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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).

enter image description here

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:

  1. My optimized portfolio (red star) is not the market portfolio

  2. 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!

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  • $\begingroup$ Consider the risk free rate as that of a 6'th asset with a volatility of zero, or better yet as a portfolio of one asset that has no risk. Consider, as a second portfolio, a point on the efficient frontier of the 5 stocks. Now if you allocate your wealth between these two portfolios you obtain a combined portfolio with metrics on a line between the risk free rate and the portfolio on the efficient frontier. The steepest line is the best. $\endgroup$
    – Attack68 ♦
    Jan 5, 2019 at 19:28
  • $\begingroup$ In the absence of a risk free rate - for example if you are trading derivatives without a wealth investment and purely leveraging risk - then the portfolio you found (red star) may be the most interesting one. I used this frequently in conjunction with considering interest rate swap portfolios. $\endgroup$
    – Attack68 ♦
    Jan 5, 2019 at 19:36
  • $\begingroup$ I understand how the CML works, what I still not get is how to interpret it when my portfolio is obviously not the market portfolio. Also, beta < 0 for my portfolio? Shouldn't it be greater than 1? $\endgroup$
    – Fernando
    Jan 5, 2019 at 20:00
  • $\begingroup$ You have found a portfolio which maximizes the sharpe ratio ex-post over a specific interval of time. This is not necessarily the market portfolio. However it is not guaranteed that your portfolio will outperform market portfolio in future. So practical value is limited, since it is based on hindsight (ie. Knowing the past means and variances exactly), not prediction. $\endgroup$
    – nbbo2
    Jan 5, 2019 at 21:03
  • $\begingroup$ That's what I thought. But does the tangent line have some interpretation? It doesn't intercept the y axis at my rfr. $\endgroup$
    – Fernando
    Jan 5, 2019 at 21:26

2 Answers 2

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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)

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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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