they tap into, and the relative weights they place on each source. At one end of the spectrum, we find high-conviction managers, ...

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