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Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions

Yes, I am proposing a new branch of stochastic calculus. It drops Ito's assumption that the parameters are known. There is a Bayesian branch and the conjecture of a Frequentist branch. It is ...
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Investors degree of risk aversion in capm model

in the CAPM model all investors share the same utility function and the same degrees of risk aversion. It is not necessary (and rather unusual) to assume that. Rather, all investors are assumed to ...
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Definitions of Beta

One thing to note is that the CAPM can be rewritten as $$r_i=r_f(1-\beta_i)+\beta_i r_m$$ Thus, one can identify $\alpha_i$ with $(1-\beta_i)r_f$. Then, we we have, for the CAPM, $$\beta_i=\frac {r_i-...
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What is the relation between "Capital Market Line" and "Capital Asset Pricing Model (CAPM)"?

Is this right? No. $\beta_{i,M} = \frac{\sigma_i \rho_{i,M}}{\sigma_M}$ (note the correlation $\rho_{i,M}$ that is missing from your formula.) The first formula (CML) is only for portfolios on the ...
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Geometry of Efficient Frontier of Portfolios

Not sure I understand all of your questions. But briefly: If you have a risk free asset, then your efficient portfolios (maximising expected return for given variance) will be on a straight line (...
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Deriving the CAPM from the CML

This is a terrible paper. $\rho_{pm}=1$ is trivially true, in a CAPM with risk free asset, for all efficient portfolios on the CML (combinations of risk free asset and the market portfolio) (except, ...
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Difference between CAPM and mean variance optimization

The CAPM is basically mean variance optimisation plus equilibrium. Mean variance optimisation answers a simple question: what portfolios have the greatest expected return for a given variance? Those ...
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