What is Modified Duration?

Key Takeaways

• Because duration tells nothing about a bond’s or bond strategy’s credit quality, duration is not a complete measure of bond risk. 

• Bonds with higher durations are more volatile, price-wise, than bonds with lower durations.

• While most often used with bonds, modified duration is also utilized with preferred stocks, mortgage-backed securities, and other financial instruments that are directly affected by interest rate changes.

Calculating risk is at the heart of all investing. As such, investors often avail themselves of formulas aimed at helping them do just that. One such formula is called modified duration, which can help investors judge risk based on changing interest rates. But just what is modified duration? Here is that and more.  

What is Modified Duration?

As interest rates fall, the prices of some securities go up. And the opposite is also true. As such, modified duration is a formula that expresses the measurable change in a security’s reaction to an interest rate change. In other words, the formula is used to establish what impact a 1% (100-basis point) interest rate change will have on a bond’s price.

Bond investors zero in on modified duration because it helps them gauge the effect of interest rate fluctuations on their investment. In turn, this can help them determine their bond’s modified duration so that they can better decide whether to sell or hold, based on the rate changes. 

While most often used with bonds, modified duration is also utilized with preferred stocks, mortgage-backed securities, and other financial instruments that are directly affected by interest rate changes. Pension funds and insurance companies frequently use the formula as well.

It is important to note that modified duration aligns with the concept that bond prices and interest rates track in opposite directions: lower interest rates raise bond prices, and vice-versa.

How Do You Calculate Modified Duration?

Modified duration extends from the Macaulay duration, a metric that is the weighted average term to maturity of a bond’s cash flows. Another way to say that is, the Macaulay duration is the weighted average number of years that a position must be maintained in the bond until the current value of the bond’s cash flows is the same as the sum paid for the bond. The weight of each cash flow is found by dividing the cash flow’s current value by the price:

Meanwhile, Modified Duration = Macaulay Duration divided by (1 + YTM/n)

where:

• Macaulay duration equals weighted average term to maturity of the cash flows from a bond.
• YTM equals yield to maturity and “n” equals the number of coupon periods annually.                   

It is important for retail investors, financial advisors, and portfolio managers to know a bond’s average cash-weighted term to maturity when considering investments. That is generally because bonds with higher durations are more volatile, price-wise, than bonds with lower durations.

Note that all parts of a bond are used to calculate duration, including its price, maturity date, coupon, and interest rates.

Here are some duration principles to remember:

• The bond becomes more volatile as maturity and duration increase.
• The bond becomes less volatile as a bond’s coupon increases and its duration decreases.
• The bond’s vulnerability to more interest rate hikes goes down as interest rates increase and duration decreases.   

Modified Duration Example

Here is an example of a modified duration in action. Say a $1,000 bond matures in three years and pays a 10% coupon, and interest rates are at 5%. The bond would have a market price of $1,136.16.

Market price = $100 + $100 + $1,100

                            ——-     ——-    ——-

                                                   2           3

                              1.05       1.05      1.05

                         =   $95.24 + $90.70 + $950.22

                         = $1,136.16

Then, employing the Macaulay duration formula, the duration is calculated as follows:

Macaulay duration = ($95.24 x 1)

                                                 ———

                                              $1,136.16

                                       + ($90.70 x 2)

                                                  ———

                                                $1,136.16

                                        + (950.22 x 3)

                                                  ———

                                                $1,136.16

= 2.753

The result indicates that it would take 2.753 years to recoup the bond’s true cost. To get the modified duration, the investor should divide the Macaulay duration by 1 + (yield-to-maturity/number of coupon periods per year). With the above example, the calculation would come out to 2.62%, or 2.753/ (1.05/1). In other words, each time the interest rate moves 1%, the bond here would inversely move in price by some 2.62%.

Pros and Cons of Modified Duration

All investment formulas, even the ones most commonly used, have their benefits and drawbacks. Modified duration is no exception.

Pros:

• The investor learns their bond’s duration, which is very important as bond price volatility is directly related to bond duration.
• The formula can help the investor better plan a future course of investment.
• Modified duration help with risk management. The portfolio’s average duration can be adjusted as the interest rate outlook changes.
• A fund’s average duration reveals how sensitive it is to market interest rates.

Cons:

• Duration is not a complete measure of bond risk. For instance, duration tells nothing about a bond’s or bond strategy’s credit quality.
• The average duration could change as the bonds mature and interest rates change.
• Modified duration is relatively complicated due to the Macaulay duration calculation. 

Is Modified Duration Relevant in Private Markets?

Yes, modified duration can be used in some private markets such as income-producing real estate, since these kinds of properties are generally subject to interest rate risk. In general, real estate remains popular as what is called an “alternative” investment. This category of assets – basically comprised of any securities other than stocks and bonds — is less volatile due to its low correlation to public markets.  

Take Yieldstreet’s offerings, for example. The alternative investment platform, which offers passive-income opportunities across a wide range of asset classes, has a thriving Growth & Income real estate investment trust fund that invests equity in commercial properties in key markets throughout the nation. Minimums are as low as $10,000.

A mix of portfolio assets also serves to diversify portfolio holdings, which can mitigate overall risk and help protect against inflation. In fact, over the long term, financial planners widely agree that diversification is necessary to investment success.   

Alternative investments can be a good way to help accomplish this. Traditional portfolio asset allocation envisages a 60% public stock and 40% fixed income allocation. However, a more balanced 60/20/20 or 50/30/20 split, incorporating alternative assets, may make a portfolio less sensitive to public market short-term swings. 

Real estate, private equity, venture capital, digital assets, precious metals and collectibles are among the asset classes deemed “alternative investments.” Broadly speaking, such investments tend to be less connected to public equity, and thus offer potential for diversification. Of course, like traditional investments, it is important to remember that alternatives also entail a degree of risk. 

In some cases, this risk can be greater than that of traditional investments.

This is why these asset classes were traditionally accessible only to an exclusive base of wealthy individuals and institutional investors buying in at very high minimums — often between $500,000 and $1 million.  These people were considered to be more capable of weathering losses of that magnitude, should the investments underperform.

However, Yieldstreet has opened a number of carefully curated alternative investment strategies to all investors. While the risk is still there, the company offers help in capitalizing on areas such as real estate, legal finance, art finance and structured notes — as well as a wide range of other unique alternative investments. 

Learn more about the ways Yieldstreet can help diversify and grow portfolios.

Summary

By using modified duration, investors can gauge a bond’s sensitivity to interest rates. While the formula has limitations, it can be helpful since bonds generally are more complicated than stocks. It can also help investors decide whether to sell or hold, and even inform future investment strategies.

Note that modified duration can also be used in alternative investments such as real estate, which are not subject to stock market volatility.