CAPM, the Market Portfolio, and the Tangency Portfolio
Summary
The document addresses how a limited stock portfolio optimized for the highest Sharpe ratio relates to the CAPM market portfolio and the efficient frontier. It explains that an efficient risky portfolio can be combined with a riskless asset, such as cash, to form portfolios that dominate other frontier choices. The portfolio at the point where a line from the riskless return touches the efficient frontier is called the tangency portfolio.
The questioner provides a five-stock portfolio’s expected return, volatility, beta, and Sharpe ratio, but these figures alone do not establish that it is the market portfolio. A response also points out that the chart’s displayed volatility range may obscure the geometry; showing the axis from zero could change how the capital market line appears relative to the plotted portfolio. The discussion is introductory and does not derive CAPM or establish whether the portfolio is truly efficient.
Key ideas
- The market portfolio in CAPM and a portfolio optimized from a limited stock universe are not automatically the same.
- A tangency portfolio lies where a line from the riskless return touches the efficient frontier.
- Combining the riskless asset with an efficient risky portfolio creates alternative risk and return exposures.
- The displayed volatility scale can affect how the capital market line appears on a chart.
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# CAPM - market portfolio vs real portfolio # CAPM - market portfolio vs real portfolio I'm trying to understand the relation (if there is any) between the market portfolio, as described by the CAPM theory, and a real portfolio (just like the one I plotted in the image below). More specifically, my portfolio consists of 5 stocks, which I optimized to get the highest sharpe-ratio (The risk free return used was 5%). Looking at the figure, it is clear that a straight line from the y-intercept at 5% will not be tangent to the red star (the optimal portfolio). So, can I say the following: - My optimized portfolio (red star) is not the market portfolio - The y-intercept for the tangent line at the red star has no meaning in this case (its value lies between 10% and 15%) My basic source of confusion is, how do I relate my limited portfolio with the CAPM theory? What can I say, and what I cannot say bout tangent lines and risk-free rates? Here is the data from the red star portfolio: ``` Sharpe ratio:1.04530 Expected return: 0.18899 Volatility: 0.17681 Beta: 0.49825 ``` I appreciate any inputs on this, as I'm new to finance. Thank you! ## Answer by zero (score 1) https://quant.stackexchange.com/a/53198 Fernando. cash is a proxy for a riskless asset and an efficient portfolio on the efficient frontier serves as the risky portfolio such that any allocation between cash and this portfolio dominates all other portfolios on the efficient frontier. This portfolio is called a tangency portfolio because it is located at the point on the efficient frontier where a tangent line that originates at the riskless asset touches the efficient frontier.(MATLAB) ## Answer by Paul Lyons (score 1) https://quant.stackexchange.com/a/53794 Try showing the full scale of the x axis. You’re starting at a vol of ~12% and going up to 30%. If the x axis starts at 0% vol and goes up from there, your CML may come closer to intersecting your red star.
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