Macaulay Duration

This video discusses the concept of Macaulay Duration. The video uses a comprehensive example to demonstrate how Macaulay Duration is calculated, and it explains how Macaulay Duration is used to compare the interest rate risk of different bonds.
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[@bhall2323]

“The definition of genius is taking the complex and making it simple.” - Albert Einstein

[@MrYevin]

Amazing how a 3 year old video explains exponentially better than my professor! Thanks ♥️

[@alexkladny4651]

Same

[@Tigeressss0051]

WTF dude same WTF my teach sucks

[@emaN-ei8ny]

Same here but 7 years

[@michaellai6619]

“Exponentially better” lmfao

[@lisama2538]

@@emaN-ei8ny same

[@phatz2494]

The awkward moment when your university book cannot explain the concept as quickly as this video does...

[@carolinachavezlopez8820]

Thank you, been trying to understand the whole concept and your video helped me a lot (more than my own lecturer at uni), :)

[@monezbassard4092]

Carolina chavez loggwZ` a `pez

[@justinwr092]

same

[@UltimateOnionSupream]

I am glad I am not the only one

[@Manboy007]

you didnt explain why you multiplied the pv of cash flow by the time period. what is the purpose for that? why does it have to be done?

[@davidtalarico5932]

How did you get 834.55?

[@potato-cc7249]

Thanks for the video. I've been contemplating on the "time-weighted' PV for so long as how come some thing is weighted by A when it is not divided by the sum of A....after your video somehow I figured out and share it here: it actually is a PV-WEIGHTED time Duration solves the question "for every dollar of PV, how many years does it take to receive?" for PV1 it takes 1 year, for PV2 it takes 2 year....then sum them up and divided by the sum of PV, it goes to the conclusion. the hard part of this concept is that "xx-weighted" has always been integers rather than continuous numbers.

[@poohjh0515]

I have been confused with the time-weighted part of MC duration. Your explanation is excellent. Thanks.

[@ВалерийЦарёв-ъ8ш]

Wow, thanks for your comment. I couldn't understand the meaning of "time-weighted" and you finally made it clear for me.

[@user-kg1od9es5d]

Let me make it simpler fpr you. We are interested in present value -correct? Ok. So the further out we go we need to weight it. Eg 1 year out -> weight the PV by a factor of 1. 5 years out? Weight the Pv by a factor of 5. You must do this!! Or the average won’t make sense. The numbers are not of equal magnitude - they are weighted!! By weighing them we can put them in the same unit for comparison of PV - that’s why we divide by the sum of PV to get the duration in years.

[@user-kg1od9es5d]

Also you need to remember - cash flows accumulate rapidly at the tail end - hence why the heaviest weight is at the end. Another way to look at it - weights are added in relation to the cash flows contribution to the total PV of cf. eg t = 1 contributes a lot less to the sum of PV CF compared to t+5. If we don’t adjust for weights, we are framing the data wrong.

[@uditvashishth311]

So the summary is : Higher the duration, more will be the volatility eventually riskier will be the bond. You explained it so smoothly man.🔥 And you are even apologizing for rounding off 😌 (You have just earned respect)

[@Edspira]

Thank you!

[@thetheoryofinterest7051]

Hate to say this, but Duration is so, so, SO much more intuitive if you understand calculus 1. All we're basically doing is essentially taking the relative rate of change of price with respect interest... Done. :)

[@gracebarwe1474]

You made this so simple to understand. I love it, thank you life saver

[@zhideliang]

The thing with Duration is it’s easy to talk about what it means, what it does, and the implications, but it’s rather difficult to explain the process of computing the duration. After summing all the time weighted cashflows, we get a figure with a unit of “years” , then we start telling people what this period means. But it is not so obvious why the process leads to this conclusion ...

[@dakotakirby4112]

You've made my entire life easier with these videos! Thank you!

[@juliezhu7508]

You explained it so clearly and made this concept so easy to understand. I just had an eureka moment after watching your short video. Thank you so much, Sir!

[@lisama2538]

Omg you saved my life for real. There can't be a more intuitive explanation.

[@vmerino04]

Thanks very much for your video! One note about using the term "time-weighted". Since we're finding a weighted average of times to cashflow(years), I was able to understand it more clearly by thinking about time being multiplied by a weight. In other words, the weight is the PVi/V fraction. That weight is applied to t. Consider that if all the weights were the same.. then it would be a regular average 1+2+3+4+5 / 5 = 3. But since this is a weighted average where each year is weighted differently, the duration average ends up higher. The math ends up being the same.. so this is just a different way to think about it. Thanks again for the video!

[@evantighe696]

Don't get me wrong, my finance & markets professor is an immensely clever guy, but a lot of his stuff goes straight over my head. Being able to see it written out with a clear example given helps give me the building blocks that I was lacking. Thank you so much!

[@larshenrikSG]

Surely it should be cash flow weighted time and not time weighted - there is no total time concept in the denominator. Present value of all cash flows should equal the price if the bond is priced at fair value.

[@quesy227]

45minutes class in 7 minutes.. Apparently my professor has no idea what he was talking about... thank you so much.

[@Edspira]

No problem!

[@DC-Academy]

Why do we multiply with the no of years in numerator? Doesn't it increases the value of cash flows??

[@kleenx73]

I've thought that too. To me, I don't think "time-weighted" is an appropriate description here. To me it seems like, reverse time weighted. Any one else have a good explanation for this?

[@potato-cc7249]

I've been contemplating on the "time-weighted' PV for so long as how come some thing is weighted by A when it is not divided by the sum of A.... it actually is a PV-WEIGHTED time Duration solves the question "for every dollar of PV, how many years does it take to receive?" for PV1 it takes 1 year, for PV2 it takes 2 year....then sum them up and divided by the sum of PV, it goes to the conclusion. the hard part of this concept is that "xx-weighted" has always been integers rather than continuous numbers.

[@csdcsdcsd-]

this is very useful and I have gained a much better understanding of the concept, however, I do have a question. Is there any way of shortcutting this process on say a financial calculator? If under time pressure and the bond has 18 years to maturity for example?

[@andrewgrady1]

Anyone know how to get the PV in year 5 of $834.55? I’ve got $33.54 = 1.045 = $32.10*5 = $160.48. Then I can’t get to the PV of cash flow number in year 5…

[@Aesthetics604]

Literally sat here for an hour trying to figure it out. But there's another way to calculate that made sense for that. Coupon/(Current int. rate^n) current rate here is 4.5%. n=what number of payment you're on. So, for the final $1040 the calculation is: $1040/(1.045^5) = $834.55

[@andrewgrady1]

@@Aesthetics604 Thank you!

[@akashkalyana8295]

This was awesome i didn't even get bored:D

[@Edspira]

Excellent!

[@tausal1]

Great explanation! Thank you so much.

[@Edspira]

No problem. Glad you found the video helpful!

[@devdattanm2721]

Thanks man

[@Edspira]

No problem!

[@BPBC6624]

This is great but what about problems that have much more than 5 cash flows, where you would have to actually take the sum instead of doing the calculations all by hand?

[@raffi3o3]

use a finance calculator such as the TI BAII

[@thebatman8895]

Thank your for your easy to understand video. I have spent about 3 hours trying to figure this out in my textbook. Your 7 minute video made this so clear to me. Wish I had watched this first. Would have saved me a lot of time and mental energy.

[@GGG-527]

Does that mean that if there is one per cent increase in bond rate in the market, there is 4.3 per cent decline in that bond?

[@FragmotionArts]

Thank you so much for that video! Professor sent us out to figure out the formula of the Duration only by the vague definition of it and your video makes it so easy to understand!

[@rashvinsingh386]

This is amazing! Thank you so much for this! So much better than the uni professors!

[@husnuatakantuglu6193]

It is so good that it made me write a youtube comment for the first time. Great work, thanks a lot.

[@thisisnirab]

Thank you. But why do we multiply it by time period when we do PV of time weighted cash flow?

[@lordlopikong6940]

Is there a shortcut for really high maturities? Like for example a 16 year simi annual one?

[@adilasyahzanni5291]

can someone tell me how we get that 978.05 and 4523.61 please?? thanks

[@infinnityentretenimento3071]

i'd like to understand some part of the sum. How did you reach the 834,55 value in the 5 year? what sum did you use to discount the cash flows ?? how does is this calculation???

[@h.d.2630]

+infinnity entretenimento The equation is payment/[(1+rate)^n] The last payment is much larger than the others because you have to add the principal to the last payment. Instead of just getting the $40 coupon, you'll also get the $1000 face value. The calculation is $1040/1.045^5 To discount the cash flows with only the coupon payment, you do $40/1.045^(n), where n is the number of the periodic payment (yr 1 would be 1.045^1, yr 2 is 1.045^2, etc). Hope that makes sense!

[@Tiberius_Gracchus]

This man is a god send. I'm in a top rated MBA program and I'm learning more from a smart guy online with a good heart than an expensive professor. Thank you so much.

[@Mzzcurlyhead]

Agree. I feel like I'm getting my MBA from KZbin University

[@seith5606]

Hi. Can someone tell me how to get the 834.55 under pv of cash flow

[@bemineni]

Is the market rate of interest the current Fed interest rate?

[@andrewstoehr]

Brilliant. This and the Modified Duration video are the only ones of yours I've watched, and you hit both out of the park. Thanks for the attention to detail, excellent work!

[@Edspira]

I really appreciate you saying that Andrew, thank you!

[@AlexB-gk1no]

Am I the only one listening to these lessons thinking Greg from Succession is teaching the lesson?

[@christopherbarrett9900]

Thank you for the clear explanation!

[@usmanzahid3711]

Thanks for easing my life

[@chikezieezenna1629]

Wow, so simplifeid. many thanks

[@makhosimoses7434]

I didn’t understand how you got those last values for the 5th year

[@thatomashopha]

thank you so much: now i'm ready for tomorrow's exam :)

[@dieterdelaet9760]

This man explains the theory that is honestly rather boring and makes it not only easy to comprehend but also gives a very interesting way to look at it which makes these videos priceless for everyone on the internet

[@Edspira]

Thank you!

[@elliotklein4412]

can someone please tell me where $834.55 came from?

[@minecraftoniansminecraft3584]

Anyone here for Debt Market Assignment??

[@marcelllnunes1]

Way easier to understand with this video! Ty

[@kristianpolic9188]

Thanks a lot 👍

[@Edspira]

You're welcome!

[@ILikeGuns24]

how is this so easy but professor makes it look so hard smh

[@Alpakaflakka]

So helpful. Thank you so much for the video. Definitely better than my prof's lecture. Please update more videos!

[@nickname3900]

Are you the investopedia guy?

[@jaironcm91]

Thanks so much. I completely understand it. You're a great professor!

[@praj9498]

Why do we multiply it with years ?

[@6alisk]

Thanks for the videos Khan

[@mindyyyyyp.3480]

This helped me a lot when I couldn't understand the CFA text lol

[@Edspira]

Good luck on the exam!

[@mindyyyyyp.3480]

@@Edspira thank you so much!

[@sumeetkadam8362]

Thanks

[@Edspira]

Welcome

[@Nick-yn2uz]

Quick question: If I see that an investment grade corporate bond has a duration of 6, I understand that a 1% move in rates results in -6% in the bond price, but WHAT RATES ARE WE TRACKING? The 10 Yr treasury? 5 year treasury? Thank you!!

[@connorgioiafigliu]

Thank you!

[@zhideliang]

If you take any single year of weighted cashflow out, and ask people “what does this mean?”, I doubt any one can give you a very satisfactory answer.

[@6alisk]

Khan has to have a 180 IQ lol

[@heysupremee3883]

Good morning! Very nice video, very clear. I have question, what happens to duration if there's negative interest rate?

[@claude77573]

Edsoura has a brilliant way of explaining these concepts clearly and completely. Amazing. I wish he could do a series on calculus, but I guess that is getting too far afield.

[@imperialwarhawk123abc5]

I have been trying to refresh my knowledge of bonds. Thanks for the video.

[@br4ndyaw4l]

kinda confused, the practice question that I am trying to do currently doesn't have a market interest rate

[@conraddenzer5077]

You're a god

[@harmankardon478]

excellent content as always!

[@Edspira]

Thank you my friend!

[@yanxiangli4253]

The graphic is always better than the text. Thank you for this fantastic video.

[@ekowannan8891]

Thank you…this explanation is way better !

[@SolutionsWithin]

Thank you. Very helpful : )

[@sanikakhatu5894]

Thank you

[@yiweijia543]

Thank you for the video. To calculate the Macaulay D, the discount rate we use is the continuously compounded yield.

[@atulkumarjangade4036]

Amazing Video. Thank you so much.

[@weibinli2141]

You can actually use annuities if you are studying for financial mathematics for the actuary exam

[@Zero.freingetei]

K1

[@paul5324]

Isn't Macaulay Duration based on force of interest?

[@alecvan7143]

Great video :)

[@Edspira]

Glad you enjoyed it

[@niteshsonar9458]

Why we give time weight to cash flows

[@argenturatbek787]

Thank you!

[@Edspira]

You're welcome!

[@brandonhall6471]

you make great videos

[@jakaisherriff8060]

Absolutely fantastic

[@ryrylove7]

Very helpful video and well explained!

[@davidremilio7449]

Lmao I came here from discord 😂😂

[@dckeitshokile3390]

Now I duly understand. Thanx. D...

[@rupaalsingh4047]

Prof... Wud the time weighted maturity calculation change if say the bond paid semi annual coupon... I mean wud the time weighted factor then be double for each period as compared with an annual coupon paying bond.

[@katiehendrixson]

Yes, your MacD would be a little shorter, because you're getting those cash flows sooner.

[@chengqian6406]

very clear, thank you !

[@yasaswisriram1285]

Wonderful video. Thank you for your videos. Keep up the good work. You helped me a lot.

[@devez7]

in an exam instead of current market rate of interest i was given yield to maturity. whats the process i should have followed? i did exectly the same thing as in the video.. was it correct?

[@Edspira]

Yes, a bond's market rate can also be called "yield to maturity" or "effective rate of return". Good Job!

[@bhargavvenn]

What an amazing video. Thank you so much

[@reazulkabir6890]

thank you

[@wordlifesanchit]

wonderfully explained..!! thank you so much for this video.

[@sanashruf]

Thank you for the video. It was a bit confusing though. For year 2, discounting we use year 1's discounted cash flow not $40. Then we get $36.63.

[@ifungabuserik6228]

how do you find the $40 cash flow figure?

[@fasihasukhram2389]

@@ifungabuserik6228 its the annual coupon payments for the bond: 1000 x 0.04 = $40

[@chrisborgman9155]

great videos!

[@Edspira]

Thanks!

[@orkhanhasanov1922]

Thank you!

[@minsookang2850]

Thank you very much sir

[@sghantode]

Thank u sooo much.. helpful..

[@DynastyJr]

Can you explain the PV of cash flow for the last period?

[@MrYevin]

(Face value+coupon)/ (1+r)^5 Too late? :P

[@akumarkumar5409]

Excellent

[@marianandrews4490]

how did you get 1,040 on the last year?

[@surgalips9]

You get the FV of the bond back + the coupon payment

[@DuhComputerGuy]

If you're looking for a faster solution, D=((1+r)/r)-((1+r+(N(c-r)))/(c((1+r)^n -1)+r)) where, r = mkt rate (in percent) c = coupon rate (in percent) n = duration in years