Fixed Income Investments - Duration

Duration is an estimated measure of the price sensitivity of a bond to a change in interest rates. It can be stated as a percentage or in dollar amounts. It can be helpful to "shock" or analyze what will happen to a bond when market rates increase or decrease.

Let's assume that the calculation yields a duration of 6.14, this means that if interest rates change, the value of the bond will change by 6.14%. If there is a 50 basis point change, the value will change by 3.07% and for a 25 basis point change would equal a 1.53% change.

Calculating Duration
The easiest way to calculate duration or the percentage price change is to average the percentage price change coming from an equal increase and decrease in interest rates measured in basis points. To compute duration one needs to develop a valuation model to determine the new prices. The duration value is only as good as the valuation model.

Stone & Co. bonds are selling at 95, yielding 5.25%
Let's assume that yields increase by 25bps, causing the price to decline to 93.
Therefore, the price changes by 2.1%.
Then, take 2.1% and divide it by 25bps equaling a .084% change. This represents a 1 basis points move.

Now let's assume that yields decrease by 25bps, causing the price to increaseto 98. The price change is now 3.06%.
Then, take 3.06% and divide it by 25bps equaling a .1224% change. This represents a 1 basis points move.

As a final step, just average the two percentage price changes for a 1 basis points move in rates.

Here's how the calculation should look:
Duration = (.084 + .1224)/2 = .1032 = price change of 10.32% (.1032*100).

Formula 15.4

Duration = Price if yield decline - Price if yield increase / 2 * (initial price) *change in yield in decimals

As such:
98-93/ 2*95*.0025 = 10.52

Approximate Percentage Price Change of a Bond Given a Change in Duration
Let's continue with the above duration of 10.52. This would equal a percentage price change of 10.52 % for a change of 100 basis points in either direction. If the basis points change were 50, then the percentage price change would be 5.26% (10.52/2). If it were a 25bps change, the value would be 2.63% (10.52 / 4).

Approximate New Price of a Bond Given the Duration and New Yield Level
Let's return once again to working with a duration of 10.52. This time, we'll add a total market value of the Stone & Co bonds of $10,000,000.

Assume that the rates change by 100 bps. This would cause the value of the bonds to change by $ 1,052,000 ($10,000.000 *.1052). This is also known as dollar duration.The price will then range from $11,052,000 to $8,948,000.

If rates increase by 50 basis points, however, the dollar change would be $526,000 giving the bonds a price range of $ 10,526,000 to $ 9,474,000.

Duration and Yield-Curve Risk for a Portfolio of Bonds
Portfolios have different exposures to how the yield curve shifts. These differences represent yield-curve risk. Because a portfolio tends to have different maturities, if there is not a parallel movement of rates or an equal amount of change in the yield curve across all maturities of the yield, the durations for the different maturities will not react in the same manner. Therefore, the simple procedure discussed above concerning duration will not be able to be applied to the entire portfolio, but will have to be applied over the different maturities as well as to the amount of rate changes in those maturities.

International Bonds
Related Articles
  1. Personal Finance

    How To Choose A Financial Advisor

    Many advisors display similar skillsets that can make distinguishing between them difficult. The following guidelines can help you better understand their qualifications and services.
  2. Investing

    Asset Manager Ethics: Investment Process and Actions

    Managers, in developing their investment process, need to determine some “general rules” that make it meaningful. We offer six.
  3. Professionals

    Career Advice: Financial Analyst Vs. Investment Banker

    Read an in-depth comparison about working as a Financial Analyst vs. working as an Investment Banker, two highly prestigious business careers.
  4. Professionals

    Advisors: Which Certifications Are Essential?

    The right advisor credentials can make all the difference, but wading through some 100 certifications can be a challenge. Here's some help.
  5. Investing Basics

    Asset Manager Ethics: Valuation Is A Tricky Business

    Asset managers must accurately represent all of a clients assets in the client portfolio. This can be tricky for unique and hard-to-value assets.
  6. Personal Finance

    Top 10 Most Valuable Sports Teams in 2015

    Cleats, pads and profits: we take a look at the top 10 most valuable sports teams in the world.
  7. Professionals

    Chinese Slowdown Affects Iron Ore Market

    The Chinese economy's ongoing slowdown is having a major impact on iron ore demand.
  8. Personal Finance

    Invest in Costco? First Understand Its Balance Sheet

    A strong balance sheet sets a company apart and boosts investor confidence. How healthy is Costco based on an analysis of its balance sheets from the last two years?
  9. Investing Basics

    Brokers and RIAs: One and the Same?

    Brokers and registered investment advisors have some key differences. Here's what you need to know.
  10. Professionals

    DCF Vs. Comparables: Which One To Use

    DCF and Comparables models are widely used in equity valuation. We explain the pros and cons of each method.
  1. Personal Financial Advisor

    Professionals who help individuals manage their finances by providing ...
  2. CFA Institute

    Formerly known as the Association for Investment Management and ...
  3. Chartered Financial Analyst - CFA

    A professional designation given by the CFA Institute (formerly ...
  4. Security Analyst

    A financial professional who studies various industries and companies, ...
  1. What are the differences between a Chartered Financial Analyst (CFA) and a Certified ...

    The differences between a Chartered Financial Analyst (CFA) and a Certified Financial Planner (CFP) are many, but comes down ... Read Full Answer >>
  2. How do I become a Chartered Financial Analyst (CFA)?

    According to the CFA Institute, a person who holds a CFA charter is not a chartered financial analyst. The CFA Institute ... Read Full Answer >>
  3. What types of positions might a Chartered Financial Analyst (CFA) hold?

    The types of positions that a Chartered Financial Analyst (CFA) is likely to hold include any position that deals with large ... Read Full Answer >>
  4. Who benefits the most from prepaid expenses?

    Prepaid expenses benefit both businesses and individuals. Prepaid expenses are the types of expenses that are bought or paid ... Read Full Answer >>
  5. If I am looking to get an Investment Banking job. What education do employers prefer? ...

    If you are looking specifically for an investment banking position, an MBA may be marginally preferable over the CFA. The ... Read Full Answer >>
  6. Can I still pass the CFA Level I if I do poorly in the ethics section?

    You may still pass the Chartered Financial Analysis (CFA) Level I even if you fare poorly in the ethics section, but don't ... Read Full Answer >>
Hot Definitions
  1. Gross Profit

    A company's total revenue (equivalent to total sales) minus the cost of goods sold. Gross profit is the profit a company ...
  2. Revenue

    The amount of money that a company actually receives during a specific period, including discounts and deductions for returned ...
  3. Normal Profit

    An economic condition occurring when the difference between a firm’s total revenue and total cost is equal to zero.
  4. Operating Cost

    Expenses associated with the maintenance and administration of a business on a day-to-day basis.
  5. Cost Of Funds

    The interest rate paid by financial institutions for the funds that they deploy in their business. The cost of funds is one ...
  6. Cost Accounting

    A type of accounting process that aims to capture a company's costs of production by assessing the input costs of each step ...
Trading Center
You are using adblocking software

Want access to all of Investopedia? Add us to your “whitelist”
so you'll never miss a feature!