Macaulay Duration Modified Duration Average Maturity in Debt Funds

Using the Modified Duration information of a Debt Fund, you can understand the Fund Manager’s view regarding future interest rate movements.

  1. In certain fixed income market, such as US government bonds and US mortgage-backed securities markets, the price is quoted in 1/32nds.
  2. While the first approach is the more theoretically correct approach, it is harder to implement in practice.
  3. This slight “upside capture, downside protection” is what convexity accounts for.
  4. There are other variations of dollar duration that market participants tend to use.
  5. The Macaulay duration calculates the weighted average time before a bondholder would receive the bond’s cash flows.

An investor must hold the bond for 1.915 years for the present value of cash flows received to exactly offset the price paid. In the above table, you can see that both of these schemes have posted significantly high returns during periods when RBI has decreased Interest Rates. This strategy can deliver significantly high returns for the investor if a fall in Interest Rates is predicted accurately. You might also have noticed that the opposite happened when RBI increased Interest Rates i.e. both the schemes underperformed. This is due to their higher Interest Rate Sensitivity and the inverse relationship between Bond Prices and Interest Rates, i.e., an increase in Interest Rates leading to lower Bond Prices.

Macaulay duration is the weighted average of the time to receive the cash flows from a bond. Macaulay duration tells the weighted average time that a bond needs to be held so that the total present value of the cash flows received macaulay duration and modified duration is equal to the current market price paid for the bond. This equation approximates the slope of a line tangent to the price-yield curve by calculating price when yield decreases PV− and price when yield increases PV+.

In summary, Macauley duration is a weighted average maturity of cash flows (measured in units of time) and is useful in portfolio immunization where a portfolio of bonds is used to fund a known liability. Modified duration is a price sensitivity measure and is the percentage change in price for a unit change in yield. Modified duration is more commonly used than Macauley duration and is a tool that provides an approximate measure of how a bond price will change given a modest change in yield. For larger changes in yield, both the modified duration and convexity are used to better approximate how a bond price will change for a given change in yield.

Each of the bars represents interest cash flows, or coupons, and a final cash flow consisting of the principal and the final interest payment. A fixed income security with a greater duration indicates a higher sensitivity to interest rates and thus, the greater the interest rate risk it has. And as the price of most fixed income securities have an inverse relationship with yields, a security with a greater duration will have more interest rate risk than a security with a shorter duration.

Macaulay Duration: Definition, Formula, Example, and How It Works

It considers the time value of money and the present value of future cash flows, helping investors manage risk-return trade-offs effectively. The entire sum of these discounted cash flows is then divided by the current price of the bond to arrive at the Macaulay Duration. The formula accounts for the time value of money by incorporating the periodic yield in the discounting process. Modified duration is mathematically the derivative of the price of the bond with respect to its yield (or interest rates). A modified duration of 1.89 means that for every 1% change in yield, the price of the bond changes by -1.89%.

Hence, if interest rates are expected to rise, an investor may prefer bonds with shorter Macaulay Durations to limit price volatility. Effective Duration takes into consideration the potential changes in cash flows that result from changes in interest rates. Macaulay Duration quantifies this inverse relationship and helps investors understand how much a bond’s price will change with a change in interest rates.

But it has cash flows out to 10 years and thus will be sensitive to 10-year yields. If we want to measure sensitivity to parts of the yield curve, we need to consider key rate durations. Macaulay duration and modified duration are chiefly used to calculate the durations of bonds. The Macaulay duration calculates the weighted average time before a bondholder would receive the bond’s cash flows. Conversely, modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity.

Average Maturity’s Impact on Volatility in Debt Funds

Macaulay duration is frequently used by portfolio managers who use an immunization strategy. As an example, a $1,000 bond that can be redeemed by the holder at par at any time before the bond’s maturity (i.e. an American put option). No matter how high interest rates become, the price of the bond will never go below $1,000 (ignoring counterparty risk).

What Modified Duration Can Tell You

An easy way to think of convexity is that convexity is the rate of change of duration with yield, and accounts for the fact that as the yield decreases, the slope of the price – yield curve, and duration, will increase. Similarly, as the yield increases, the slope of the curve will decrease, as will the duration. Convexity is a measure of the amount of “whip” in the bond’s price yield curve (see above) and is so named because of the convex shape of the curve.

Average duration

It is often measured per 1 basis point – DV01 is short for “dollar value of an 01” (or 1 basis point). The name BPV (basis point value) or Bloomberg “Risk” is also used, often applied to the dollar change for a $100 notional for 100bp change in yields – giving the same units as duration. PV01 (present value of an 01) is sometimes used, although PV01 more accurately refers to the value of a one dollar or one basis point annuity. There are many types of duration, and all components of a bond, such as its price, coupon, maturity date, and interest rates, are used to calculate duration. Dollar duration measures the change in bond prices for a given change in yield to maturity.

Macaulay Duration vs. Modified Duration: An Overview

It’s the percentage change of a bond’s price based on a one percentage point move in market interest rates. Modified duration is a bond’s price sensitivity to changes in interest rates, which takes the Macaulay duration and adjusts it for the bond’s yield to maturity (YTM). For instance, say you want to calculate the modified Macaulay duration of a 10-year bond with a settlement date on Jan. 1, 2020, a maturity date on Jan. 1, 2030, an annual coupon rate of 5%, and an annual yield to maturity of 7%. Although Macaulay Duration is a valuable indicator for simple bonds, modified or effective durations are more suited to complex bond features and non-parallel shifts in the yield curve. By understanding the concept of Macaulay Duration, investors can better manage the risk and return profile of their bond investments.

So, one way in which you can minimize the impact of rising Interest Rates on Your Debt Portfolio is to increase your investments in Debt Funds with low Average Maturity. This way, using the relationship between Average Maturity and Interest Rate Sensitivity, you can determine the best way to actively manage your Debt Investments to balance the overall risk and return in your portfolio. Dollar duration measures the dollar change in a bond’s value to a change in the market interest rate, providing a straightforward dollar-amount computation given a 1% change in rates. The modified duration of a bond is an adjusted version of the Macaulay duration and both methods are used to calculate the changes in a bond’s duration and price for each percentage change in the yield to maturity. Macaulay duration equals the time to receipt of bond cash flows weighted at the proportion of the present value of the relevant cash flow to the bond’s full price.

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