Data assignment based on Stephen’s Weeks 4 & 5 lectures

Data assignment based on Stephen’s Weeks 4 & 5 lectures (Warning to those noble few who attempted the week 4 assignment: this is pretty similar in the early sections, but has changed in a couple of places, quite apart from the extra questions.) 1. Using the data provided to you in the spreadsheet on Moodle (for the Sensex stock price index for India, and the CPI for India), calculate and plot a graph of the Sensex Index in nominal and real terms, both expressed as an index=100 in 1979. (Hint, this should look very like the chart from lecture notes) 2. Using data that you will need to download from FRED (https://fred.stlouisfed.org/) calculate the real value of the Sensex Index for a sterling investor, expressed as an index=100 in 1979, and plot on the same chart. Hints:  FRED does not have data for the rupee-sterling exchange rate directly, you will need to download the Rupee-Dollar Rate (search for “India / U.S. Foreign Exchange Rate”) and the Dollar-Sterling Rate (search for “U.S. / U.K. Foreign Exchange Rate”) separately. You will then need to construct the Rupee-Sterling rate using these two series. Warning! It is very easy to get this wrong!  You will also need a measure of the UK CPI, as discussed in the lectures. There are a number on offer. I used the (extremely long) annual series “Consumer Price Index in the United Kingdom©, Index 2015=100, Annual, Not Seasonally Adjusted”, but changed the sample to run from 1979 only. You should get very similar answers whichever measure you use.  Remember you want annual series! FRED may well offer you some series in monthly terms (though if you search including the word annual this may stop this happening). If you find yourself with monthly series you can click on “edit graph” and change it to annual.  You can collect all the series together or download them one at a time (which seems to be easier – but maybe I’m missing a trick!)  The series you should end up with should look very similar to the real series in Rupee terms. If it doesn’t you’ve probably made a mistake somewhere! 3. Using the formulae given in lecture notes, calculate (in Excel) compound average growth rates, over two samples, 1979-2015 and 1992-2015, for the following series I. Sensex in nominal terms II. Sensex in real rupee terms III. Sensex in real terms for a sterling investor IV. UK CPI V. Indian CPI VI. The Rupee Sterling Exchange Rate and comment briefly on the relationships between the long-term growth rates of the different series in the next lecture over the two sample periods. 4. Do the same calculations for the implied continuously compounded growth rates (see lecture notes from week 4) and explain why the numbers are so similar to those you found in question 3. 5. Using the same dataset a) on the same graph, plot the percentage change in the CPI (expressed as a decimal: ie 10%=0.1) alongside the change in the natural log of the CPI b) do the same for the real value of the Sensex index c) Show mathematically why the change in the log and the % change are so similar for the CPI… d) … but are much less similar for the Sensex index at certain points in history. 6. a) Calculate the average of the log changes calculated in question 5 parts a) and b) and compare with the continuously compounded growth rates you calculated in question 4. What do you notice? b) (harder) If you can, use the properties of of logarithms to explain why. 7. Assume an investor has an initial wealth of £100 in year 0, and has the following sequences of returns (% change in wealth) over years 1 and 2: a) – 5%, + 5% b) – 50% ,+ 50% c) -50%, +100% d) -100% ,+50% In each of the 4 cases, calculate i) the investor’s wealth after 1 and 2 years, ii) the change in the log of wealth in year 1 and year 2 iii) the compound average return over the two years, iv) the simple average percentage change in their wealth over the two years v) the simple average of the change in the log of their wealth over the two years. and comment briefly on the differences and similarities between the different calculations.