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A large amount of literature in finance accepts the standard deviation in return as if it were an accurate measure of "risk."

What are some other financial theories for how to allocate capital between assets that are not correlated? What principles would lead to an equal, cagr, or some other weighting?

Using sigma is arbitrary and also 70 years old. Are there other models for how to allocate between non-correlated assets?

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Risk Budgeting, to which Risk Parity is closely related.

Related to that: Risk Parity / Equal Risk Contribution with Tail Risk Measures

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  • $\begingroup$ Any quantification of risk based on the variance of a distribution has the same form as the CAPM. I'm looking for allocation schemes which do not assume such a parameter. $\endgroup$
    – Machinus
    Apr 8, 2020 at 18:15
  • $\begingroup$ @Machinus this is semantics, but imo risk parity does not have the same form as capm. i agree that it uses volatility as an input, but that's because the volatility matters. maybe i just don't understand your question, or maybe this is me just saying that i don't have an answer for you, or that sigma is absolutely not arbitrary. watch this from dalio on his holy grail of investing: youtube.com/watch?v=Nu4lHaSh7D4 you could argue that and say future estimates of sigma and the correlations are arbitrary. to that i would say we just do the best we can? hopefully this helps? $\endgroup$
    – RWP - Down by the Bay
    Apr 9, 2020 at 11:43
  • $\begingroup$ anyway this topic really interests me because over the years i haven't found anything better so please let me know what you think of that. i too yearn for something different. $\endgroup$
    – RWP - Down by the Bay
    Apr 9, 2020 at 11:52
  • $\begingroup$ Sigma is an artificial proxy for risk used in quantitative finance, but it does not actually measure risk. Over long time periods, volatility does not matter for returns. CAGR contains all of the information about the returns of an asset. Risk parity uses sigma so it is just a different calibration of the same risk proxy. I am looking for an allocation model that does not use standard deviation. $\endgroup$
    – Machinus
    Apr 9, 2020 at 13:23
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    $\begingroup$ A method which uses only past returns is the Universal Portfolios of Thomas M. Cover. But not widely used in practice AFAIK, more of a theoretical construct. $\endgroup$
    – nbbo2
    Apr 9, 2020 at 18:10

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