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Il Trucco Segreto di Bessent sui BOND a 30 Anni (Ecco Perché Wall Street Sta Tremando) — Transcript

by Marco Lippiello · 5,254 words · 733 segments · language en · Watch on YouTube

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0:00What is happening in the US Treasury
0:03market. Hello everyone, guys, and
0:05welcome to this new video. I have
0:08decided to finally cover bond duration,
0:11since you've been asking me about it
0:14lately after I made a video on American
0:16bonds and what is going on. The first
0:21thing I would like to tell you is that
0:24on September 10th I will be speaking on
0:27the BNP Paribas channel around 9:25 or
0:299:30 in the morning. Secondly, and this
0:34is very important to me, on September
0:3618th, Renegade and I will do a live
0:39stream on memories; I’m 99%sure that
0:41Andrea Cartisano has confirmed it for
0:44me. We will do it on his channel at
0:476:00 PM. Okay. Guys, I am preparing all
0:51the live content, all the slides on
0:53memories. We truly have, look, so much
0:55stuff to talk about. They are very,
0:57very nice; I am making them on Canva
0:59and they are very, very detailed. I
1:02suggest you attend because, let's say,
1:04during this live stream we will also
1:07give a little bit of our view on what
1:09could be, how should I put it, what
1:12could be the end of the cycle or a
1:14recovery and rise for memories. I don't
1:17want to spoil anything for you, come to
1:19the live stream, see you there. So,
1:21let's try to take a moment to focus on
1:23what is happening in the American
1:25markets. The first thing I want to tell
1:29you is, if you remember, we have talked
1:31many times about the fact that yields
1:33tend to incorporate three things, okay?
1:37And I'll show them to you here. When we
1:38look at yields, in this case, you see
1:40on the thirty-year American bond we are
1:42at 5.235. We have growth expectations,
1:47that would be growth expectations plus
1:49inflation expectations plus term
1:51premium, so what does that mean? That
1:54if the economy rises and grows,
1:56therefore if there are positive growth
1:58expectations for the economy,
2:00consequently we must also have positive
2:02growth expectations for inflation,
2:04right? Because if the economy rises,
2:07most likely the price level of goods
2:09and services will also tend to rise.
2:13And then the term premium is obviously
2:15an important slice that concerns that
2:18risk premium the investor wants to
2:20receive for obviously investing longer
2:22over time. So, the longer the maturity,
2:27the more the term premium in theory
2:29should be, let's say, a slice that
2:30should cover a fairly important part
2:32within the yield calculation. So, if we
2:36compare a thirty-year and a ten-year,
2:38know well that there is an important
2:39difference. That said, obviously
2:43geopolitical tensions can also affect,
2:45okay, the term premium, but also the
2:47credibility or lack thereof of the
2:49Federal Reserve with respect to what is
2:52obviously the investors 'perception. So
2:56now we have a scenario that is quite,
2:58shall we say, peculiar, because on one
3:01hand, the U.S. Treasury wants to try to
3:04absorb a good portion of the duration.
3:08You will understand what I mean now. So
3:11they are trying to lower the yields on
3:14the long end of the curve, on the 10,
3:1620, and 30-year notes. How so? By
3:18conducting buybacks. Because we know
3:21that if a bond's price, okay, tends to
3:23increase, so if this is the bond price
3:25and it tends to go up, if these are the
3:28yields, the yields are inversely
3:30proportional and tend to go down. Okay?
3:34So if I have, let's say, a bond that I
3:36buy at 100 and it tends to rise, going
3:38to 101, 102, it very likely means that
3:41interest rates are falling, okay? I
3:44mean, no, it's not very likely, it's
3:45certainly the case. So what does that
3:47mean? That in this historical phase,
3:50Bessent declared that the buyback size
3:53will increase from 2 to 4 billion. Guys
3:57, by "size" we don't mean the totality
4:00of the buyback, also because with 4
4:02billion in U.S. debt you can't do
4:05anything, but it is the "size" per
4:07operation that can be executed, and I
4:10can guarantee you that a 4 billion
4:13buyback per operation on a 30-year bond
4:16makes a huge difference compared to a
4:19buyback you could do on a 10-year note,
4:22okay? or even on a 5-year bond, because
4:26the longer the expiration, so the
4:29maturity, the greater the duration,
4:33okay? It will be quite broad, so let me
4:36give you an example: a modified
4:38duration on a 30-year bond is around 16
4:41years. I will take you through the
4:43calculation now, so stay until the end
4:45of the video because I will do it for
4:46you step by step. Uh, the only thing I
4:49always want to tell you from a, let's
4:51say, macro point of view is that at
4:53this moment we are in a phase where, in
4:55my opinion, the Federal Reserve is in a
4:57phase, as they say in jargon, behind
4:58the curve, right? So behind the curve.
5:02For what reason? Because he gives
5:04absolutely no guidance, he doesn't
5:06anticipate any moves. So what does that
5:09mean? That Kevin Warsh, if he said "I
5:12will look at the trend, I will look at
5:14the data" and the Federal Reserve will
5:16have work to do, that's what he said,
5:18it will have work to do should
5:20inflation rise, it is obvious that you
5:22are telling the market that if and only
5:25if the Federal Reserve sees an
5:26increasing inflation trend, then it
5:28will act. In this case, you are not
5:31ahead of the curve, you are behind the
5:33curve. Actually, guys, more or less in
5:35the G20, in the G20 countries, the
5:37United States and Japan are in the same
5:39phase, and probably only Brazil is a
5:42little bit ahead of the curve. As for
5:44the rest, if you look, well, there's
5:46nothing, let's say, different. Behind
5:50the curve, just to explain it to you,
5:52means that the monetary authorities
5:54have, let's say, allowed inflationary
5:57dynamics to consolidate without
5:58properly and timely tightening
6:00financial conditions. So, the Fed is
6:04being criticized for having missed the
6:06inflation target for 5 years. Okay? In
6:09fact, if you've noticed, Kevin Warsh
6:11says it often, okay? During his
6:14meetings—he's only had three—it
6:16seems it's a recurring phrase, so I
6:18want you to understand that showing the
6:20market a certain independence of the
6:22Fed is definitely an important concept.
6:25Okay? So, right now, I see Kevin Warsh
6:28wanting to show strong credibility to
6:30the market, the independence of the Fed
6:33, and so he has a somewhat more hawkish
6:35tone. However, in fact, he hasn't
6:39mentioned any type of rate hike, and I
6:41still see a September hike as difficult
6:43, if I can give you my take, despite
6:46today's strong labor market data,
6:48especially thanks to—I'm talking
6:50about non-farm payrolls—especially
6:52thanks to the education level, because
6:55out of 162,000 payrolls, over 40,000
6:57came from, let's say, the education
6:59sector because it's a seasonal issue.
7:03It's August; you have to know that in
7:05America schools reopen already towards
7:07the end of August, so it's obvious
7:09there are these hires due to a seasonal
7:10effect. Okay, so let's keep that in
7:13mind too. But then the food sector also
7:16multiplied its hiring by five, so I
7:18must say I was particularly surprised
7:20by today's data. So, what did I want to
7:23tell you? Let's try to look at an
7:24example. So, we now need to understand
7:27what duration is and we need to, look,
7:29wait for me to move a bit higher up.
7:32Here we go. Let's select a—so, guys,
7:34I'm actually going to get a tablet
7:36because otherwise, writing here becomes
7:38complex. So, if we look at duration, it
7:42basically tells us, okay, by how much
7:44the value—I would call it, to make it
7:46simple for you, of a promise—changes.
7:50What do I mean? So, let's try to
7:53imagine that I have to give some money
7:55to a friend. Okay? Keep in mind that in
8:00finance, duration measures the
8:02sensitivity of a bond's price to
8:04changes in interest rates. That means
8:09if I increase rates by 1%, I want to
8:12understand the impact on the price of
8:15my bond. That's what I need to
8:19understand. Ok? So, the further away
8:23the maturity is, like we said before,
8:25if we consider a thirty-year bond, see,
8:2730 years, ok? The greater, excuse me,
8:32the longer the maturity, the higher the
8:33duration will be. This means that,
8:36generally, a 30-year bond undergoes
8:40massive price swings, even if interest
8:44rates move very little. And now we will
8:48try to get to that. Consider this: if
8:51we wanted to give a fairly simple
8:53example, we can use two examples, guys.
8:57So, I was telling you before, we have a
8:59friend who has to pay me back € 100.
9:02All right? I am giving you a really
9:05basic example, a truly simple, simple
9:07example. Imagine he has to give us €
9:09100. It's one thing if he gives them to
9:12me in a year. By Y I mean, ok? To be
9:14brief, because guys, it's not easy
9:16writing on these small boards. two. If
9:19these € 100, instead, a second friend
9:22wanted to give them to me in 30 years,
9:24what value will they have? And this is
9:28where we have to start reasoning,
9:31because in finance you absolutely must
9:33absorb the concept of discounted cash
9:36flows, otherwise, even when we talk in
9:39videos about uh discount rates, WACC,
9:42how we look at terminal value, why it
9:44gets crushed, for what reason? I want
9:48you to follow me, and so I decided to,
9:50uh, let's say, cover this in this video
9:52. It will certainly be a bit longer,
9:55guys, but if you stay focused, I'll
9:57show you it will all be simpler. So,
10:00now I'll erase this and show you
10:02something. The one-year one is
10:03obviously the friend who will give me
10:05the money right away, so let's say I
10:07have no impact. Ok? The 30-year one,
10:10instead, means that I remain locked in,
10:12and in the meantime, obviously, the
10:14market could offer higher returns. Ok?
10:18So the further away my cash flows are,
10:19the greater the duration will be, and
10:21the higher the sensitivity to rates I
10:23will have. Let's do a numerical example
10:27. So guys, if I have a Treasury, ok,
10:32we'll take the 30-year Treasury in this
10:34case, ok? And let's give it a face
10:40value, I'll give you an example, of $
10:42100, all right? Let's say, for example,
10:47the coupon is 5%, let's use simple
10:49numbers. The market return, so in this
10:53market, at this moment the market is
10:55pricing yields, ok? I'll do it here.
10:58Market return. Let's pretend the market
11:03is currently pricing Treasuries at 5%,
11:05see? It prices them at 5.238, but for
11:07the sake of calculation, I'll leave it
11:09at 5. And we said that the maturity, ok
11:13? The maturity is indeed 30 years. Very
11:19well. The essential thing we need for
11:24the calculations is that the coupons,
11:26look, must be semiannual, okay?
11:30Otherwise, we can't perform the
11:33calculations. So, remember that the
11:37duration tells us how far away in time
11:40the money that this bond, in fact, will
11:42have to return to me is. It’s not
11:45enough to say, "No, I will receive the
11:47money in 30 years." No, guys, that's
11:49incorrect; it doesn't work like that
11:50because that is only the final
11:52repayment. In the meantime, we will
11:54receive coupons, and I want to give you
11:56an example. So, for those of you
11:58following along, you might want to
12:00pause here and take these notes down;
12:02I'll erase and move on. So, I want to
12:05show you in a fairly simple way. What
12:08do I receive? I receive two points, $
12:142.50 in 6 months is the first coupon,
12:18right? Because we said the coupons are
12:20semiannual. If I get, I remind you here
12:23, 5%per year, in 6 months I will
12:25receive the first coupon of 2.50
12:27because, well, we pretended the bond
12:29only cost € 100, that I put € 100
12:32into the bond. Okay, very good. Pardon
12:35me, dollars. Then what happens? I get
12:40another 2.50 in a year, so for the
12:43moment, in one year I have received
12:462.50 + 2.50, which makes $ 5, which is
12:495%, okay? Based on 100. Then in a year
12:55and a half I get again, in 1.5 years I
12:58get what? Another $ 2.50, and so on. So
13:04, the duration performs a sort of
13:06weighted average of all these cash
13:07flows. Giving more weight to the flows
13:10that are worth more, obviously, today.
13:13Okay, I'll stop here, I'll erase to
13:16make space. Now we need to learn how to
13:18discount these flows. So, if I have a 5
13:22%annual yield, since we said it pays
13:24semiannually, what does that mean? That
13:28the 5%I mentioned before, divided by 2,
13:31gives me 2.5%every 6 months. Okay? Very
13:39good, so each payment is discounted
13:42every 6 months. So what do we do? We
13:46take a formula that starts with PV,
13:48which indicates the present value, and
13:50we go to see what the current value is,
13:51okay? And in the numerator, we put the
13:55cash flow, the future value. You will
13:57find it in a thousand ways. If you put
13:59"present value formula" into Google,
14:01okay, you'll find a thousand entries in
14:03the denominator, but which in the end
14:04—sorry, in the numerator—which in
14:06the end all lead to the same concept.
14:09So we can also put FV, which stands for
14:13future value, divided by 1 + r
14:16discounted, sorry, let me do it like
14:20this. 1 + here it is r, which is raised
14:28to the n. Okay? Now you need to
14:31consider one thing. If in finance we
14:34want to discount, that is, bring back
14:37to today's value money that I will
14:40receive in 6 months, I have to divide
14:42by 1 plus the discount rate. In this
14:46case, the 6-month discount rate is 2.5.
14:49What is the logical reason? It is the
14:51time value of money. Why? Because a
14:55dollar today—this you really need to
14:57get into your heads—a dollar I get
14:59today is greater, is worth more than a
15:01dollar I will collect tomorrow. This is
15:05exactly the time value we are assigning
15:07to money. So if the bank pays 2.5 every
15:106 months, how much money must I invest
15:13today to have $ 2.50 in 6 months? So
15:18what do I do? I take the PV formula,
15:22which is equal to 2.50/1 + 0.025
15:33because if you remember, in the
15:34denominator we had 1 + r. All of this
15:38is equal to 2.5/1.025 which equals—
15:46I'll tell you—2.43. What does that
15:51mean? If I divide by 1.025, it means
15:54that that payment of $ 2.50, guys, this
15:57one right here, okay? that I will
16:00receive in 6 months, since I cannot use
16:03it today, it's worth a little less in
16:05my pocket, let's say, in my wallet, and
16:07it is worth $ 2.43, because if I had
16:09that money today, I could earn 2.5%on
16:11it. Remember that in finance, the logic
16:15of opportunity cost always applies.
16:18Meaning, if in these 6 months I don't
16:21have the chance to invest, I am losing
16:24a 2.5%return. If the cash flow had been
16:28in a year, therefore two periods, how
16:30would I have divided it? By 1 + 0.025
16:36sq. Okay? If it had been in 3 years,
16:40therefore 6 six-month periods, I would
16:43have divided by 1 + 0.025 ^ 6, because
16:48if it's 3 years, okay guys, 3 years
16:52equals 6 six-month periods, okay?
16:57Because remember we are calculating
16:59based on the six-month coupon, and
17:02obviously if I do 2.5/1 + 0.025 ^ 6,
17:05the calculation starts to change
17:07drastically. Okay? Now, if you want to
17:13do all the calculations yourself, I
17:15suggest you build an Excel model, you
17:17make it once and for all, you save it,
17:19and basically the work to be done is
17:21this. You need to see the present value
17:24, okay? 2.5/1 + 0.025. This is the
17:31first one, then you do present value 2,
17:34and so on. 2.5/1 + 0.025 you square it,
17:41then you do the third. PV 3 = 2.5/1 +
17:470.025 ^ three and so on. Okay? until
17:54you eventually reach, just to be a bit
17:58faster, PV 60, because we said it's 30
18:01years, guys. So 30 years times two
18:05coupons per year because it's
18:06semi-annual, we have 102.50. And you'll
18:11say, Marco, why is there 102 in the
18:13numerator? Well yes, because at the
18:1660th semester we will have the
18:19repayment of 100, if obviously the bond
18:22is repaid at par, as in this case, plus
18:25the last coupon of 2.5. That's why
18:30102.50 divided by 1 + 0 raised to the
18:3660th. At the final maturity I receive,
18:40as I told you before, also, uh, let's
18:42say the principal, right? So if I added
18:45up, just to give you an example, guys,
18:48if I added up all the coupons received
18:52for the 59 quarters before reaching the
18:55last one, which is here, I could do 2.5
18:59*59 which is, wait let me do it, it's
19:02147.50. If I then add the final coupon
19:10+ 2.5 I arrive perfectly at 150. But
19:15future money is worth less than today's
19:18money, okay? Precisely because of
19:20inflation, the cost of money, and so on
19:22. So, if I take the sum of all the
19:26discounted values and the discounted
19:29values were obviously those, the result
19:32of all these divisions I was showing
19:34you, we had the first year 2 point,
19:37excuse me, the first semester 2.44,
19:402.38 and so on. Okay? If we think that
19:45the value 100 is a mathematical
19:47consequence, it is also inevitable that
19:49the coupon rate and the market yield
19:51are the same. But guys, I mean what
19:53does that mean? That everything I am
19:56telling you is valid as long as the
19:58market prices the Treasury always at 5%
20:00. Because what happens? And this is
20:04where we need to get to the reasoning.
20:07If a war suddenly breaks out, the Fed
20:10goes crazy, raises rates and the 30-
20:13year goes from 5 to 6%, for those
20:15holding bonds in their portfolio, bad
20:18times are coming. For what reason?
20:22Especially on long maturities and
20:23therefore high duration, right? Because
20:25if the maturity is long, the duration,
20:27which is not the maturity, let's not
20:29get confused, eh, that is a very very
20:32wrong thing. Anyway, um, what happens
20:35to the bond? the denominators, based on
20:37the calculations we did earlier, would
20:39become larger and therefore the present
20:41values of the coupons would decrease.
20:43Now we'll see it. The total would no
20:46longer be 100, but I'll tell you
20:49quickly, if we go from 5 to 6, the
20:51value of the bond drops between 85 and
20:5490, guys. So it reaches between -10 and
20:58-15%, and the bond goes below par. Okay
21:01? Let's get to our calculation. We must
21:05now consider that we need to explain
21:08duration well so that this concept is
21:10clear once and for all. For each cash
21:15flow, we must also assign the moment we
21:18receive it; that is, we multiply each
21:21individual discounted flow by the exact
21:23time in years when we will receive it.
21:27Let me give you an example. If I take,
21:30okay, the first semester, we can
21:33indicate it as 0.5 in terms of years,
21:37times the present value 1 that we had
21:40calculated, if you remember it was 2.50
21:44/1.025. which gave me 2.4344, okay?
21:51more or less, with a few decimals. If I
21:55multiply this by 0.5, and if we now do
21:58this for all the other flows, okay? So
22:02it would mean that for the second one
22:05we would have to do 2.50/1.025. Every
22:10now and then I’m a bit slanted, guys,
22:12forgive me. It is not easy to write
22:14with this pen and the small board, it
22:16really isn't easy, huh. Excuse me. The
22:19parenthesis, here we go, I messed it up
22:21, I made it too long. The parenthesis
22:22goes in the denominator. Squared, we
22:25said 2.38. If we multiply it by 1, why
22:30by 1? Because we are talking about two
22:32coupons, so the first year; the result
22:34obviously doesn't change, it's 2.38.
22:38Then we have to do a year and a half,
22:40we multiply by 1.5, and so on. If we
22:44add up all this calculation up to the
22:4760th, it means we have 30 in terms of
22:51years times PV60. Okay? What does that
22:56mean? That by summing everything up—
22:58I'll tell you the calculation already
22:59because I did it before starting the
23:00video, otherwise we'd never finish—it
23:02comes to 1584.07. I take this figure,
23:09okay? I divide it by what? by the price
23:13of the bond. And what does that come to
23:16? It comes to 15.84. So it means that
23:22ours is called the Macaulay duration,
23:25which is not the only duration, hey,
23:28now I'll show you another one. Macaulay
23:34Duration tells us that our capital will
23:37be returned in 15.84 years. So the
23:41duration, guys, of a thirty-year
23:44Treasury is 15.4. Okay? But the one
23:49that interests us later for the price
23:52is the modified duration, okay? So what
23:56does that mean? that we are going to
23:58look at the modified duration, because
24:01the Macaulay duration tells us that
24:03even though the bond lasts 30 years on
24:05paper, thanks to the fact that it pays
24:07coupons every 6 months, I recover the
24:09capital in more or less 16 years. Just
24:12to clarify a concept for you, how can I
24:14say that the capital is recovered in 16
24:16years? It doesn’t mean that we’ll
24:18recover everything by the 16th year,
24:19right? If I give you two examples, let
24:22me make a quick parenthetical note: we
24:24have a Case A where, for example, we
24:26have, I don’t know, a zero-coupon
24:28bond, okay? For the zero-coupon bond, I
24:33obviously wait for the repayment, so I
24:35have a duration of 30 years, right?
24:38Because I don't receive any coupons in
24:39the meantime. Case B, on the other hand
24:41, is the one we just looked at. In Case
24:45B, if we have a 30-year Treasury that
24:48pays coupons semiannually—so every 6
24:50months—my duration is around 16 years
24:53. 15.84, we saw it just a few seconds
24:57ago. Okay? This means the financial
25:01center of gravity of my returns, guys,
25:03in terms of cash flows, shifts backward
25:06. Because it goes from 30 years down to
25:1016 years. So, even though I have a
25:13maturity, okay, at the 30th year—so
25:16if today is 2026, my maturity is in
25:192056—my duration helps me understand
25:24that I'm actually shifting my center of
25:26gravity back to around 16 years, okay?
25:29So please, make sure to distinguish
25:31between maturity and duration; they are
25:34two different concepts. Now, therefore,
25:37we said that the number we saw earlier,
25:40which was 15.84, is the average
25:46financial duration of our 30-year
25:47Treasury, naturally weighted based on
25:49the time we receive the coupons. But to
25:53calculate how much the price drops if
25:56rates move, okay, in finance, we use
25:59modified duration. As I was saying
26:02earlier, the formula to move, guys,
26:05from, uh, Macaulay duration to modified
26:08duration is very simple. Basically,
26:11modified duration is nothing other than
26:15Macaulay duration, okay? Divided by 1
26:20plus the semiannual rate. Here it is.
26:27So in our case, the Macaulay duration
26:30was 15.84, okay? If you remember, the
26:35semiannual rate was 2.5%, so it would
26:38be 0.025, therefore the denominator
26:43will be 1 + 0.025. This result drops to
26:4915.45 if you do the calculation. Now
26:54let’s look ahead; the situation gets
26:56a little more complicated now, so pay
26:57attention. Let’s try to look at the
27:01bond’s sensitivity. So, let’s take
27:04the percentage change. By this, I mean
27:08percentage change—that is, how much
27:10the price changes—divided by the
27:13initial price itself, and you’ll see
27:16the formula, I’ll show it to you,
27:18it’s this one here. So, I want to
27:23know by what percentage my investment
27:25goes up or down as a function of the
27:28change in rates. Remember that the
27:31minus sign is mandatory; it is the
27:33golden rule of the bond balance,
27:35because if you recall, bonds and
27:36interest rates have, let’s say, an
27:38inversely proportional relationship. As
27:42for D mod, that would be the modified
27:44duration, which in our case we said is
27:4715.45. Here it is. The higher this
27:53number is, the more volatile it will be
27:55. Guys, remember that the higher the
27:58modified duration, the more volatile it
27:59will be and the more sensitive it will
28:01be to shocks from central banks or
28:03whatever happens in the market. Delta Y
28:06in this case is the change in rates,
28:09okay? In this instance, if we take a
28:12rate of 1%, okay? which in math you
28:15know we write as 0.01. When rates go up
28:20by 1%, we need to understand what
28:21happens to our bond, and I want to show
28:23you, okay? In a fairly simple way. So,
28:26let's take the coefficient, I’d call
28:28it of fragility, which is 15.45. Here
28:32it is. We multiply it by the push that
28:36rates can receive in this case, meaning
28:39by 1%, so by 0.01 and it gives me 0.15
28:46and 45. If we then apply the minus sign
28:50, okay, it means that here it becomes
28:53-0, excuse me, -0.1545. Here it is,
28:590.1545. And here it is. If I then
29:05convert it into a percentage, obviously
29:09the result is -15.45%. Okay? Because I
29:16multiply this by 100. Now let's
29:20hypothesize a shock in rates going from
29:245%to 6%, as I was telling you, so we
29:27have 5%going to 6%. Very simple. In the
29:34old situation at 5%, I was paid every
29:37semester, which means I have a 2.5%
29:40coupon here, while here I have a 3%
29:43coupon per semester. Are we on the same
29:46page? So the new discount rate to use,
29:48guys, will be 0.03. 1 + 0.03, we will
29:53put 1.03 in the denominator. Okay? I'm
29:57telling you this now so everything is
29:58clear. So, I’ll erase this here. If
30:01we take the present value now of the 60
30:02coupons, I’ll tell you right away,
30:04it's different, it comes out to 69.19.
30:09Okay? Because obviously everything
30:11changes, right? Now if we take this
30:14formula, the present value, okay, of
30:19the coupons is equal to 2.50 and I
30:26multiply it by the numerator, I put
30:291-1.03 ^ -60/0.03. What does that mean?
30:38If I take 1.03 ^ -60 it means, okay,
30:42I’ll make it fairly simple for you
30:44down here, that this 1.03 ^ -60 means,
30:49I'll make it quick for you, 1/in
30:52parentheses (1.03 ^ 60) which is equal
30:56to 0.1696 done with the calculator; we
31:04subtract it from 1, so we have 1-0.1696
31:10which is equal to 0.830. You have to
31:16keep in mind, guys, that the result
31:19coming out here of 16.96 is what a
31:22dollar is worth 30 years from now. This
31:26helps us to discount, to understand how
31:29time and the value of time impact the
31:31value of our money. Okay? So 1-0.1696
31:36gives us 0.8304. If we divide it by the
31:42new discount rate, then we have, look
31:45here, I'll erase for space reasons, we
31:47still have 0 .8304, we divide it by the
31:55new discount rate which is 0.03 gives
31:59me 27.6804. which is a discounting
32:05factor. If I multiply this factor by
32:08the coupon, I get 69.20. Okay? The
32:15second block, this is the first part of
32:17the price, we are getting to calculate
32:19the bond's price. Okay? What is the
32:22second block? We take the principal
32:25that will be returned to us in 30 years
32:27and discount it at the new discount
32:29rate, which is 6%per year and therefore
32:313%per half-year. Does that make sense?
32:34I'll clear everything here for you,
32:35we're almost done anyway, guys, don't
32:37worry, we're almost there. Uh, so, if
32:41we have the present value of the capit,
32:44we want to know the, okay, present
32:47value of the capital, we have 100/1.03
32:50^ 60. How do we solve it? This value
32:58gives us 5.8916. it would be 1.03 to
33:04the 60th power. Then we divide 100 by
33:09that number, so we get 100/5.89 and 16
33:16gives us 16.97. Okay? Now if I go and
33:23add the two blocks, we said we had
33:2669.20 + 16.97. What does that give us
33:31as a result? it gives us 86.16 or 17.
33:36Okay? So this is the new Bond price.
33:41What does that mean? If I have 86.16 as
33:46the new Bond price, guys, it means that
33:49my change in percentage terms was
33:5186.16-100, which was the previous price
33:54, minus the previous price again times
33:57100 in percentage terms, meaning my
34:00bond will drop by 13.84%. We are
34:07finished. This is the down, uh, let's
34:12say the drop of the bond when interest
34:15rates rise by 1%on a 30-year bond. Try
34:21to imagine why at a time when higher
34:23interest rates are being priced in,
34:26with central banks starting to position
34:28themselves a bit more, okay, why it
34:30becomes dangerous to have long
34:32maturities in your portfolio if you
34:34don't know macroeconomics. While the
34:37argument obviously also applies to the
34:39upside, right? Because it's wonderful
34:43to do, in my opinion, when you have
34:45macro knowledge, bond trading, because
34:48if instead I expect a 1%rate cut, I can
34:50make a 13.84%upside without any problem
34:56. Okay? So guys, keep in mind that this
34:59video might definitely be a little more
35:01difficult in terms of concepts or
35:02otherwise. I wanted to, let's say,
35:04write out all the calculations for you,
35:07but I'll put it very simply. You can
35:10just have an AI build a little model
35:12for you; tell it to make you an Excel
35:14file to calculate duration and you're
35:16set. Okay? I want to show you, if you
35:20want to understand how the curve reacts
35:22for a moment, look here. I have this
35:25Excel model, okay? Where we can see the
35:27duration and we can see the exact price
35:29. Okay, right now I have hypothesized
35:32exactly what I told you, okay? With the
35:35bond we saw earlier. So, 5%base yield,
35:395%coupon rate, 30-year maturity, and
35:43coupons, so basically two payments per
35:46year, okay? The base bond price is 100,
35:51okay? For duration estimates, I put
35:54about 15.45. So, if I go from 5%to 6%
35:58here, look, I just type 6%, and you see
36:01, the base bond price goes to 86.16.
36:06And watch now, look at the graph; I
36:08click back in here, I put 5%, look at
36:11how the curve changes because,
36:12obviously, you have the price level
36:15here too. If I put 6%back in above, see
36:19? Look, obviously the bond price has to
36:23fall, but notice that the graph below
36:25also changes. So keep in mind that all
36:29these calculations we’ve done show
36:32that, more or less, with a 1%change and
36:35a modified duration of about 16 years,
36:3815-16 years, the market impact on your
36:41portfolio is 13-14%. Very good guys, as
36:44I promised you, I made the video on
36:47duration. We'll see each other next
36:49week. I invite you to come to the BNP
36:52Paribas channel, and please, don't miss
36:55my live stream on memory products.
36:57Honestly guys, there is incredible work
37:00behind it, and there are many new
37:02things to talk about. We'll see each
37:04other in the next video. Bye everyone.

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