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Quick question, isn't modified duration what tells you how the price of a bond reacts to changes in interest rates while duration is the number of years for a bond to repay the investor?
Your first statement is correct - it’s modified duration, not Macaulay duration, that’s used in estimating price changes. In today’s low interest rate environment (compared to the early 80’s for example), it doesn’t matter as much if you incorrectly use Macaulay rather than modified, but why do it incorrectly? But your second phrase, “duration is the number of years for a bond to repay the investor” is just flat out wrong. (It’s true only for zero coupon bonds.) For example, in this illustration, are you suggesting that the investor has his money back at 2.75 years? That’s obviously not correct. Another incorrect version you’ll hear is that duration is the time it takes to recoup half the present value. Also demonstrably wrong, but often repeated. And it bugs me that his whiteboard example has Macaulay misspelled!
I really enjoyed a discussion of bonds that develops it beyond "if interest rates go up, the price of the bond will go down and vice versa". Thank you!
Well explained.Thanks so much. Personally I think they could have used a better word than "Bond duration" for this. it doesn't make much intuitive sense why the word duration will be used for such a sensitivity calculation.
Glad it was helpful! It is also a measure of duration of time outstanding until you expect to get the payments for the bond so I think that is why they called it duration
You are combining two measurements of duration. Macauley is a measurement of time in which, for example, the appreciation gain of the bond due to a decrease in interest rates, is completely off set by the re-investment risk assumed by YTM. YTM assumes that the coupon payments can be re-invested at the YTM, when rates drop, the coupon payments must be reinvested at a lesser rate, this lowers overall YTM. At the same time, the bond appreciates due to the interest rate decrease - raising YTM. The point in time in which these two values are completely off-setting is Macauley Duration. Modified duration is the sensitivity change to bond prices with a change in interest rates.
Hello, this video is a simplified explanation of duration! The explanation you provided conflates a few distinct financial concepts. Macaulay Duration measures the time it takes to recover a bond's cost through its cash flows, not the specific interaction between price appreciation and reinvestment risk that you've described. Modified Duration, on the other hand, accurately captures a bond's price sensitivity to interest rate changes, separate from the concept of Yield to Maturity (YTM), which deals with the total expected return assuming all payments are reinvested at the YTM rate. For anyone looking for an accurate and nuanced video on the differences between macaulay, modified and effective duration, you can find that here: ruclips.net/video/2tXjJR1W0YU/видео.html
Great video. Loved the explanation of the friend owing you money. Would you be able to explain intuitively why bonds with lower yields have higher durations?
Yes, it is because the lower the yield, the lower the coupon, which means you will be getting your money back later on. For example, a zero yield bond will pay no coupons and all of the money will be paid back at the very end. So with lower yields, it takes longer time (or a higher duration of time) to get the money back from the loan
@@RyanOConnellCFA Hey, thank you for the response. Do you have a video example using semi-annuals? Or is the calculation the same? I have seen it done a couple different ways with regards to the discount factors exponent ...some use 1 2 3 4 5 6...while some use 1, 1.5, 2, 2.5, etc. I noticed the results are different. (I maybe calculating it wrong)
@@retro8919Technically the duration formula is denominated in “periods” that normally correspond to how frequently the rate is compounded. In the US, we normally use semi-annual discounting, and in the duration formula you use the “period” as the number that goes into the formula. The first coupon in 6 months is “1”, the second coupon at the end of the year is “2” etc. Then, the duration calculation results in the number of “periods” not years, and you have to halve it to put it into years. This is true for all semi-annually discounted bonds, whether they pay coupons semiannually or not. The duration calculation has to match the periodicity of the yield calculation.
I get how a bond duration tells you its price sensitivity in connection to a change in market interest rates. Doesn't Duration also tell you how long it takes for the investor to get their money back on their investment? If so, what would the 2.75 mean in terms of that?
Yes, you're correct that bond duration can also be interpreted as the length of time it takes an investor to recoup their investment in a bond. However, it's important to note that it's not simply a matter of waiting 2.75 years in the case of a bond with a duration of 2.75. Rather, duration in this sense is a weighted average of the present value of a bond's cash flows, which include periodic interest payments and the eventual repayment of the bond's face value. What this means is that if a bond has a duration of 2.75, the investor would, in theory, recover their initial investment over the course of 2.75 years, considering both the regular coupon payments and the principal repayment, and adjusted for the time value of money. However, this assumes a constant interest rate environment, which is rarely the case. Changes in market interest rates can significantly impact the actual time it takes to recoup an investment, which is why duration is also used as a measure of a bond's sensitivity to interest rate changes. Remember, lower duration means lower interest rate risk, and vice versa. So, a bond with a 2.75 duration would be less sensitive to interest rate changes compared to a bond with higher duration.
Thanks Mirza! I think this article will answer your question better than I could in a simple comment: etfdb.com/rising-interest-rates/duration-hedging-and-rising-rates/ Does that help?
So if the Macaualy Duration is 2.5Yr. That means it takes us 2.5 yr to recover our initial investment, and also means if rates go up 1% that our price changes by 2.5%? What confuses me is how the concept of years and % is interchangeable
That is not entirely correct. You are thinking about it more like a break even point of a project you'd learn about in corporate finance. It is a weighted average, not a breakeven time period. The percentage change component of what you said is correct however. Just know this is a simplified assumption that doesnt account for convexity
Wouldn't the 2.75 that you calculate at the end be the modified duration, not the Macaulay duration as it is measuring the % change to a 1% change in interest rates and not measuring the time in years??
It is the Macaulay Duration that I calculated but you are correct that the Modified Duration better describes the relationship of how bond prices change with yield. Check out this video that I just published that goes into the nuanced details of Macaulay Duration, Modified Duration, and Effective Duration: ruclips.net/video/2tXjJR1W0YU/видео.html
Thanks for clarifying this. I know understand that Macaulay duration is the years required to receive the fixed cash flows from the bond. Modified duration measures the sensitivity of the bons price to changes in int. Rate.
So, regard Macaulay duration (not ModMacDur) - can it be thought of as the amount of time to receive your initial purchase price back? Essentially the break even amount of time?
Yes. Think like you would with discrete probability: at each time, there's a proportion of the bond's price that occurs at that time. MacDur is then the "expected time" regarding these proportions (i.e. "probabilities").
Hey Erick, I wouldn't necessarily say break even point as you don't make money on every bond (due to an uncertain interest rate environment). It is the weighted average amount of time that you expect the present value cashflows to pay out. Don't worry about the initial price you paid
@@RyanOConnellCFA The part about not worrying about the initial amount paid is not correct. The initial amount paid determines the yield, and the yield is used in the calculation of duration (both Mac and Mod), so you can’t ignore it. It actually is a break even point but it’s a little more complicated to discuss.
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I have watched videos of 30- 60 Mins on Duration and none of those explained the meaning and calculation so easy to understand as yours. Thanks man.
Finally I was able to understand how duration is calculated. Thanks for the clear and well-organized explanation.
Great to hear! My pleasure Bovino
This is the only explanation that I ever understood! It’s bothered me decades that I never understood it. Thanks.
The best explanation ever! literally summarised 2 weeks of uni lecture into 5 mins. Brilliant work!
Thank you so much! It means a lot
Quick question, isn't modified duration what tells you how the price of a bond reacts to changes in interest rates while duration is the number of years for a bond to repay the investor?
Your first statement is correct - it’s modified duration, not Macaulay duration, that’s used in estimating price changes. In today’s low interest rate environment (compared to the early 80’s for example), it doesn’t matter as much if you incorrectly use Macaulay rather than modified, but why do it incorrectly? But your second phrase, “duration is the number of years for a bond to repay the investor” is just flat out wrong. (It’s true only for zero coupon bonds.) For example, in this illustration, are you suggesting that the investor has his money back at 2.75 years? That’s obviously not correct. Another incorrect version you’ll hear is that duration is the time it takes to recoup half the present value. Also demonstrably wrong, but often repeated. And it bugs me that his whiteboard example has Macaulay misspelled!
I like how you breakdown everything, it's a lot easier to understand. ty :)
Glad it was helpful Alyssa! I try to make it as simple as possible
Thanks for the explanation. Really liked your approach in making it easy to understand.
I really enjoyed a discussion of bonds that develops it beyond "if interest rates go up, the price of the bond will go down and vice versa". Thank you!
My pleasure, there is a lot more to it than that!
Thank you! This really helped me for my level 1 CFA study
My pleasure and glad it helped!
Thank you for the explanation, you just solved my problem.
My pleasure and thanks for the feedback Guobo!
At last!!!someone who actually makes sense..thanks mate!!!
Appreciate the feedback Nkosi!
Thank you, this helped me for my capital market theory course.
You're very welcome!
@@RyanOConnellCFA hi do you have videos on option trading strategies like covered calls, protective puts, straddle etc.?
I love you, Ryan! Not in weird way, just a big fan of your teaching😊
Haha thank you! I really appreciate the support 🙏
Thank you soooo much, finally got that part! Wish you all the best!
Glad it helped! Thank you
Well explained.Thanks so much.
Personally I think they could have used a better word than "Bond duration" for this. it doesn't make much intuitive sense why the word duration will be used for such a sensitivity calculation.
Glad it was helpful! It is also a measure of duration of time outstanding until you expect to get the payments for the bond so I think that is why they called it duration
You are combining two measurements of duration.
Macauley is a measurement of time in which, for example, the appreciation gain of the bond due to a decrease in interest rates, is completely off set by the re-investment risk assumed by YTM. YTM assumes that the coupon payments can be re-invested at the YTM, when rates drop, the coupon payments must be reinvested at a lesser rate, this lowers overall YTM. At the same time, the bond appreciates due to the interest rate decrease - raising YTM. The point in time in which these two values are completely off-setting is Macauley Duration.
Modified duration is the sensitivity change to bond prices with a change in interest rates.
Hello, this video is a simplified explanation of duration! The explanation you provided conflates a few distinct financial concepts. Macaulay Duration measures the time it takes to recover a bond's cost through its cash flows, not the specific interaction between price appreciation and reinvestment risk that you've described. Modified Duration, on the other hand, accurately captures a bond's price sensitivity to interest rate changes, separate from the concept of Yield to Maturity (YTM), which deals with the total expected return assuming all payments are reinvested at the YTM rate.
For anyone looking for an accurate and nuanced video on the differences between macaulay, modified and effective duration, you can find that here: ruclips.net/video/2tXjJR1W0YU/видео.html
Great video. Loved the explanation of the friend owing you money. Would you be able to explain intuitively why bonds with lower yields have higher durations?
Yes, it is because the lower the yield, the lower the coupon, which means you will be getting your money back later on. For example, a zero yield bond will pay no coupons and all of the money will be paid back at the very end. So with lower yields, it takes longer time (or a higher duration of time) to get the money back from the loan
Great video and done so easy to comprehend. Thank you
My Mahendra! Thanks for the feedback
Finally someone explain it clearly
Appreciate it!
THANKS A LOT...... GOT CLARITY.. VERY USEFUL FOR MY PROFESSIONAL COURSE❤
Glad to hear that!
Easiest way to understand.....thnk a ton
Thank you Priti!
Very short and clear explanation
Glad it was helpful!
I LOVE YOU!! You explain amazingly. Thanks so much for this amazing content!
It is my pleasure Lidia! Thanks for the nice comment
thank you for the explanation, very well explained
Glad it was helpful!
Finally, I understand
Glad to hear!
Great Explanation !
Glad you liked it!
爱你的教程，love from China
Much appreciated!
Good explanation
Thank you!
Thanks a lot for the amazing explaination.
Glad it was helpful!
Thank you ☺️
You’re welcome 😊
Just to be clear, this example would have the bond only paying 1 annual coupon payment right? In reality most bonds pay semi-annual right?
Yes, that is correct. I find it easier to explain by using an annual bond as an example
@@RyanOConnellCFA Hey, thank you for the response. Do you have a video example using semi-annuals? Or is the calculation the same? I have seen it done a couple different ways with regards to the discount factors exponent ...some use 1 2 3 4 5 6...while some use 1, 1.5, 2, 2.5, etc. I noticed the results are different. (I maybe calculating it wrong)
@@retro8919Technically the duration formula is denominated in “periods” that normally correspond to how frequently the rate is compounded. In the US, we normally use semi-annual discounting, and in the duration formula you use the “period” as the number that goes into the formula. The first coupon in 6 months is “1”, the second coupon at the end of the year is “2” etc. Then, the duration calculation results in the number of “periods” not years, and you have to halve it to put it into years. This is true for all semi-annually discounted bonds, whether they pay coupons semiannually or not. The duration calculation has to match the periodicity of the yield calculation.
This is FUCKING AMAZING THANK YOU SO MUCH!
God bless you this is super helpful
Thank you!
I get how a bond duration tells you its price sensitivity in connection to a change in market interest rates. Doesn't Duration also tell you how long it takes for the investor to get their money back on their investment? If so, what would the 2.75 mean in terms of that?
Yes, you're correct that bond duration can also be interpreted as the length of time it takes an investor to recoup their investment in a bond. However, it's important to note that it's not simply a matter of waiting 2.75 years in the case of a bond with a duration of 2.75. Rather, duration in this sense is a weighted average of the present value of a bond's cash flows, which include periodic interest payments and the eventual repayment of the bond's face value.
What this means is that if a bond has a duration of 2.75, the investor would, in theory, recover their initial investment over the course of 2.75 years, considering both the regular coupon payments and the principal repayment, and adjusted for the time value of money.
However, this assumes a constant interest rate environment, which is rarely the case. Changes in market interest rates can significantly impact the actual time it takes to recoup an investment, which is why duration is also used as a measure of a bond's sensitivity to interest rate changes.
Remember, lower duration means lower interest rate risk, and vice versa. So, a bond with a 2.75 duration would be less sensitive to interest rate changes compared to a bond with higher duration.
@@RyanOConnellCFA helps. Thank you 🙏🏼
How can IRS hedge portfolio duration?
Great video btw and you just earned yourself a new subscriber!
Thanks Mirza! I think this article will answer your question better than I could in a simple comment:
etfdb.com/rising-interest-rates/duration-hedging-and-rising-rates/
Does that help?
@@RyanOConnellCFA great video, thanks.
@@robertcesar9752 Much appreciated my friend
Thank you 😭
No problem 😊
太感谢你了！
So if the Macaualy Duration is 2.5Yr. That means it takes us 2.5 yr to recover our initial investment, and also means if rates go up 1% that our price changes by 2.5%? What confuses me is how the concept of years and % is interchangeable
That is not entirely correct. You are thinking about it more like a break even point of a project you'd learn about in corporate finance. It is a weighted average, not a breakeven time period. The percentage change component of what you said is correct however. Just know this is a simplified assumption that doesnt account for convexity
@@RyanOConnellCFA Got it, thank you.
You are the GOAT
Much appreciated!
Wouldn't the 2.75 that you calculate at the end be the modified duration, not the Macaulay duration as it is measuring the % change to a 1% change in interest rates and not measuring the time in years??
It is the Macaulay Duration that I calculated but you are correct that the Modified Duration better describes the relationship of how bond prices change with yield. Check out this video that I just published that goes into the nuanced details of Macaulay Duration, Modified Duration, and Effective Duration: ruclips.net/video/2tXjJR1W0YU/видео.html
it actually is the Macauley duration but the last sentence is wrong in my opinion. The unit of the macaulay duration is years and not unitless..
Thanks for clarifying this. I know understand that Macaulay duration is the years required to receive the fixed cash flows from the bond. Modified duration measures the sensitivity of the bons price to changes in int. Rate.
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Thats great! Glad you enjoyed
The video won’t load
I think this has more to do with your internet connection than the video or RUclips
So, regard Macaulay duration (not ModMacDur) - can it be thought of as the amount of time to receive your initial purchase price back? Essentially the break even amount of time?
Yes. Think like you would with discrete probability: at each time, there's a proportion of the bond's price that occurs at that time. MacDur is then the "expected time" regarding these proportions (i.e. "probabilities").
Hey Erick, I wouldn't necessarily say break even point as you don't make money on every bond (due to an uncertain interest rate environment). It is the weighted average amount of time that you expect the present value cashflows to pay out. Don't worry about the initial price you paid
@@RyanOConnellCFA The part about not worrying about the initial amount paid is not correct. The initial amount paid determines the yield, and the yield is used in the calculation of duration (both Mac and Mod), so you can’t ignore it. It actually is a break even point but it’s a little more complicated to discuss.
Thank you!
You're welcome!