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Applying CAPM to Estimate Expected Returns for Three Assets

Article Quant Q&A · Author: R Dobby
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Summary

The document poses a one-year CAPM calculation for three assets. It supplies each asset’s annual volatility and market capitalization, assumes the returns of distinct assets have equal pairwise correlation, and gives the risk-free rate and expected market return. The requested output is the expected annual return for each asset.

The setup points toward estimating each asset’s beta from its covariance with the market portfolio, then applying the CAPM relation between beta, the risk-free rate, and the market risk premium. Market-cap weights and the correlation and volatility assumptions provide the inputs needed to form the market portfolio’s variance and each asset’s covariance with it. The document gives no worked calculation or resulting asset returns, so implementation details and numerical answers are not established. The result also depends on the stated CAPM assumptions and the specified one-year holding horizon.

Key ideas

  • CAPM expected return is determined by an asset’s beta, the risk-free rate, and the market risk premium.
  • Market-capitalization weights define the market portfolio in the scenario.
  • Pairwise correlations and asset volatilities provide inputs for estimating covariance with the market.
  • The document asks for a calculation but does not show the worked steps or numerical results.

Tags

EquitiesStatisticsPortfolio construction
Full text
# Calculating expected annual returns


# Calculating expected annual returns












An economy contains these three assets:

Asset A has standard deviation of returns (per annum) of 25% and market capitalisation $600m

Asset B has standard deviation of 20%, market capitalisation $300m

Asset C has standard deviation of 10%, maket capitalisation $100m

The correlation coefficient for the returns on each pair of distinct securities is 0.25.

The risk-free rate of return is 3.3% per annum and the expected return on the market is 8.38% per annum.

The assumptions underlying CAPM are valid and all investors will hold their portfolios for the next year.

How can I calculate the expected annual returns for each 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.