Interest Rate Risk and Its Impact on Price Volatility

Market → Price Volatility & Models
| 2025-11-14 13:50:29

Introduction Slide – Understanding Interest Rate Risk and Its Effect on Price Volatility

Key Drivers of Interest Rate Risk and Its Effect on Price Volatility.

Overview

Interest Rate Risk arises from the possibility that changes in market interest rates will adversely affect earnings or capital, impacting fixed-income assets and borrowing costs.
Understanding Interest Rate Risk is critical as it influences the price volatility of bonds and loans, affecting investors, banks, and corporations.
The slides cover definitions, key drivers, analytical frameworks, visual data trends, and risk management implications.
Key insights include the inverse relationship between interest rates and bond prices, different types of interest rate risk, and approaches to quantify and mitigate risk.

Key Discussion Points – Drivers and Impact of Interest Rate Risk on Price Volatility

Implications of Interest Rate Changes and Underlying Risks.

Main Points

Interest Rate Risk stems from repricing risk, yield curve risk, basis risk, and option risk embedded in financial products, causing earnings and market value fluctuations.
Higher interest rates typically decrease fixed-rate bond prices, increasing volatility and risk exposure for lenders and investors.
Risk implications include potential declines in asset values, increased borrowing costs, and reduced net interest income impacting institutional financial health.
Managing this risk requires understanding rate movements driven by central bank policies, inflation expectations, credit supply-demand, and economic cycles.

Graphical Analysis – Historical Trend of Interest Rate Impact on Asset Values

A Visual Representation of Changes to Interest Rates and Volatility.

Context and Interpretation

This visualization shows both the quarterly U.S. Treasury 1-Year yield levels over time and the calculated 4-quarter rolling annualized volatility of yields.
The first chart illustrates the rising trend in interest rate levels over recent years.
The second chart provides a dynamic measure of bond price volatility through annualized standard deviation of quarterly log returns.
Together they highlight the relationship between interest rates and risk exposure, helping inform forecasting and risk management strategies.
The use of rolling volatility calculated from yield changes offers a statistically sound assessment of interest rate risk.

Source: Board of Governors of the Federal Reserve System (US), Market Yield on U.S. Treasury Securities at 1-Year Constant Maturity, Quoted on an Investment Basis [DGS1], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DGS1, November 14, 2025.

Figure: Interest Rate Levels and Rolling 4-Quarter Volatility (2015-2025)

{
  "$schema": "https://vega.github.io/schema/vega-lite/v6.json",

  "description": "Treasury yields with 4-quarter rolling volatility derived from shared data.",
  "hconcat": [
    {
      "title": "Treasury Yields",
      "width": 300,
      "height": 300,
      "data": {"name": "treasury"},
      "mark": {"type": "line", "point": true},
      "encoding": {
        "x": {"field": "Date", "type": "temporal"},
        "y": {"field": "Yield", "type": "quantitative", "title": "Interest Rate (%)"},
        "color": {"value": "#1f77b4"}
      }
    },

    {
      "title": "Rolling 4-Quarter Volatility",
      "width": 300,
      "height": 300,
      "data": {"name": "treasury"},

      "transform": [
        {
          "calculate": "log(datum.Yield/100 + 1)",
          "as": "logYield"
        },

        {
          "window": [
            {"op": "lag", "field": "logYield", "as": "logYield_lag"}
          ],
          "sort": [{"field": "Date", "order": "ascending"}]
        },

        {
          "calculate": "datum.logYield - datum.logYield_lag",
          "as": "logReturn"
        },

        {
          "window": [
            {"op": "mean", "field": "logReturn", "as": "meanReturn"}
          ],
          "frame": [-3, 0],
          "sort": [{"field": "Date", "order": "ascending"}]
        },

        {
          "calculate": "(datum.logReturn - datum.meanReturn) * (datum.logReturn - datum.meanReturn)",
          "as": "squaredDeviation"
        },

        {
          "window": [
            {"op": "mean", "field": "squaredDeviation", "as": "rollingVariance"}
          ],
          "frame": [-3, 0],
          "sort": [{"field": "Date", "order": "ascending"}]
        },

        {
          "calculate": "sqrt(datum.rollingVariance * 4)",
          "as": "annualizedVolatility"
        }
      ],

      "mark": {"type": "line", "point": true, "strokeDash": [4, 2]},

      "encoding": {
        "x": {"field": "Date", "type": "temporal"},
        "y": {
          "field": "annualizedVolatility",
          "type": "quantitative",
          "title": "Annualized Volatility"
        },
        "color": {"value": "#d62728"}
      }
    }
  ],

  "datasets": {
    "treasury": [
      {"Date": "2015-07-01", "Yield": 0.35},
      {"Date": "2015-10-01", "Yield": 0.47},
      {"Date": "2016-01-01", "Yield": 0.58},
      {"Date": "2016-04-01", "Yield": 0.57},
      {"Date": "2016-07-01", "Yield": 0.56},
      {"Date": "2016-10-01", "Yield": 0.76},
      {"Date": "2017-01-01", "Yield": 0.89},
      {"Date": "2017-04-01", "Yield": 1.13},
      {"Date": "2017-07-01", "Yield": 1.24},
      {"Date": "2017-10-01", "Yield": 1.55},
      {"Date": "2018-01-01", "Yield": 1.94},
      {"Date": "2018-04-01", "Yield": 2.25},
      {"Date": "2018-07-01", "Yield": 2.46},
      {"Date": "2018-10-01", "Yield": 2.67},
      {"Date": "2019-01-01", "Yield": 2.54},
      {"Date": "2019-04-01", "Yield": 2.26},
      {"Date": "2019-07-01", "Yield": 1.85},
      {"Date": "2019-10-01", "Yield": 1.58},
      {"Date": "2020-01-01", "Yield": 1.07},
      {"Date": "2020-04-01", "Yield": 0.17},
      {"Date": "2020-07-01", "Yield": 0.13},
      {"Date": "2020-10-01", "Yield": 0.11},
      {"Date": "2021-01-01", "Yield": 0.08},
      {"Date": "2021-04-01", "Yield": 0.06},
      {"Date": "2021-07-01", "Yield": 0.08},
      {"Date": "2021-10-01", "Yield": 0.20},
      {"Date": "2022-01-01", "Yield": 0.98},
      {"Date": "2022-04-01", "Yield": 2.20},
      {"Date": "2022-07-01", "Yield": 3.40},
      {"Date": "2022-10-01", "Yield": 4.61},
      {"Date": "2023-01-01", "Yield": 4.76},
      {"Date": "2023-04-01", "Yield": 4.95},
      {"Date": "2023-07-01", "Yield": 5.39},
      {"Date": "2023-10-01", "Yield": 5.23},
      {"Date": "2024-01-01", "Yield": 4.90},
      {"Date": "2024-04-01", "Yield": 5.14},
      {"Date": "2024-07-01", "Yield": 4.46},
      {"Date": "2024-10-01", "Yield": 4.25},
      {"Date": "2025-01-01", "Yield": 4.15},
      {"Date": "2025-04-01", "Yield": 4.03},
      {"Date": "2025-07-01", "Yield": 3.88}
    ]
  }
}

Analytical Explanation & Formula – Quantifying Interest Rate Risk Impact

Mathematical Specification for Price Impact of Changes to Interest Rates.

Concept Overview

Interest Rate Risk can be modeled by examining the sensitivity of asset prices to interest rate changes using duration and convexity metrics.
The core formula relates price change to yield changes through duration (first derivative) and convexity (second derivative), providing an approximation of price volatility.
Key parameters include bond price, yield, duration, convexity, and interest rate changes.
The formula assumes small changes in interest rates and helps investors estimate potential losses or gains in varying rate scenarios.

General Formula Representation

The general relationship for price change $ \Delta P $ can be expressed as:

$$ \Delta P \approx -D \times P \times \Delta y + \frac{1}{2} C \times P \times (\Delta y)^2 $$

Where:

$ \Delta P $ = Change in price.
$ P $ = Current price of the bond or asset.
$ D $ = Duration (sensitivity of price to yield change).
$ C $ = Convexity (curvature adjustment to duration).
$ \Delta y $ = Change in yield or interest rate.

This formula approximates the impact of interest rate fluctuations on asset prices, essential for risk management and portfolio valuation.

Analytical Summary & Table – Interest Rate Risk Metrics and Their Interpretation

Duration and Convexity as Drivers for Interest Rate Risk and Its Impact on Price Volatility.

Key Discussion Points

Duration and Convexity are the principal metrics to assess price sensitivity to interest rate changes and estimate potential volatility.
Duration measures the linear price-yield relationship, while convexity accounts for curvature, improving accuracy for larger rate shifts.
This quantitative approach aids institutions in simulating risk scenarios and stress testing their interest rate exposure.
Assumptions include stable market conditions and small yield changes; limitations arise in volatile or illiquid markets.

Illustrative Data Table

Example of bond metrics illustrating sensitivity to interest rate changes.

Bond ID	Price ($)	Duration (Years)	Convexity
Bond A	100	5.2	45
Bond B	95	3.8	32
Bond C	102	6.5	56
Bond D	98	4.1	40

Graphical Analysis – Interest Rate Risk Exposure by Asset Category

A visual representation relevant to Interest Rate Risk and Its Impact on Price Volatility.

Context and Interpretation

This bar chart displays different asset categories with their relative exposure levels to interest rate risk.
Categories with longer durations or fixed rates generally exhibit higher risk exposure.
Recognizing exposure distribution assists in prioritizing risk management efforts and capital allocation.
The visualization underscores the varying sensitivity across asset classes and informs portfolio diversification strategies.

Figure: Interest Rate Risk Exposure by Asset Category

{
  "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
  "width": "container",
  "height": "container",
  "description": "Bar chart showing interest rate risk exposure by asset category.",
  "config": {
    "autosize": {"type": "fit", "resize": false, "contains": "content"}
  },

  "data": {
    "values": [
      {"Category": "Government Bonds", "Exposure": 85},
      {"Category": "Corporate Bonds", "Exposure": 65},
      {"Category": "Mortgage-backed Securities", "Exposure": 75},
      {"Category": "Variable Rate Loans", "Exposure": 30},
      {"Category": "Cash & Equivalents", "Exposure": 10}
    ]
  },

  "transform": [
    {
      "calculate": "split(datum.Category, ' ')",
      "as": "CategoryLines"
    }
  ],

  "mark": "bar",

  "encoding": {
    "x": {
      "field": "CategoryLines",
      "type": "nominal",
      "title": "Asset Category",
      "axis": {
        "labelAngle": -45,
        "labelAlign": "right",
        "labelBaseline": "top",
        "labelOffset": -10,
        "labelFontSize": 10
      }
    },
    "y": {
      "field": "Exposure",
      "type": "quantitative",
      "axis": {"title": "Exposure Level"}
    },

    "color": {
      "field": "Category",
      "type": "nominal",
      "title": "Asset Category",
      "legend":null
    }
  }
}

Conclusion

Summary and Key Takeaways.

Interest Rate Risk significantly influences price volatility of fixed-income assets and affects financial institution earnings and capital.
Understanding risk drivers and quantifying sensitivity via duration and convexity enable better risk management and decision-making.
Future scenarios and stress testing remain crucial for anticipating impacts under varying rate environments.
Recommendations include continuous monitoring, diversified portfolios, and employing dynamic hedging strategies to mitigate adverse effects.

← Back to Insights List

Risk Knowledge Insights

Explore the details behind: Interest Rate Risk and Its Impact on Price Volatility

Interest Rate Risk and Its Impact on Price Volatility

Introduction Slide – Understanding Interest Rate Risk and Its Effect on Price Volatility

Overview

Key Discussion Points – Drivers and Impact of Interest Rate Risk on Price Volatility

Main Points

Graphical Analysis – Historical Trend of Interest Rate Impact on Asset Values

Context and Interpretation

Analytical Explanation & Formula – Quantifying Interest Rate Risk Impact

Concept Overview

General Formula Representation

Analytical Summary & Table – Interest Rate Risk Metrics and Their Interpretation

Key Discussion Points

Illustrative Data Table

Graphical Analysis – Interest Rate Risk Exposure by Asset Category

Context and Interpretation

Conclusion