garvia.es

Foundations of Finance (FoF) – Session 18

NYU | March 18, 2026
Instructor: Luis Garvía Vega
Duration: 1h 20min

1. Opening: Macro Context (Critical Moment)

The session begins with a strong macro message:

“You can enter a cave for one week and come out to a completely different world.”

We are in a moment of:

1.1 Central Banks Week

Within a few days:

→ ~16 central banks speaking

Key uncertainty:

1.2 Structural Tension

Two opposing forces:

Inflation pressure → rates ↑

Credit stress → rates ↓

This creates a policy trap.

1.3 Private Credit Stress (Critical Insight)

After 2008:

Today:

This creates:

“A private-sector bank run”

1.4 Liquidity Crisis

Key dynamics:

Examples:

1.5 Gold vs Dollar Paradox

Normally:

Now:

Why?

  1. High interest rates (opportunity cost of gold)
  2. Liquidity preference
  3. “Buy the dip” mentality

1.6 Behavioral Shift: Buy the Dip

Market psychology:

→ Risk appetite remains high

This explains:

Why fear is not translating into defensive positioning.

1.7 AI Shock Example (DeepSeek)

Example:

Lesson:

Information shocks now move markets instantly.

1.8 Key Message

“Things are changing too fast. What I thought last week is not what I think today.”

2. Transition to Fixed Income

After macro discussion:

“We go back to basics: bonds.”

3. What is a Bond?

A bond is:

“An IOU (I owe you)”

Key components:

4. Types of Bonds

4.1 By Issuer

4.2 By Maturity

4.3 By Structure

4.4 By Credit Risk

Key assumption:

Finance requires trust in repayment.

5. Price vs Yield Relationship

Fundamental rule:

\[\text{Interest Rate} \uparrow \Rightarrow \text{Bond Price} \downarrow\] \[\text{Interest Rate} \downarrow \Rightarrow \text{Bond Price} \uparrow\]

6. Yield Measures

6.1 Coupon Rate

\[\frac{\text{Coupon}}{\text{Face Value}}\]

Fixed.

6.2 Yield to Maturity (YTM)

\[YTM = IRR\]

Internal rate of return of bond cash flows.

6.3 Current Yield

\[\frac{\text{Coupon}}{\text{Price}}\]

(Not very useful in practice)

7. Bond Pricing Cases

If:

8. Core Exercise: Yield and Price

3-year bond:

Prices:

9. Core Concept: Price-Yield Curve

If interest rates change:

At:

9.1 Key Insight

The bond price is the present value of future cash flows.

10. Sensitivity to Interest Rates

Longer maturity bonds:

Reason:

11. Semiannual Compounding

If coupons are paid twice per year:

\[(1 + r/2)^2 - 1\]

Key idea:

More frequent payments → higher effective yield.

12. Realized Return (HPR)

Example:

New price decreases → capital loss

\[HPR = \frac{FV}{PV} - 1\]

Key Insight

Expected return ≠ realized return

Depends on:

13. Reinvestment Risk

If:

If not:

14. Final Exercise (Critical)

3-year bond:

Price:

\[= 1000\]

Reinvest coupons at 8%:

\[HPR = 8\%\]

15. Key Takeaways

  1. Bond = present value of cash flows
  2. YTM = IRR
  3. Price and yield move inversely
  4. Longer maturity → higher sensitivity
  5. Realized return depends on reinvestment
  6. Liquidity and macro conditions affect all pricing

16. Preparation for Next Class

Critical exercises:

  1. Zero-coupon bond pricing
  2. Coupon bond pricing
  3. Yield vs price intuition

Next session:

Interest rate sensitivity (duration & convexity)

Transcription

18 de marzo de 2026, 5:06p.m. 1 h 20 min 21 s OK, I’m going to take attendance in in 2 minutes if you don’t mind.
Hey.
One hand, they will look for a single one. Also they you should have a upload problem said for who was problem said for.
How was it? It was OK. Do you want me to go through? It’s not really complicated. It says working and understandable. If you can give me one of the slides.
Yes, Morgan, welcome. And this is just and and.
And and yes, several things.
Take it out. I need a red rule also. I don’t need it. I have. I’m full of energy. This is for the.
Yes.
Play Uma song.
There are thumbs. OK, several of his hand.
OK, uh, set it.
Sorry for demand and from for those that are not here today. I’m going to start with the.
This now is not that day for not coming to class.
Let me talk. What I mean is that.
Lot of things are happening just right now, not in that.
You come into a cave that’s weak and you go out of the cave in one week time.
Probably you will come in a different world.
This two weeks, 3 weeks, 4 weeks.
Lots of things are happening. A lot of things. I’m talking about macroeconomy. I’m talking about finance. I’m talking about geopolitics.
Last last, sorry, last week I am more star. At the beginning of this year, Venezuela, Venezuela was Maduro was taken from Venezuela.
20th of January Trump wasn’t sorry, 5th of November Trump was elected and the 20th of January Trump start. Yes, there are a lot of things happening.
Back.
Bring to your question and your question was, but I think Pavel is going to do what is going to happen.
Now, now a lot of things that we thought last week were on one way. We are discovering that everything is changing. We are in a point of inflation.
Now this week, yesterday, today’s no yesterday, Australia’s central bank talk has increased in the rates. They felt tomorrow European Central Bank, Bank of India, Bank of Japan.
Friday Chinese Central Bank within three days order 1616 central banks are going to talk.
What are they? What are they going to say? Because they are going to say a little things. You know reserve who’s going to say that interest rates will stay. European Central Bank is going to say that interest rates are going to stay.
Baris. No. See. See. I’m sure. I’m sure. Hello.
You understand what I mean? I don’t care to stop for one second.
You can stop. So I don’t want you to miss a call because I’m not stopping. I want to take this whatever.
16 central banks are going to talk this week.
Also.
Now we are in the harvest.
Crisis regarding international commerce. I’m not the one that is saying this. International home manager, international. I don’t know how to say it in this. In Spanish is FM I is for international monetary home.
I am the the CEO, not the CEO, the chair of the.
I, I, I say that we are in the hardest global crisis. Also with Ukraine, Ukraine is making. I’m going to say several things. I want you to have the complete review.
Have you studied in history when the First World War started?
You remember it from 39 that it was one person was killed because that the first World War started started. This is what is written in history books, but if.
But I’m clear enough. We’re not having him. There should have been another reason that meant. I mean, there were things that were that you cannot stop things to happen. Yeah, there is one excuse. I imagine that this Maria and us to have a problem, yes.
We don’t like each other because of this call we had. There were not the call, it were something else, but if there is something that should happen.
Iran war is an excuse. Who are the two principal army exporters?
Who is the? Who is the country in the world that exports more army USA sport before the pandemic 38% of all global weapons after the pandemic 42? Who is the second one?
Same, same. And I have been talking about Iran, Irani war for two weeks and all times I talk about Irani war. I also talk about Afghanistan and Pakistan. Same day Iran was attacked attack.
Pakistan start bombing Afghanistan and if you see a map, all these places are in the same place. Yeah, there was one hack, one hack that was going to be given between XI and Trump.
The 31st of March, there was a great meeting between them.
What is my thought? I’ve been talking about this week for weeks, about this meeting for weeks. What is the thought of this meeting? They worship. They want to meet each other once everything was here, here once everything was.
So, yeah, Trump has said two days ago that they post all this meeting understand why.
Why? Because they want to have this prepared and all these things. OK, Paul, have you seen what is going on with gold prices?
Are you following gold? Gold up has gone up and gold is now going down.
And I want you to understand this. Normally in a war boat goes up.
If there is a war, gold was was up. Why? Because coal is a refugee. Yes, coal is a refugee. People normally buy gold. Why gold now is going down? Because of three factors. Because of three factors. And for me, the last factor is the most important.
What is that? There was a rally called Lounce in Maxim.
Another factor has to do with interest rates because there are high interest rates. Why you are going to buy metal when you can buy things that has return. OK, because this return is in dollars and does not matter to us. And which one is the third?
Factor. This is the most important and I want you to fully understand this factor, yes.
Do you have, do you know what is by the deep? Have you ever heard of by the deep?
You are a crypto, bro. I know that you are not at this. Traders know about buy the deep. What is buy the deep? And I want you to fully understand this.
In crypto it has happened a lot and with the media and media, but Trump was elected the 20th. Sorry, what Trump was elected? Trump was president the 20th and 29th Deepseek appeared. Once Deepseek appeared from China in China, Deepseek is.
It’s it up here, Emilia, just one day.
17% of value more than 700 billion in one day within hour and SP500 plus more than.
The New York Monday, yes.
deepseek is an AI company, a Chinese AI company. It was released and it made because deepseek could make a lot of things that GPP do and with less effort media sells tips.
And doing this means we are going to sell less ships. Yes, one day 717 percent. What means by the bean?
If a price of a stock goes up, a lot of people see it as an opportunity. If a stock goes down, a lot of people see it as an opportunity. And if you see opportunities, how do you want to be equally? You understand what I’m saying?
You want meeting me?
There is a war in Iraq. How do you say that in English? There is a war in Iraq.
People normally should be frightened, but people are not frightened. People want, oh, I want the opportunities and because people want the opportunities.
You have gold. You cannot buy stocks with gold. You cannot buy that with gold. You can with gold. You cannot buy things. Gold is not liquid.
Do you understand what I mean? What do you mean if you want to buy things dollar? Because of that, there are a lot of people taking dollar.
And the dollar is going up and gold is going down. Do you understand what I’m saying? We are good because there is a second derivative. This is a lot. This is really, really important you to understand and you have.
I have told you about Imam class Imam Brothers class 2008.
After Lehman Brothers class banking business.
Start not giving too much credit. Banks start. There was a credit credit grants. Banks. Banks were giving credits, but not as much. There were a lot of people that need money.
And banks didn’t lend them money and there was something that appeared there that is called sub banking private credit.
And also there is there is.
Private money, private capital, private capital that there is private technically and also there is private lending, private credit, yes. So there is a big industry regarding lending but in a private way.
Before Lehman, there was bank. There were banks wouldn’t money. They would get on fire and they would have Lehman Brothers crush after Lehman.
Private credit as a start point on. What is the problem now with private credit? Private finance things when when interest rates were low.
The rate has gone up and now a lot of people wants to be liquid, but they want to be liquid in order to take advantage of new opportunities. People are running for from private capital, both equity.
And credit. People are running from them. It’s like a bank, like a bank, like a like a bank run, like a bank run, but in a private way and.
A better would be firms as AVR or Apollo has lost less than one month, more than 20% of their money because people wants to be liquid. They are right now from private credit.
They want money now and you cannot take credit equity homes from one day to another one. You cannot sell gold immediately. You need time.
What is happening now? What is happening now? That there is a high demand of liquidity. Also, there are a lot of private firms that has problems and need financing, but there is no more private lending.
There are private and blending firms that has laid.
One dollar and the 8th world at the amenates world is 0.75. So they are they are losing 25% that there are firms have seen yesterday one world of 50% of total price people that has lend money.
They are sending all these companies, people are running from these companies and they are sending these monies that has left around 100%, not dead 100% that can be bought.
What should it be 5%?
What is going on?
That’s what if you ask me what central bank was going to do. That’s what if you ask me what central bank was, what was going to do, I would have told you that there were two.
But interest rates were going to be dropped two times within this year. They know that probably was getting worse start following tomorrow and now there is a credit grants in the private sector.
There are enormous, enormous problems regarding equity.
And personally, I think that central banks are not going to need this liquidity just right now.
And if there is also inflation, if there is also inflation, if there is inflation, what you should do with better rates?
And if you increase interest rates, what is going to happen with lending? What is going to happen with private lending? What is going to happen with liquidity?
It will go down, but I want you to see that last week.
If you asked me last week, I will tell you that freelance is going to continue that they are going to central European Central Bank is going to draw interest rates in order to give free money or cheap money to governments, to dep.
Coming back, yes.
But now we can be changing so, so fast. Why? Because there is a grant lending.
A lot of people is asking for liquidity. Who normally give liquidity to the system? The providers.
Personally, I think that today, today.
You know Paul will not talk about equity, but we will be. Paul will give liquidity to banks, the banking system, and he’s not going to give liquidity to the private sector, but this is not within his mandate.
Answering to your question, what Gerald Cole is going to say, I don’t have any idea. I don’t have any idea but but I thought last week.
It’s different from what I’m thinking just right now and also you see oil prices, you see commerce, you see energy and you see monetary policy.
Everything is happening now and also also there is.
A I I told you about the A I you had me two weeks ago about the A I I would have told you that year 2026 was going to be the year of the IP OS.
What do you need in order to make public a company? Liquidity. Is there liquidity?
I don’t know. As we I would have told you that we are going to see a SpaceX. We are going to see, we are going to see.
Today, I don’t know anything. So today’s an important day in order to be awakened, in order to see, to hear, to hear what their poll is going to say, because their poll will say that everything will stay.
Back.
There are important problems regarding.
And baby.
Regarding what I got, Cindy.
That equity.
At the end, if lending a lending store, there will be companies that should that we go to bankruptcy.
These companies go into a bankruptcy, then they will be firms and lending companies are going to have problems. So this thing that I’m talking about would be systemic.
And this thing becomes systemic.
There will be, you say, of course, of course there will be motions in the near future.
Did I explain myself a little? So the important thing, Paul, why why gold price is going down? Because people are thinking about buying the meat, buying. And not only that, people who are on Buffett is living.
More than 200 billion from we talk about this whatever is liquid. Now there is an enormous liquidity crisis, enormous in the private sector and what do we expect from central banks?
On one hand, I understand interest rates will drop, but if there is inflation, interest rates should go up. But if there is a credit grants, interest rates should bring money or we put it into the system that is printing money.
It’s not an uneasy situation. Things are becoming complicated.
And personally, I think that we are going to have.
Before the end of the course, I told you that, oh, I told you, oh, I’m sorry because midterm will happen in November. If midterm will have happened during the discourse, I would have been talking more about midterm collections. Why? Because it’s important.

  1. But.
    What?
    I think that what we are going to leave is bigger than the meters.
    What is going to happen? I don’t have any idea, but I feel I see something is about to happen. You see my concern, using my coin private lending, private credit, private equity firms, look, look for information regarding ADR. Take today’s transcription.
    Until today’s you have take take to the file of today’s transcription, you can upload the file and send it to you each day. You can upload it directly to.
    Upload the file and add scientific here or cloud sending more information regarding what this great Spanish professor is saying. Give me more context. Give me more.
    I’m gonna run today. I’m gonna go through today’s class little bit more quickly because of faith and because we are not gonna see anything.
    Me today. What are we going to do today?
    We are going to start talking about fixed income. I say fixed income, what I’m talking about.
    Bonds. Bonds. And there are zero coupons and bonds with coupons, yes.
    I’m trying my best. I’m trying my best and you want to finish earlier. I mean, I won. I won. I mean.
    I mean, we know each other. I know. I’m trying my best. I’m not worried, but I’m trying my best.
    And I know that this is not the most amazing course in the world.
    This afternoon he’s going to go. He’s going to talk. Eron Paul is going to talk. The word is about to explode, but he’s fixing. So I’m trying my best. OK, what is fixing come about? So it.
    What is a bone? What is a bone?
    What is a CEO como? Yes, I owe you. No, I owe you. I owe you. I owe you.
    They are. Are you using Republic Dominicana? How do you call? I am use in Spain. No, in Spain, in Spanish. I don’t know in Spanish. In Spain it could be called.
    Pagare. Pagare means is a pagare. The document is written. Pagare stands for I will pay you.
    I will pay you that I owe you this. I owe you, you know you too. You do the issue group.
    You don’t know who you do. You don’t know who you do. Like, you do like, you do like. No, you do this. I’m missing. Did you show it to us on something? Yeah, you show this. I, I, I, I we want to go.
    And you do. If it’s a music group, you should know it and and you should remember it. You should remember the important thing now. Do you know K both demon hunters?
    Yeah. Oh, they were not there. I saw them back with IT. NYU alumni. NYU alumni. Yeah.
    Yeah.
    Ladies not the day for talk about K-pop. I mean, I love, I love, I mean, if it has to do with music, I love everything.
    It has to do with war. I prefer not to think too much about it and war has to do or whatever. People has to do with Korea and it’s not something. I mean, it’s shocked, but it’s shocked power. We have also power and her power.
    Our power has to do with military power.
    It’s nice forward from that minister. Sofia, listen to me.
    This is how power. Listen to me. Nobody. So here you have a wonder. This is so power. So power is not power instead of instead of.
    Inviting a country better free and buying the country. I’m not talking about Pakistan and China.
    Thank you.
    With Kito, Kapo, but respectively China and Korea, so Korea is doing.
    What sign is doing? Introducing the sign is introducing your head. Your head. Yeah. OK, Mo, Victoria, you know, Gaman style.
    It was the first you know BTS. They have this, they have. They have in the 90s Korea, Korea Ministry, Foreign Affairs Ministry site to start exporting a.
    And they put a lot of echo in Kpop and what Kpop demon, what Kpop Monster Hunter. They won’t hunter and so was.
    It’s the power of the power.
    If Marie in order to finish, first thing I should please start and what is about?
    I have talked a lot about bonds, depending on the issuer, the government issuer in the case of the states pressures. What is the difference between a big bill and a big bond?
    Treasury Bond and Treasury Bill. No, both are same regarding liquidity at the bills. Yes, Jessica, the bills are short term.
    And because there are short term, there are 0 poop of bones.
    Is exactly that is that zero combo he bones.
    About, so not only CBS, a commercial paper.
    Don’t have.
    And loan to bonds, corporate bonds are bonds, depending on price versus par value, par, I mean Gio coupon bonds, Gio coupon bonds are always.
    Yes.
    Is bond bond. What is a part or price bond is the relationship between face value and the price. If I have a bond with coupons, bond with coupons will always be.
    We can be part or depending on the phrase.
    For example, if the coupon rate is 5% and the yield is 4%, it will be about a premium, a premium. If it is 5% coupon rate and rates are of 6%.
    It will be a discombo and if it is 5% coupon rate and yield 5%, it will be a parvo. We have seen this in class several times before the winter, in the winter and after the winter.
    OK, more fixes coupon regarding the coupon. I can talk about zero compos. There will be some somewhere should be you can still component. If not, trust me, they exist regarding credit risk. What is that risk free home?
    Which ones are risk free?
    Pressures, pressures. Does this mean that countries always pay their debt?
    In my class, yes. And I’m not telling you that countries always pay their debt. What I’m saying is that in case a country will not pay their debt, all things that I will be talking about this.
    All things that I have been saying during this class will be rabies, rust.
    I’m not saying that I’m trustable.
    I’ll tell you what you mean regarding this. Marie, let’s keep now, let’s keep. What? What I’m saying is that in the country we will not pay the debt, come in, will not work. All things present value of these will not work. We cannot. Finance will not work.
    I guess has to do with breaking the future. And regarding breaking the future, I need something secure. I need to believe in something.
    I need to believe in job.
    Why is we getting the dollar? Go with us.
    We make a dollar written in vote, we trust.
    We need to trust. What do we trust?
    Yeah, finance has to do with risk management, whatever. Let me go. Security and security covenants. I mean, these are what is a covenant? It’s something that you write in a contract.
    The more we can make votes. This is so, so important. We can make votes as complicated as we want. We can want a vote is a contract, so we can complicate it as much as we want.
    But the more complicated a board becomes, the less standardized, the less.
    The more complicated, the more explanation. So by this bond that is so complicated, but then we can find for example.
    Convertible bonds. What is a convertible bond? It’s a bond that depending on the performer. I you are that is an entrepreneur. Are you have rate your company plus the money, yes.
    What are which document you are going to give me? You are going to give me a bond. Why? Because a bond goes before equity, yes, but if things goes well, I would like my bonds to become equity.
    So I issue convertible bonds. These bonds are not so little, but in our relationship it makes sense because I am getting bonds for your financing and if things goes well.
    My bones will become.
    Makes sense.
    OK, but these are.
    Edit.
    Give to maturity. Forget about, forget about. This is the line. Give to maturity is the same as the internal rate of return.
    Here there is something that we are not going to repeat and we are going to see one example that we are not going to repeat.
    I’m gonna repeat what I have said.
    The yield to maturity is the same as the internal rate of return.
    This will be contained in this class forever, except next slide.
    The yield maturity is the same as the internal rate of redraw.
    Now thinking about next slide, I’m going to talk, I’m going to make an exercise regarding next slide and then I will come back.
    For an annual paid coupon ball, but if the the coupon rate is not annually.
    We are going to go next flight. We will see, but you can forget it later.
    I don’t want your life to be more complicated. I want your life to be simple. OK, let me. So not this is like this. Let me come. This is like here.
    Yes, this is 9 is correct. I know this is like the one that I hate is I hate.
    Let me go.
    I.
    I want to go quickly. I have a ball with three prices. Yes, I have to suppose at this year. Please, we did this week now.
    I’m I’m too far from there.
    I mean you inside this.
    And we use with that.
    OK.
    You have a three-year bond with face value of 1000, an annual book on payments of eight, yes.
    3 years.
  2. 808108 yes.
    You have this call.
    What I’ve said in the bond sales at 1000, what is the maturity if the bond sales at 900 or 101,100? Yes.
    The free prices.
    900 and 1100.
    Yep.
    How do you can play the maturity?
    With the IRR form, yes, give maturity.
    I’m too far the connector and not all the.
    Holy, I’m going to flag.
    The price, yes.
    And I’m going to calculate the hint facility. I’m going to calculate the hint facility.
    Equal to IRR, yes.
    I am.
    Of this make sense.
    What this IRR will be around?
    Oh, you don’t know.
    Let me start with another number, yes.
    But this high alarm will be around.
    But this higher will be around, not around. I mean, look, please look at me up there and think.
    I am paying 1000 in order to get the 9% the 9% and last year 1000 + 9%.
    How much return I’m getting?
    I pay 1000 in order to get 8 percent, 8% and at the end 1000 + 8%. What should be my return?
    8%, no. So if the if there is 1000 a year, I will be.
    And.
    And papers.
    Make sense?
    Today’s class, fully understanding today’s class is absolutely important. They are not explaining anything new. All things that I’m going through are new things, are things I’m reviewing all things, OK.
    Yeah.
    Yes, and in order to calculate the other, I need to put the negative for I know all things possible. Understood.
    I’m gonna copy. I’m gonna copy. I’m gonna just take this now.
    Ayadar.
    Of this is in person, yes.
    I mean, I want all these notes.
    This is 1.
    A percent of what if I change this to 900?
    If you can replace, goes up, price will go down.
    So the price goes down is because interest rates has gone up, so they give maturity.
    I don’t know about what, but it should be higher than 8%.
    I’m back, yes.
    Recent.
    I’m here.
    Please.
    And.
    Or.
    You don’t know to. You don’t need to know how to calculate IR with Excel for the time, but I want you to understand what I’m doing, yes.
    If the price is 1100.
    I can say that there are 400 basic columns between 12% and 8%. The IRR will be around, I don’t know, 5%, 4%. Yep, make sense.
    That’s true.
    Now the what I have just written is the. No, I have written the Gil Machuli.
    What is the open rate?
    We’re ready.
    The rate is 8%. The rate will not change no matter what the price will be fixed.
    Because of this, this is fixing and then they talk about.
    Current deal. You will never see current deal. You will never see this number. What is current deal?
    80 over 80.
    Over. Let me fix safety.
    Over. Yes, the review is closed.
    When deal is close to 8%, yes, interest rate say yes.
    It’s so like Jessica, Sophia is Marie.
    If there is rate 10, yes.
    Interest rate changes. Today I’m not going to talk about anything new, but next class I will talk a lot, a lot, a lot about what happens when interest rate changes.
    And if interest rate changes, how much the price will change? The answer will be today. What is today is interest rate sensitivity. I have already talked about today, same as I talk about YouTube, but I don’t care about YouTube or the music group.
    Next thing is so if you’ve got a great team, it’s good teams, but why?
    This is more this price is more sensitive.
    That because I don’t care much about the coupons, I care about 1000.
    1000 in three years matters. The things I could, I mean couples matter. A face value matters more because of face value.
    The change of in price went with the rate changes. It’s high. Make sense.
    This is done for today’s class, but for next class will be important. I will try my best in order to remember to upload next class the sooner the possible. Send me a WhatsApp and tell me Luis.
    Upload the old classes next day. I don’t have any current nursing sharing with you the slides just right now.
    But next class is also important. This class is important, but next class. Why today’s class is important? We are not seeing anything new, but you have been preparing next class. OK, now the slide that I don’t like.
    For semi-annual day, the maturity is composed in two start. We talk instead of the maturity, we will talk about what is written. We will talk about the effective annual deal. I have never heard anyone.
    Talking about defective family apart from this light.
    Like the idea. You remember the idea? I’m going to do these two exercises so quick, but I don’t care too much about these two exercises, yes.
    Here and let’s do this ball. What I’m going to do with this exercise I have.
    I have.
    I’m not saying only because you’re not the same, but instead of 80 once a year, I’m going to have 40 twice.
    They were reporting.
    Excels.
    Suppose a three-year bond has a fixed value of 1000 and pay semi annual coupons of 40. If the price is 900, what is the yield to maturity?
    The price is 900, yes.
    What is the yield to luxury?
    But I will always recommend you to look and see.
    This is.
    Yes.
    Important. Is this IRR in a yearly basis? No. So.
    If you don’t memorize, if you just think what you will do with this in a year basis, yes, in a year basis what you will do is.
    One plus this raised to the square -1 no.
    And calculating their well I said HPL and this would be.
    12.44 make sense?
    In my head, in my head, this should be the yield to mature. Careful, because this is not the yield to mature.
    The maturity is this is what it’s called.
    Thank you. And what do you?
    And what is the?
    Why is the deal to maturity?
    What is the need to maturity?
    I don’t want you to learn this. Yes, the maturity should be these times should that is 12,000, yes.
    You see what I’m doing, what I’m saying? Please forget about.
    But because I don’t want you to have in your head.
    I don’t want you to have in your head something that is not from home.
    I want you to keep yes in your head compounding things.
    Make sense? OK, here you go. Now compare. Understood this example. You can forward it. Compare the effective annual deal of each one, the three-year and the three-year, which has a higher annual deal.
    And why?
    Obviously you receive the money sooner the rate will be high.
    OK. Suppose a three-year CEO Kompon has a OK reverse question. I’m not going to do the reverse question. Is that or yes, I’m going to do the reverse question. So yes.
    I want to do the rest course so quick, so quick this 1/2.
    Yes.
    12345 I’m talking in, yes.
    This is yearly years that we don’t know how to write the semiano.
    Hey.
    I don’t know. I promise I didn’t want to write the truth.
    Again, there are twins. Oh, I don’t know. I don’t know. Whatever. Sorry, 40.
    I miss him. I.
    The soon, the faster I want to go, the worse I’m doing. Yes, 1040, yes.
    I am told the year to maturity is 10%. Forget about this 10% and the year to maturity is.
    10% rate.
    Is paper over to? Yes, please forget about, forget about.
    Tenu Bach.
    Yes, go to some 5%.
    What I’m gonna do, I’m gonna calculate the price. How will I calculate the price? This rate is send me.
    Hello.
    This rate is semi annual, yes. Oh, I’m going to calculate the price.
    Or we’re going to calculate the price with the present value home. We’re going to calculate present value future cash flow.
    Let me calculate 40 / 1 plus this one fixed.
    Price to make sense.
    All belong with me.
    All of you are with me, speak up and calculated present value of this.
    Are you?
    Yes. And what is the price? Yes, the sun.
  3. Stop.
    Now I want your whole attention. I want your whole attention. Yes, 123.
    8081 thousand.
    Yeah.
    I’m going to say that the rate is.
    8%.
    I’m going to complete the price.
    Please is the I want you to know how to calculate the price of.
    And I’m calculating the price of amount for the. I don’t know how much times I have already done it. Yes, I’m calculating the price of amount.
    The first, no.
    No.
    Oh.
    All of you are following me.
    Where is?
    The sum of these.
    I I am calculating the price of a bonus at 8% rate.
    8% coupons, 8% rate. What should be the price of the ball?
    Take up 8% coupons, 8% rate. What should be the price of the goal?
    I posted.
    A function.
    What happened if I?
    Troy, please, I need you because this is the climax. I’ve been working for weeks in order to.
    Have this moment. Whatever after, I’m always waiting for me. OK, imagine that. What is?
    the deep would be zero percent.
    Did you would be your person?
    If money will not give me return.
    The money in one year will work the same than today. Only two years will work the same than today. Money three years will work the same than today. So what should be the price of the gold?
    Eight nights.
    3241 thousand 1240 make sense.
    Please 112 thousand 1200 forty 1240.
    What if I increase interest rates to 1%?
    Rise will drop.
    No, Luke, Super said.
    3% No 33 I’m getting nervous. 3%, 4% Are you following me? 5%.
    10 percent, 8%.
    Repeat the same person.
    1009%.
    10%, 11%.
    What I’m doing? I am changing interest rates.
    I am changing interest rates. As I increase interest rates, price of the bond withdraw.
    What I’m gonna do here, I’m gonna write here.
    In a person, no.
    Sorry, this moment of the class is absolutely important if interest rate is 0%.
    In the rate is 0% only will work the same today than in the future. So the price of the loan will be the sum of future cash flows. The rate is 0%.
    I say increase interest rates.
    The price goes down and once I go to 8%, I continue increasing interest rates.
    Please.
    The guy is withdrawn, yes.
    I’m going to change the formula. Look what I’m going to do instead of I’m going to calculate the price.
    With net present value formula, yes, net present value formula.
    Represent value formula.
    At this rate, yes.
    Oh.
    This gas flows and I’m gonna fix it.
    You see what I mean?
    I’m using the present value formula and what I’m going to get with this formula.
    What I’m gonna get?
    Debrish out. Yes. Are you following me?
    This is same result. I’m going to clean this one and here the interest rate is 0%.
    1200 lessons.
    And what I’m going to do here, I’m going to say this number is going to be this plus 1%.
    This number is gonna be this one.
    And I’m gonna run.
    Yes.
    And I’m going to get insert.
    Ready split our charts.
    That there, yes.
    Next day I will review this. I will also give you.
    More information next day.
    But what does this graph show me?
    What does this graph show me?
    The relationship between price and interest rate, price and interest rate. If interest rates increases, what will happen with the price? It will go down. The rate is 0, 1200.
    For when which one is this point when the price will be 1000?
    But in person today, today we are not going to talk about the slow. Next day we will talk about the slow. What does the slow tend to be? How much the price will change or integrate changes?
    Or what we’re going to call this law? Race. Next day we will talk about that, yeah.
    It is.
    Today’s class is absolutely important. Today’s class is absolutely important. Why? Because we are not seeing anything new.
    And I can that this is, this is the one, the one on the right. This is the one that I have, yes, but I can.
    At once I go beer. Make sense.
    OK, realize return.
    I’m going to go quickly to both data three years. Your bond has a little maturity of 5%.
    Compose that.
    A few years, your bond has a maturity of 5%, yes.
    Here, your command has a infatuity of 5%.
    Sophia, what is space value?
    For example, I mean I don’t get it. What 1000 or 100? Let me see. Oh there there are no numbers, so I’ll write the numbers. Yes 1000.
    Rice.
    Price is 1000.
    Again, I have already changed.
    I’ve already done it this.
    Price is 1000 / 1 5% price to the third is the price of a zero como.
    Make sense?
    It not shows three years.
    Next year.
    After one year, actually difficulties, 2 years makes sense.
    That is one year after.
    Exempt after one year into maturity changes to 7%. Yes, what is going to be the price?
    1000 / 1 7% price today.
    Price today.
  4. Yes.
    What is the realized holding period return over one year? What is the HPI?
    There is nothing new in this exercise. What is the HPR?
    Future value over present value -1.
    The HPR within a year. Make sense.
    Why? Why? Because I have both thinking I was going to get a 5% and after one year the new variety is going to get a 7%. We have done this kind of exercises for the midterm.
    And fully understanding this exercise is absolutely important. I will ask things like this in the final.
    It demonstrates remain and change.
    This price, this price will be higher. Why? Because less time, less, less time, less immaturity. That one will be HPR.
    But maybe 8:00 PM.
    I have bought thinking I was gonna get a 5% and the new buyer gets a 5%. How much I should have bought in this year?
    A 5%.
    And if interest rates grow, I will be really, really, really happy.
    We have really, really know I will be happy, more happy than a 5%. I will be happy at 7% for it.
    Yes, there is nothing new in this exercise and in order to finish.
    A three-year coupon bond has face value of 1000, coupons of 80 and a lead to maturity of 8%, yes.
    I’m going to go so, so quick through these exercises.
    Because upset of it, because I have not fulfilled my promise of visiting early. Sorry, Emily, I feel.
    And also I’m going to go do this exercise so, so quick because again it’s the same exercise of the meter.
    This is the same exercise of the group.
    I’m not exactly the same, but it’s the same idea.
    You buy at a you too match rate of 8%. What is the price?
    If the lift maturity is 8%, what is the price?
    How many times do I have asked this question today?
    What is the price?
    Minimation service 123 What is the price?
    I’m getting absolutely nervous because this should be fixed.
    If the lead to maturity is 8%, what should be the price? The coupon rate is 8%, the lead to maturity is 8%. What is the price?
    800,000 is bad. Make sense.
    Now what is the bond reprise?
    What is the future? What is the future value of the bond? If the if you reinvest coupons at the heat of maturity, please, I’m going to write here reinvestment rate. Yes, I’m going to reinvest.
    These coupons this one for one plus 8%.
    If one for this coupon is being paid year one, I’m going to retest in maturity for two years.
    I’m going to replace this for two years.
    I’m gonna reinvest this one for one year, one plus percent.
    Yes.
    And I’m going to have this, yes.
    How much money would I have in the future?
    1259 mutual value if I remiss what I’m going to calculate now the annualizing HPR.
    HPR will be. Let me calculate it. HPRHPR is.
    It’s your value over present value price to 1 / 3 yes -1.
    What should be analyzed this year?
    The giving maturity is 8%. I am reinvesting at the 8% rate.
    Which beer should be?
    Thank you.
    Yes, HPR should be 8%. What if reinvestment rate will be lower than HPR then will be lower. What if reinvestment rate will be higher? HPR will be higher.
    Any sense?
    This exercise.
    It’s the same exercise than the meter, please.
    Please.
    Take today slides.
    Take this class.
    OK, OK, about this one.
    Forget about this one. Thank you. No, sorry, I don’t want to make jokes with me.
    Yes, they talk too.
    Please take this.
    This one not too much.
    Thank you. This one.
    Best.
    Start with this one with the zero components. Try to fully understand this slide.
    Yes. Then second, the bond with coupons. Try to fully understand this slide, this slide, sorry, this seat, yes and then.
    There understanding this one is going to be really important for fully understanding next day. So take this exercise, let me go back. This example absolutely important with zero balls, so simple to understand.
    This example so important, so simple. This is the first one.
    This is the second one you should understand.
    And you understand these two exercises for next week. I will be happy.
    Really happy. Make sense.
    What is the future value? And I have a yes. Any questions? I’m gonna no, no, no before running.
    The more you are in a hurry, the more oh.
    Where are you? I didn’t share with this life with you.
    They’ll serve the flights with you.
    Again, Sir, these are not you.
    The more we’re in a hurry, the more relaxed we should be.
    These are you. Oh, I guess, Sir, this is right with you. I will do it later.
    Bing.
    That is resident.
    And.
    Thank you.
    Thank you.
    Mhm.
    I promise I know how to.
    More with.
    It’s time to run. Thank you very much. An absolutely pleasure.
    Bye.
    Welcome, Leika. If you need, I mean Leika or all of you can you talk in towers? Welcome.