6. Summary

In this section, we have learned how to compute the expected return and volatility (return standard deviation) of a portfolio P that constitutes of two assets, A and B.

 

In the formal part, we have presented the most important equations (and Excel implementations) to master these tasks. Thereby, we have used the following notation:

 

  • \(\mu\) = average expected return
  • \(w\) = Portfolio weight of an asset
  • \(\sigma\) = standard deviation (volatility)
  • \(\sigma^2\) = Return variance
  • \(\rho\) = correlation coefficient

  

Using this notation, the main formulas to compute the mean return and standard deviation of a portfolio are:

  

Metric Variable Formula
Portfolio return \(\mu_P\) \(w_A \times \mu_A + w_B \times \mu_B \),
Portfolio variance \(\sigma_P^2\) \(w_A^2 \times \sigma_A^2 + (1-w_A)^2 \times \sigma_B^2 + 2 \times w_a \times (1-w_A) \times \rho_{AB} \times \sigma_A \times \sigma_B \)
Return standard deviation \(\sigma_P\) \(\sqrt{\sigma_P^2}\)

 

Then we have applied these equations to real portfolios. This has allowed us to get a first impression of the power of diversification: By combining assets with low correlations, we should be able to reduce the risk of the portfolio without necessarily giving up return. 

 

These considerations have built the foundations for the next steps, where we talk about diversification with multiple assets and then discuss the implications for the cost of capital of a project.