First, we have the Capital Asset Pricing Model
Before anything else, let us first discuss the Capital Asset Pricing Model. CAPM describes a trade-off that happens between the risk and returns for optimal portfolios. All investors choose a position on the capital market line in equilibrium. It can be done by borrowing or lending at a rate that does not have risks. This will makes returns for a particular risk become possibly more. So, what does the capital market line mean?
What is the capital market line?
The capital market line or CML refers to the portfolios that have risk and return combined. This concept is based on a theory representing all portfolios that incorporates the risk-free rate of return and the risky assets market portfolio. The theory says that portfolios falling on CML makes the most out of the risk and return relationship. Hence, the performance is maximized.
A term called capital allocation line (CAL) makes up the allotment of risk-free assets and risky portfolios. In this case, we can say that CML is CAL special case because the risk portfolio is also the market portfolio. So, it means that the CML slope is the market portfolio’s Sharpe ratio. In a nutshell, you can buy if the Sharpe ratio is more than the CML, and you can sell if it is lower.
The tangency portfolio and mean-variance analysis
There are more popular frontiers that have risk-free investments. However, CML is not similar because its intercept point and efficient frontier would end up as the most efficient portfolio, and we can call it a “tangency portfolio.”
What connects the tangency point and the risk-free rate of return? It is the CAPM. The tangency point is on the excellent portfolio’s efficient frontier of optimal portfolios that gives the highest expected return for a defined risk level. It may also be the lowest risk for the expected return given. Every portfolio is different, but the ones with the best-expected returns and risk trade-off lie on the CAPM. As we mentioned earlier, the tangency point, also known as the market portfolio, is the portfolio that contains risky assets. The mean-variance analysis assumes that investors look for more expected returns for the variance risk given. Furthermore, it assumes that there is a risk-free rate of return, and every investor will choose the portfolios that lie on the CML.
Here are the people who made significant contributions to today’s topic:
- Mean-variance analysis. The pioneers are Harry Markowitz and James Tobin.
- Efficient frontier of optimal portfolios. Markowitz identified it.
- Risk-free rate. James Tobin added this to Markowitz’s Modern Portfolio theory.
- Capital asset pricing model. William Sharpe developed it.
James Tobin’s theorem
Tobin’s theorem says that finding the best market portfolio is one thing, and looking for the best market portfolio and risk-free asset combination is another. Every investor may hold a risk-free asset. However, they may also hold a combination of risk-free assets and market portfolios. It all depends on the risk-aversion. The more the investor gets close to the CML, the more risk and return. Hence, risk-averse investors will always choose risk-free assets. Braver investors will choose the portfolios closer to the CML. There is more variance, but their expected return is higher.
A quick recap
CML represents portfolios that combine risk and return well. It is a CAL special case because the risk portfolio is also the market portfolio. Hence, the CML slope is the market portfolio’s Sharpe ratio. The tangency portfolio is the most efficient. It is the result of both the CML intercept point and the efficient frontier. In a nutshell, you can buy if the Sharpe ratio is above the CML, and you can sell if it is below.