The Tangency Portfolio and the Optimal Risky Asset
If you are going to take on risk, the ideal combination would give you the most excess return for that same risk. Theory gave that combination a name: the tangency portfolio.
What Is the Tangency Portfolio?
The Tangency Portfolio is the single combination with the highest Sharpe ratio (excess return per unit of risk) among all combinations that can be built from risky assets alone.
If you draw a straight line (the CAL) from the risk-free asset toward the efficient frontier, the line touches the efficient frontier at exactly one point, and that point of tangency is this portfolio. That is why it is named the 'tangency' portfolio.
Why It Matters
According to the two-fund separation theorem, a rational investor fills the entire risky portion with this tangency portfolio, and adjusts how much risk to take purely through the ratio to the risk-free asset.
In other words, the answer to the question 'which risky assets should I hold' is theoretically fixed to a single one. Two people with different risk preferences hold the same risky-asset composition, differing only in the weight of the risk-free asset.
Its Relationship to the CAPM's Market Portfolio
In the world of the CAPM, all investors are assumed to have the same information, so everyone ends up wanting the same tangency portfolio. As a result, the tangency portfolio becomes identical to the 'market portfolio,' which holds the entire market at market-cap weights.
This is one of the roots of the index-investing logic that 'an index holding the whole market is theoretically efficient.'
In reality, investors differ in information, taxes, and constraints, so the tangency portfolio does not exactly match the market portfolio. It is a theoretical conclusion only.
常见问题
Q. Is the tangency portfolio always the same combination?
In theory, if the inputs (expected returns, volatility, correlation) are fixed, it is determined uniquely. But these inputs are estimates, so if the data period or assumptions change, the composition of the tangency portfolio changes too. It is a 'unique but not stable' value.
Q. Do I get the highest return if I buy the tangency portfolio?
No. The tangency portfolio is the combination with the highest 'efficiency per unit of risk (Sharpe ratio),' not the combination with the 'highest expected return.' If you want higher return, the risk grows too.
相关页面
📋 结果基于历史数据计算,过去的收益不代表未来的收益。
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