Lab for Lecture 4: Measuring Risk and Expected Return
Descriptive statistics, risk premiums, Sharpe ratios, and tail risk measures
1 Measuring Risk and Return for Stocks and Bonds
1.1 Data
Use the asset_class_returns.xlsx dataset to obtain annual returns on the S&P 500 (sp500) and 10-year Treasury bonds (tbond10). You will also need the T-bill rate (tbill) to calculate risk premiums.
| Column Name | Data |
|---|---|
| sp500 | Annual returns on S&P 500 (includes dividends) |
| tbond10 | Annual returns on US T. Bonds (10-year) |
| tbill | Average 3-month T.Bill rate per year |
1.2 Analysis
Using this data, for both the S&P 500 and 10-year Treasury bonds:
- Calculate basic summary statistics: mean, standard deviation, minimum, maximum, and the 25th and 75th percentiles.
- Plot histograms of the return distributions for each asset class.
- Assuming returns are normally distributed, calculate the return levels that are 1, 2, and 3 standard deviations away from the mean.
- What is the probability of returns falling below each of these thresholds under the normality assumption?
- Calculate the risk premium (mean return minus the average T-bill rate) and the Sharpe ratio for each asset class.
1.3 Questions
- How do the mean returns and standard deviations of stocks compare to those of bonds? Is the relationship between risk and return what you would expect?
- Looking at the histograms, do the return distributions appear roughly normal? What features, if any, look different from a normal distribution?
- Based on the 2 and 3 standard deviation thresholds you calculated, how often would you expect extremely negative returns under normality? How does this compare to what actually happened historically?
- What does the Sharpe ratio tell you about the risk-return tradeoff for each asset class? Which asset class offers better compensation for risk?