1. Introduction

The preceding section has discussed the distribution characteristics of individual assets using the example of U.S. stocks and bonds over the period 1928-2018:

 

  • We have introduced the assumption of normally distributed returns and we have seen that this assumption makes an acceptable approximation of reality (at least for the purpose of our analysis). 
      
  • Moreover, we have seen that under the normal distribution, all we need to know is the mean (\(\mu\)) and the standard deviation (\(\sigma\)) of the return to completely characterize the return distribution.

 

With this knowledge, we are now ready to take the next step and look at the risk and return implications when investors start combining assets into portfolios. As it turns out, the return of a portfolio that consists of assets with normally distributed returns will itself be normally distributed. Consequently, we can study all relevant investment opportunities in a two-dimensional space of average return and risk (standard deviation; volatility).

 

The section proceeds as follows:

  • Using U.S. stock and bond returns over the period 1918-2018, we illustrate the risk-return trade-off that investors face when deciding about how to invest their money.
     
  • A simple example introduces the idea of diversification: By combining assets with low correlations into a portfolio, we can reduce the risk of our investment without necessarily giving up return. Diversification is said to be "the only free lunch" in investments.
     
  • We bring the idea of diversification back to the case of U.S. stocks and bonds. We show how to compute the return and volatility of portfolios that consist of two assets.
     
  • Finally, we take a closer look at the crucial role that correlation plays in the context of diversification.
     
  • We conclude with a summary of the most important formulas of this section.