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How practitioners or academics answer this question will tell you a lot about their view on the nature and sources of returns and risk. For example, the Fama-French "equilibrium" school of thought would argue that solely exposures to systematic risk exposures explain the cross-section ofsecurity returns AND(and that idiosyncratic returns are unpredictablerandom) and therefore the expected return model matches the risk model. In this view, the "expected return" is the "required rate of return" for the security. You could tilt your portfolio towards securities with high expected returns but Fama-French would say you are only picking up a risk premium as compensation for taking on greater systematic risk.

I don't know many practitioners that subscribe in full to the equilibrium view (except maybe these guys) but conceptually it's an important special case answer to your question.

My argument is that the expected return ("alpha")"alpha" model and the risk model have two different objectives and therefore are best designed separately.  

As @Owen and Markowitz points out, risk is the second-moment of returns whose dynamics can be summarized in a variance-covariance matrix. Given such a matrix we can define a number of risk-measures -- portfolio variance, cVaR, VaR, etc. -- and minimize portfolio risk accordingly using an optimizer.

How practitioners or academics answer this question will tell you a lot about their view on the nature and sources of returns and risk. For example, the Fama-French "equilibrium" school of thought would argue that solely exposures to systematic risk exposures explain the cross-section of returns AND that idiosyncratic returns are unpredictable and therefore the expected return model matches the risk model. In this view, the "expected return" is the "required rate of return" for the security. You could tilt your portfolio towards securities with high expected returns but Fama-French would say you are only picking up a risk premium as compensation for taking on greater systematic risk.

I don't know many practitioners that subscribe in full to the equilibrium view but conceptually it's an important special case answer to your question.

My argument is that the expected return ("alpha") model and the risk model have two different objectives and therefore are best designed separately.  

As @Owen and Markowitz points out, risk is the second-moment of returns whose dynamics can be summarized in a variance-covariance matrix. Given such a matrix we can define a number of risk-measures -- portfolio variance, cVaR, VaR, etc. -- and minimize portfolio risk using an optimizer.

How practitioners or academics answer this question will tell you a lot about their view on the nature and sources of returns and risk. For example, the Fama-French "equilibrium" school of thought would argue that solely exposures to systematic risk exposures explain the security returns (and that idiosyncratic returns are random) and therefore the expected return model matches the risk model. In this view, the "expected return" is the "required rate of return" for the security. You could tilt your portfolio towards securities with high expected returns but Fama-French would say you are only picking up a risk premium as compensation for taking on greater systematic risk.

I don't know many practitioners that subscribe in full to the equilibrium view (except maybe these guys) but conceptually it's an important special case answer to your question.

My argument is that the expected return "alpha" model and the risk model have two different objectives and therefore are best designed separately.

As @Owen and Markowitz points out, risk is the second-moment of returns whose dynamics can be summarized in a variance-covariance matrix. Given such a matrix we can define a number of risk-measures -- portfolio variance, cVaR, VaR, etc. -- and minimize portfolio risk accordingly using an optimizer.

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For various statistical reasons (lack of monotinicity in particular) a factor like the one above would not be picked up in a regression while in competition with other factors such as Value, Size, or Beta. Or taken to the extreme, imagine a stock-screener which filters stocks based on a constellation of factors. Suppose we had a screen for "buyout targets" that produced a "1" if the set of conditions was present and 0 otherwise. This would be a lousy factor in our risk model (but great for our alpha model which I'll get back to).

For various statistical reasons (lack of monotinicity in particular) a factor like the one above would not be picked up while in competition with other factors such as Value, Size, or Beta. Or taken to the extreme, imagine a stock-screener which filters stocks based on a constellation of factors. Suppose we had a screen for "buyout targets" that produced a "1" if the set of conditions was present and 0 otherwise. This would be a lousy factor in our risk model (but great for our alpha model which I'll get back to).

For various statistical reasons (lack of monotinicity in particular) a factor like the one above would not be picked up in a regression while in competition with other factors such as Value, Size, or Beta. Or taken to the extreme, imagine a stock-screener which filters stocks based on a constellation of factors. Suppose we had a screen for "buyout targets" that produced a "1" if the set of conditions was present and 0 otherwise. This would be a lousy factor in our risk model (but great for our alpha model which I'll get back to).

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Earlier we said that the objective of the risk-model is to construct a covariance matrix and estimate betas for the purpose of hedging. A time-series regression is well-suited to this task under most conditions (stable fundamentals, long-enough time-series, etc.). However, in the alpha-case one is better off using a cross-sectional regression strategy to identify the security mispricings. The cross-sectional regression can identify which securities generate superior relative performance (however, the estimated beta's suffer from an errors-in-variables bias that is not diversifiable hence these models are not suited for risk). This point is lost by many in the industry but Bernd Scherer nails it in his Portfolio Construction and Risk Budgeting text. So this is another reason, albeit, technical for having a separate expected-returns and risk-model.

Earlier we said that the objective of the risk-model is to construct a covariance matrix and estimate betas for the purpose of hedging. A time-series regression is well-suited to this task under most conditions (stable fundamentals, long-enough time-series, etc.). However, in the alpha-case one is better off using a cross-sectional regression strategy to identify the security mispricings. This point is lost by many in the industry but Bernd Scherer nails it in his Portfolio Construction and Risk Budgeting text. So this is another reason, albeit, technical for having a separate expected-returns and risk-model.

Earlier we said that the objective of the risk-model is to construct a covariance matrix and estimate betas for the purpose of hedging. A time-series regression is well-suited to this task under most conditions (stable fundamentals, long-enough time-series, etc.). However, in the alpha-case one is better off using a cross-sectional regression strategy to identify the security mispricings. The cross-sectional regression can identify which securities generate superior relative performance (however, the estimated beta's suffer from an errors-in-variables bias that is not diversifiable hence these models are not suited for risk). This point is lost by many in the industry but Bernd Scherer nails it in his Portfolio Construction and Risk Budgeting text. So this is another reason, albeit, technical for having a separate expected-returns and risk-model.

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