Why the Market Portfolio Is a Practical Proxy for the Tangency Portfolio
Summary
The document asks why the market portfolio is treated as the tangency portfolio in the CAPM framework when real investors hold different portfolios, including undiversified ones. The question recalls the theoretical result that investors choose the same optimal risky portfolio, combined with lending or borrowing at the risk-free rate, and asks how that result relates to real-world holdings and an index such as the S&P 500.
The response distinguishes the model’s implication from observed investor behavior. It says managers can form different risky portfolios because they use different inputs, while the value-weighted portfolio of all assets remains a reasonable first approximation to an efficient risky portfolio for passive investors. An index is therefore a practical proxy, not proof that every investor holds the same portfolio or that a familiar index perfectly represents all world assets. The discussion offers a conceptual explanation, not empirical evidence that the proxy is optimal in every setting.
Key ideas
- Under CAPM assumptions, investors share the same optimal risky portfolio and adjust overall risk through the risk-free asset.
- Real managers may hold different risky portfolios because their optimization inputs differ.
- The value-weighted market portfolio can still serve as a reasonable first approximation to an efficient portfolio.
- A market index is a proxy for the broader market portfolio, not an exact description of every investor’s holdings.
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Full text
# Why is the tangency portfolio the market portfolio in a world where not everyone holds the same portfolio? # Why is the tangency portfolio the market portfolio in a world where not everyone holds the same portfolio? I understand how the efficient frontier is formed, and that the point of tangency with the CAL is the portfolio that offers the greatest excess returns over the risk-free rate per unit volatility (i.e sharpe ratio). If I understand correctly, under the assumptions of CAPM, everyone holds this tangency portfolio, and therefore the tangency portfolio must be the market portfolio. However, we know that people in the real world don't all hold the same portfolio and many may not even be diversified. Why does the market portfolio, for which something like the S&P 500 is a proxy remain the optimal portfolio? ## Answer by KaiSqDist (score 4) https://quant.stackexchange.com/a/82199 In Investments by Bodie, Kane & Marcus (Chapter 9, The CAPM), there is a section that talks about how "The Passive Strategy is Efficient". In one of the paragraphs, and I quote - > In reality, different investment managers do create risky portfolios that differ from the market index. We attribute this in part to the use of different input lists in the formation of their optimal risky portfolios. Nevertheless, the practical significance of the mutual fund theorem is that a passive investor may view the market index as a reasonable first approximation to an efficient risky portfolio. I think this answers your question. Even though individual investors in the real-world hold different risky portfolios, the market portfolio (that consists of all assets in the world, value-weighted) is a reasonable proxy to the optimal portfolio. I don't even think all investors use this proxy, just most.
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