Interest Rates and Bond Price Sensitivity

Business Context

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.

Problem Statement

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.

Given Data

The analyst measured monthly change in the benchmark yield (in percentage points) and the bond's monthly return (in decimal form).

Month	Rate Change $x$	Bond Return $y$
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: $y = \beta_0 + \beta_1 x + \varepsilon$ .

Requirements

Compute the sample correlation between rate changes and bond returns.
Fit the simple linear regression slope and intercept.
Test $H_0: \beta_1 = 0$ versus $H_1: \beta_1 < 0$ at $\alpha = 0.05$ .
Report the test statistic and p-value.
Interpret the estimated slope in business terms.

Assumptions

Monthly observations are treated as approximately independent.
The linear relationship is a reasonable first-order approximation.
Regression residuals are approximately normal for inference.

Business Context

Problem Statement

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.

Given Data

The analyst measured monthly change in the benchmark yield (in percentage points) and the bond's monthly return (in decimal form).

Month	Rate Change $x$	Bond Return $y$
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: $y = \beta_0 + \beta_1 x + \varepsilon$ .

Requirements

Compute the sample correlation between rate changes and bond returns.
Fit the simple linear regression slope and intercept.
Test $H_0: \beta_1 = 0$ versus $H_1: \beta_1 < 0$ at $\alpha = 0.05$ .
Report the test statistic and p-value.
Interpret the estimated slope in business terms.

Assumptions

Monthly observations are treated as approximately independent.
The linear relationship is a reasonable first-order approximation.
Regression residuals are approximately normal for inference.

Business Context

Problem Statement

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.

Given Data

The analyst measured monthly change in the benchmark yield (in percentage points) and the bond's monthly return (in decimal form).

Month	Rate Change $x$	Bond Return $y$
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: $y = \beta_0 + \beta_1 x + \varepsilon$ .

Requirements

Compute the sample correlation between rate changes and bond returns.
Fit the simple linear regression slope and intercept.
Test $H_0: \beta_1 = 0$ versus $H_1: \beta_1 < 0$ at $\alpha = 0.05$ .
Report the test statistic and p-value.
Interpret the estimated slope in business terms.

Assumptions

Monthly observations are treated as approximately independent.
The linear relationship is a reasonable first-order approximation.
Regression residuals are approximately normal for inference.

Business Context

Problem Statement

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.

Given Data

The analyst measured monthly change in the benchmark yield (in percentage points) and the bond's monthly return (in decimal form).

Month	Rate Change $x$	Bond Return $y$
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: $y = \beta_0 + \beta_1 x + \varepsilon$ .

Requirements

Compute the sample correlation between rate changes and bond returns.
Fit the simple linear regression slope and intercept.
Test $H_0: \beta_1 = 0$ versus $H_1: \beta_1 < 0$ at $\alpha = 0.05$ .
Report the test statistic and p-value.
Interpret the estimated slope in business terms.

Assumptions

Monthly observations are treated as approximately independent.
The linear relationship is a reasonable first-order approximation.
Regression residuals are approximately normal for inference.

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Interest Rates and Bond Price Sensitivity

Business Context

Problem Statement

Given Data

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Your Answer

Interest Rates and Bond Price Sensitivity

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Interest Rates and Bond Price Sensitivity

Business Context

Problem Statement

Given Data

Requirements

Assumptions

Your Answer