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Interpreting Portfolio Weights Above One as Risk-Free Borrowing

Article Quant Q&A · Author: turtle101
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Summary

The note explains how to interpret a portfolio weight greater than one in a combination of a risky market portfolio and a risk-free asset. A positive risky-asset weight above 100% is funded by a negative weight in the risk-free asset, which represents borrowing at the risk-free rate. In the example, the portfolio puts 125% into the risky market portfolio and borrows 25% at the risk-free rate to target a 12% expected return.

This interpretation assumes borrowing and short positions are permitted and available at the stated risk-free rate. The post does not assess whether the target portfolio is consistent with the given market volatility or other constraints, and it offers no broader derivation of the efficient frontier. Its main lesson is how leverage appears in portfolio weights.

Key ideas

  • A weight above one means the risky investment exceeds the investor’s initial capital.
  • A negative weight in the risk-free asset represents borrowing at the risk-free rate.
  • The example finances a 125% market allocation with 25% borrowing.
  • Leverage depends on the assumption that borrowing at the risk-free rate is allowed.

Tags

Portfolio constructionPosition sizingRisk management
Full text
# How do you interpret a positive portfolio weight (when using CAPM and CML to calculate efficient portfolios)


# How do you interpret a positive portfolio weight (when using CAPM and CML to calculate efficient portfolios)












I am asked to solve the following homework question: Risk free rate: 2% Expected excess return on market portfolio: 8% Standard deviation of market portfolio: 20% The efficient portfolio has the following: Expected return: 12% Standard deviation: 25%

I am asked the following question: "How can the expected return of the wining portfolio be achieved? Specify the amount invested in each asset/portfolio of assets?" and I've used the following calculation to determine portfolio weight of 1.25: 0.12=ω0.1+(1-ω)0.02⇒ω=1.25

And here is where I am a little lost. What does it mean to have the portfolio weight >1 and what does it mean? If it's incorrect, where did I go wrong before? Thanks for any help!

## Answer by Raskolnikov (score 0, accepted)

https://quant.stackexchange.com/a/37043

Just to make this a regular reply:

A negative value for a weight means that you short that asset. Inevitably, it also means that the money you get from shorting gets invested into the other assets. Hence weights larger than 1. In your case, it is the risk-free asset you short, which means you are borrowing money. To be precise you borrow 25% at the risk-free rate and invest 125% into the risky assets.

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.