If you have got any suggestions or questions for us, you can reach us here.According to CAPM, all investors hold a combination of the same portfolio M of risky assets and the risk-free asset - though different investors will hold different combinations at different points along the efficient frontier / capital market line We would love to hear your feedback on our content. Previous lesson: We explained how mean-variance optimizing investors can obtain the tangency portfolio in the presence of a risk-free asset.Next lesson: We will make a distinction between systematic risk and idiosyncratic risk and will explain how the latter can be eliminated via portfolio diversification.This lesson is part of our free course on investments. Levy and Roll (2010), “ The market portfolio may be mean/variance efficient after all“, The Review of Financial Studies, Vol. We will further examine this portfolio within the context of CAPM in the following lessons. Moreover, we have shown that this portfolio has a beta of 1 and that it is typically proxied by a market index. We have defined it as the value-weighted portfolio of all risky assets in a particular market. In this lesson, we have explained what is meant by the market portfolio. If we let asset i be the market portfolio, then we have:Īs we have discussed before an asset’s covariance with itself is equal to its variance, so we have: Where β i is the beta of asset i, σ im is the covariance between asset i and the market, and σ m 2 is the variance of market returns. In fact, we can easily prove this using the mathematical definition of beta: If that is the case, what should be the beta of the market portfolio? The answer is easy: The market portfolio has a beta of 1. The same is true for portfolios of assets as well as individual assets. The beta of an asset quantifies that asset’s exposure to market risk. Therefore, when all investors attempt to hold the optimal risky portfolio, it becomes the market portfolio! The beta of the market portfolio Assets Market portfolio Asset A 50% Asset B 30% Asset C 20% Total 100% Table 2ĭo these investment weights look familiar? They should! They exactly match the weights of these three assets in the optimal risky portfolio. What is the overall weight of asset A in the market? $900 / $1,800 = 50%. We can now find the composition of the market portfolio, which is the value-weighted portfolio of assets A, B, and C. If Linda and Steve are the only investors in the market and their total investments in risky assets are $1,000 and $800, respectively, then the total market value of all risky assets (i.e., A, B, and C) is $1,000 + $800 = $1,800. This information is summarized in Table 1 below. Following the same logic, Steve should invest $400 in A, $240 in B, and $160 in C. In order to “hold” the optimal risky portfolio, Linda should invest $500 in A, $300 in B, and $200 in C. Linda has $1,000 to invest in the market, and Steve has $800. Let’s also assume there are only two investors in this market: Linda and Steve. And, let’s suppose the composition of the optimal risky portfolio is: Say, there are only three risky assets in a market A, B, and C. In practice, broad-based market indices such as the S&P500 serve as a proxy of the market portfolio.Īccording to the capital asset pricing model, the market portfolio is equivalent to the optimal risky portfolio when all investors behave according to the modern portfolio theory by engaging in mean-variance optimization. Value-weighting (as opposed to equal-weighting) means that assets with high market values (e.g., large-cap stocks) would have a higher weighting in the portfolio than those with low market values (e.g., small-cap stocks). The market portfolio is the value-weighted portfolio of all risky assets in an economy. The beta of the market portfolio What is the market portfolio?.
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