Estimating a Market Portfolio Price from Tangency Portfolio Weights

Summary

The document describes a two-asset portfolio exercise using monthly prices to calculate returns, means, variances, standard deviations, covariance, and correlation. The investor uses those inputs to trace a mean-variance frontier, identify the minimum-variance portfolio, and find the portfolio with the highest Sharpe ratio using a short-term government bond as the risk-free asset. The question is how to obtain a market price for the market portfolio under a no-arbitrage condition.

The included answer proposes multiplying each asset's latest price by its weight in the tangent portfolio and summing the weighted values. This gives a price for a portfolio represented by those holdings, but the document does not explain why this is specifically the market portfolio or derive the claimed no-arbitrage connection. The result depends on the chosen weights, asset units, and interpretation of portfolio value; the text offers no market-wide capitalization data or broader model assumptions.

Key ideas

• The exercise constructs a two-asset mean-variance frontier from historical return statistics.
• It identifies a minimum-variance portfolio and a maximum-Sharpe tangent portfolio.
• The proposed portfolio value is the sum of each asset's latest price multiplied by its tangent-portfolio weight.
• The document does not derive why this value represents the market portfolio under no arbitrage.

Tags

# Finding latest market price of market portfolio according to No Arbitrage


# Finding latest market price of market portfolio according to No Arbitrage












In Excel, I have the monthly stock price data for the past few years for Asset A and Asset B. I have calculated the monthly returns, mean returns, variances, and standard deviations for both stocks as well as the covariance and correlation.

Then I calculated the weighted portfolios of Asset A and Asset B calculating the return and standard deviation for each portfolio, this let me draw the mean-variance frontier (MVF).

Then I solved the optimisation problem to find the smallest variance portfolio.

Then I found the portfolio with the highest Sharpe Ratio. I used a short-term government bond as a risk-free asset. Then I drew a new efficient frontier.

I am now tasked with: finding the market price of mkt portfolio according to No Arbitrage condition. How do I do this?

## Answer by Hans-Peter Schrei (score 3)

https://quant.stackexchange.com/a/74955

To find the current market price of the market portfolio, you need to multiply the current/latest market price of each asset by its respective weight in the tangent portfolio and then sum them up. This will give you the market price of the market portfolio (tangent portfolio) according to the No Arbitrage condition.

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.