Session Ready
Exercise

The CER model

A quick recap on the constant expected return model (CER) as seen in the previous chapter:

$$R_{it} = \mu_i + \epsilon_{it} \text{, with } t = 1,\ldots,T$$ $$\epsilon_{it} \sim \text{ iid } N(0,\sigma_i ^ 2)$$ $$cov(\epsilon_{it},\epsilon_{jt}) = \sigma_{ij}$$

where \(R_{it}\) denotes the continuously compounded return on asset \(i\), now with \(i = \) Microsoft and Boeing.

As discussed in the previous chapter, the parameters \(\mu_i\), \(\sigma_i\) and \(\rho_{ij}\) are unknown to us. However, you can estimate the model parameters for both the Boeing and the Microsoft stock based on the data in returns_df.

Instructions
100 XP
  • Assign to sigma2_annual the estimates of \(\sigma_i ^ 2\) for both assets (i.e. \(i = \) Boeing and Microsoft respectively). Calculate the corresponding \(\hat{\sigma}_i\) as well and assign it to sigma_annual.
  • The annual CER model parameters for Boeing are provided. Calculate those for Microsoft as well.
  • Estimate the correlations \(\rho_{ij}\) between both stocks and assign the result to rho_boeing_msft.