Exercise - TIPS

Exercise - TIPS#

\(\newcommand{\rUSD}{r^{\text{US}}}\) \(\newcommand{\rGBP}{r^{\text{GBP}}}\) \(\newcommand{\rxGBP}{\widetilde{r}^{\text{GBP}}}\)

1 TIPS and Inflation#

Use the data in data/inflation_expectation_data.xlsx

1.1#

Use the yields for the 5-year nominal note and the 5-year TIPS to construct an index of expected 5-year inflation.

  • Plot the expected inflation over time

  • Report the minimum and maximum inflation expectations, and the dates on which they occured.

1.2#

Use the data on consumer prices to construct year-over-year inflation.

That is, measure inflation as the percentage change in CPI over 12 months, reported on a monthly basis.

Plot CPI, and report its minimum and maximum values, along with the dates on which they occured.

1.3.#

Plot the inflation expections from 1.1. against the realized inflation from 1.2.. Shift the realized inflation by 5 years such that a given date plots the TIPS-based forecast against the realized value.

1.4.#

Calculate two monthly change series:

  1. Go back to the raw CPI data, and calculate its month-over-month percentage change. Denote this as \(z^1_t\).

  2. Aggregate the inflation expectation series calculated above into a monthly series. Furthermore, take its month-over-month difference. Denote this as \(z^2_t\). Consider using

    • .resample(‘ME’).last()diff()

(a)#

Report the correlation between these two series,

\[\text{corr}(z^1_t,z^2_t)\]

(b)#

Does a change in CPI predict a futre change in the 5-year inflation expectation? Or vice-versa? Check by calculating the following two correlations:

\[\text{corr}(z^1_t,z^2_{t+1})\]
\[\text{corr}(z^1_{t+1},z^2_t)\]

What do you conclude?

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