hi
in markowitz model, we can find the optimal portfolio weights by maximizing the sharpe ratio
in single index model, we do it by the use of treynor-black model
what about in capm??
thanks
You may be misunderstanding the idea of an “optimal” portfolio.
The optimal portfolio for one investor likely will not be the optimal portfolio for another investor; the portfolio with the highest Sharpe ratio may not be the optimal portfolio for any investor. What portfolio is optimal for a particular investor depends on that investor’s risk/return indifference curves, which, in turn, depend in that investors level of risk aversion.
that was the second step… finding the optimal weights for every investor, well, depends on their risk/return indifference curves.
what i meant is that how to find the optimal “risky portfolio”, optimal weights of each asset in that combination(the risky portfolio)
look at this image, please
it does clear what i mean:
can anyone help me to understand this?
I have no access to that image.
mmm
it seems that the market portfolio is already the optimal one (in capm), isnt it? where beta = 1?
(so we do not need to do anything for optimization (like miximizing the sharpe ratio in markowitz model)
right?
CAPM is a equilibrium model, which means that it assumes all investors have already optimized. That is necessary for equilibrium. So yes, it is correct to say “we do not need to do anything for optimization” as the CAPM result is obtained by assuming equilibrium (that is optimization by all agents).
In the presence of a riskless asset, the set of portfolios that have minimum variance for a given expected return lie on the tangent from the riskless asset. So all investors hold combinations of the riskless asset and the tangent portfolio. For a particular individual the combination is determined by his risk aversion, the more risk averse an individual is the more of the riskless asset and less of the tangent portfolio he will will hold.
As the tangent portfolio is the risky part of the portfolio held by all investors, it must be the market portfolio.
The answer is “No” to the question “it seems that the market portfolio is already the optimal one (in capm), isnt it?”. The optimal portfolio for an individual would be a combination of the market portfolio and the riskless asset.
If there is no riskless asset, then in equilibrium all individuals still optimize, but locate themselves on different points of the mean variance frontier.
Best,
Jayanta Sen
thanks!
now its clear 