Tangency Portfolios and Investor Risk-Free Allocations

Summary

The document distinguishes two choices in mean-variance portfolio theory. The tangency point between the capital allocation line (CAL) and the efficient frontier identifies the optimal portfolio of risky assets, given the model’s assumptions. It is the shared risky portfolio available to investors who combine risk-free lending or borrowing with risky holdings.

An investor’s indifference curve selects a point along the CAL, determining how wealth is divided between the risk-free asset and the tangency portfolio. If the indifference curve is tangent at the tangency portfolio itself, the investor holds all wealth in risky assets and none in the risk-free asset. This explanation is conceptual; it gives no numerical example or empirical evidence, and its conclusion relies on the standard framework with a risk-free asset and common portfolio opportunities.

Key ideas

• The CAL’s tangency with the efficient frontier identifies the model’s optimal risky portfolio.
• The investor’s indifference curve determines the preferred combination of that portfolio and the risk-free asset.
• Choosing the tangency point itself means allocating all wealth to the risky portfolio under this framework.

Tags

# Markowitz portfolio optimization and CAL


# Markowitz portfolio optimization and CAL












Just had some questions regarding the efficient frontier and the CAL. As i understand it the point where the CAL is tangent to the efficient frontier is the optimal mix of risky assets. However I also noticed that on the same CAL there is a point where the indifference curve will be tangent to the CAL. What does this point represent?

## Answer by Eiffelbear (score 2, accepted)

https://quant.stackexchange.com/a/43919

The tangent portfolio is the optimal portfolio of risk assets. So under the Modern portfolio theory world, all investors will buy and hold this portfolio if they want to make an investment in risky assets.

The point where indifference curve and the CAL meets tells how much of your wealth would be invested in (1) the risk-free asset and (2) the optimal portfolio (= tangent portfolio) of risk assets.

For example, if the indifference curve happens to meet the CAL, exactly where the tangent portfolio meets the CAL, then it means that the investor would invest 100% of her wealth in the optimal portfolio of risky assets and 0% in risk-free asset.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.