BlueRiver Asset Management wants a quick statistical check on whether changes in market interest rates are associated with changes in the price of one of its 10-year corporate bonds. A fixed-income analyst collected monthly observations to quantify the relationship.
Use the sample data to test whether monthly changes in interest rates are negatively related to monthly bond returns, and estimate the size of that relationship.
The analyst measured monthly change in the benchmark yield (in percentage points) and the bond's monthly return (in decimal form).
| Month | Rate Change | Bond Return |
|---|---|---|
| 1 | 0.10 | -0.008 |
| 2 | 0.20 | -0.015 |
| 3 | -0.10 | 0.009 |
| 4 | 0.30 | -0.022 |
| 5 | -0.20 | 0.018 |
| 6 | 0.05 | -0.004 |
| 7 | -0.15 | 0.013 |
| 8 | 0.25 | -0.019 |
| 9 | 0.00 | 0.001 |
| 10 | -0.05 | 0.006 |
| 11 | 0.15 | -0.011 |
| 12 | -0.25 | 0.021 |
Assume a simple linear model: .