Lab for Lecture 3: Measuring and Comparing Returns
Real and nominal returns, total returns, average returns (geometric and arithmetic)
1 The Past Performance of Major Asset Classes
1.1 Data
Use the asset_class_returns.xlsx dataset to obtain annual returns on the major asset classes (these are nominal returns) and the inflation rate.
Remember this dataset is organized as follows:
| Column Name | Data |
|---|---|
| sp500 | Annual returns on S&P 500 (includes dividends) |
| smallcap | Annual returns on US Small cap firms (bottom 10% by market cap) |
| tbill | Average 3-month T.Bill rate per year |
| tbond10 | Annual returns on US T. Bonds (10-year) |
| cbonds_baa | Annual returns on Baa-rated corporate bonds |
| real_estate | Average annual price appreciation in residential real estate |
| gold | Annual percentage change in gold prices |
| inflation | Annual percentage change in CPI |
1.2 Analysis
Using this data:
- Calculate real returns for each asset class, every year.
- For each year in the sample, calculate compunded (i.e. “total” or “cummulative”) nominal and real returns for each asset class, from the beginning of the sample up to that year.
- Plot the cummulative nominal and real returns on the S&P 500 over time.
- Calculate total nominal and real returns for each asset class, for the full sample.
- Calculate the geometric average and arithmetic average of nominal and returns for each asset class.
1.3 Questions
- Why is the gap between the cumulative nominal and real return lines on your S&P 500 plot so large by the end of the sample? Doesn’t inflation hover around 3%?
- If you were saving for retirement 30 years from now, would you focus on nominal returns or real returns? Why?
- Which asset classes turned $1 into more wealth? Do these results surprise you in any way?
- For which asset classes is the gap between the arithmetic and geometric average largest?
- What characteristic of those asset classes do you think explains this?
- If you had to forecast next year’s return, which average would you use?
- What if you were forecasting average annual returns over the next 20 years?
- Given the massive outperformance of stocks over the full sample, why would anyone hold bonds or T-bills?
- How do the real returns on real estate compare to stocks? What’s missing from the real estate return data that might matter?
- Which asset classes appear to be good “inflation hedges” (assets that don’t get as negatively affected by inflation as others)? How can you tell from your results?