NYU | March 16, 2026
Instructor: Luis Garvía Vega
Duration: 1h 12min
The class begins revisiting market efficiency.
Key idea:
Markets react to new information.
When information appears:
Therefore:
\[\text{Efficient Market} \Rightarrow \text{Prices reflect information}\]However:
In reality there is constant new information, so markets are never perfectly efficient.
If prices do not fully reflect information:
Two concepts appear:
Arbitrage is:
Formally:
A trading strategy with no initial cost, no risk, and positive profit.
This is sometimes called:
“Free lunch.”
In reality:
Therefore:
In practice, arbitrage often means exploiting temporary price differences.
The class briefly discusses LTCM (Long-Term Capital Management).
Important points:
They generated extraordinary returns for several years.
But:
Lesson:
Even sophisticated arbitrage strategies can fail.
The professor introduces the myth of Icarus.
Story:
Interpretation:
Good ideas become dangerous when taken too far.
In finance:
can lead to collapse.
The professor gives a warning about AI in education.
Analogy:
If someone asks you to run 10 kilometers,
but you take a car instead,
you did not train.
Similarly:
Using AI to solve exercises without thinking means:
you skip the intellectual training.
University learning is like mental exercise:
There is a key relationship:
\[\text{Market Efficiency} \Leftrightarrow \text{No Arbitrage}\]If arbitrage opportunities exist:
Therefore:
Arbitrage activity makes markets efficient.
A fundamental principle in finance:
Two assets with the same future payoff must have the same price today.
If not:
\[\text{Arbitrage Opportunity}\]This principle is called:
Law of One Price
Two securities:
| Security | Price | Future Payoff |
|---|---|---|
| CAT | 94.34 | 100 |
| TIGR | 95.24 | 100 |
Both pay 100 in one year.
But prices differ.
1️⃣ Buy the cheaper security
2️⃣ Short sell the more expensive one
Cash flows:
Today:
\[+95.24 - 94.34 = 0.90\]Future:
\[-100 + 100 = 0\]Result:
Immediate profit of 0.90 with no risk.
If many investors exploit this:
Prices converge.
Arbitrage disappears.
If transaction costs exist:
Arbitrage may disappear.
Example:
Then:
\[\text{Arbitrage not profitable}\]Therefore:
transaction costs create a range of prices where arbitrage does not occur.
Given:
Zero-coupon bonds:
| Maturity | Price | Payoff |
|---|---|---|
| 1 year | 98 | 100 |
| 2 years | 96 | 100 |
| 3 years | 93 | 100 |
We want to price:
| Year | Cash Flow |
|---|---|
| 1 | 10 |
| 2 | 10 |
| 3 | 110 |
We replicate each cash flow using zero-coupon bonds.
To get:
Year 1 → 10
Year 2 → 10
Year 3 → 110
We buy:
Therefore:
\[\boxed{Bond\ Price = 121.7}\]Using zero-coupon bonds we can calculate spot interest rates.
Formula:
\[r = \left(\frac{FV}{Price}\right)^{1/T} - 1\]Approximate rates:
| Maturity | Spot Rate |
|---|---|
| 1 year | ~2.0% |
| 2 years | ~2.06% |
| 3 years | ~2.45% |
Plotting these rates creates the yield curve.
The yield curve shows:
\[Interest\ Rate \quad vs \quad Maturity\]It represents the term structure of interest rates.
The curve changes every day based on bond market prices.
The bond price can also be calculated using present value:
\[Price = \frac{10}{(1+r_1)} + \frac{10}{(1+r_2)^2} + \frac{110}{(1+r_3)^3}\]Using the spot rates produces the same price:
\[121.7\]If the bond were trading at 100 instead of 121.7:
Arbitrage strategy:
1️⃣ Buy the underpriced bond
2️⃣ Short the replicating portfolio
Result:
Risk-free profit.
Example:
Using arbitrage we can derive the price of a 2-year zero-coupon bond.
Result:
\[Price = 96.04\]This uses:
\[PV = \frac{100}{(1+r_1)(1+f_{1,2})}\]where (f_{1,2}) is the forward rate.
Next class will focus on:
16 de marzo de 2026, 5:05p.m.
1 h 12 min 43 s
Yeah.
You’re gonna start with arbitrage. Do you?
Do you remember about the PCM market hypothesis?
Efficient market hypothesis. Do you remember a little?
What if it’s a market? I thought that it has to do with what?
When a market, what is a fee? What does efficient mean?
What are we talking about when we talk about the market efficiency?
Absolutely. Information is the word I was looking for. Information is the word I was looking for here.
Here I know, so let me take.
Number 8.
This one, it has to do with information, yes.
We show market efficient technologies. We are not going to talk, not going to ask.
That I know anything regarding my the pieces, so I can tell you.
But the deal market efficient has to do with new information.
There is new information, the one that respect this.
Will use the information and once.
See use information. The advantage will disappear. Market will be efficient. Make sense. So market is efficient.
Any new information?
And market moves in order to take this information. So why there is new information market is inefficient while there is new information?
The world we are living on.
There are tons of new information everything. So at the end point is not always efficient. It’s not efficient. The point we see play with the information. Make sense.
U The I
So on one hand.
What happened?
If there is new information, if there is a lack of information.
How are we going to call it? 2 names, 2 names we are going to give to the lack of information, yes.
One name will be inefficiency, a market inefficiency.
And another name will be an arbitrage.
Are we drugs? What is arbitrage?
Is taking advantage of market inefficiency is taking advantage of new information.
But that we’re going to today.
What is the name of today’s class?
Are being tracked, yes.
RV drugs.
So.
Today’s class we will deal with three things at the same time, yes.
We will deal with three things at the same time.
First idea, first idea we are.
Do you it with not efficiency?
We are continuing with market efficiency, yes.
Take one idea when we talk about arbitrage itself.
But their idea and the most important idea.
Next class, next class. The name of next class will be fixing on one day we will.
Talk of bonds. They will will see again how to get the price of a bond. So their idea is go back the winter, think about the bond exercise.
And again, we will review today is how to calculate the price of a bond, how to deal with bond with coupons and all this stuff make sense.
No.
Let me start. No problem.
OK, Arabi trucks. What is Arabi trucks?
We are going to see today’s 3 examples how to apply your methods and what is the idea?
RV drugs. These are free drugs.
These are free lunch in here.
Here is a prelats practice.
Practice.
Careful, careful when talking about permittance in theory.
In theory, arbitrage is getting again, getting again without assuming risk.
It’s again due to a market mismatch, so it’s again without risk.
Practice. Is it possible? Is it possible? Yes, it is. And also there will always be, so in theory.
It’s a game without risk. In practice, careful with miracles. Those miracles exist, but there will always be risk. But because we cannot foresee all things because life is great, because life is a miracle because.
Jerry, I can say things, but in practice let me let me start with one example that is out of the scope of this course, but I want to show you this example.
Did I talk about the long term Capital Management Fund when talking about market efficiency? I don’t remember if I am saying this, this is the second time.
I am saying this with you.
Please forgive me.
Southern capital in Mexico.
What is the idea of this? Oh, this is sorry, whatever this is in Spanish, but you can you can Google for English version of of this.
Who is souls?
Don’t have you heard about it, the back end source formula?
One formula that rules is a formula in order to calculate the price of of options, yes.
And both. Mr. Black is not here, but Black Source American were the creators of the Black and Source formula. And because of that, they received Nobel Prize. Yes. What is the idea of this phone?
They put freely intelligent people in order to manage money in order to do fixed income arbitrage, yes.
In order to do fixed income arbitrage.
And look the phone, yes.
They spend 1234 year, four years doing things. Incredible. Well, yes, incredible. Incredible. Well.
Well, and after four years, there was a big collapse in Russian markets. They didn’t expect this collapse.
And they were close to.
Oh, they use everything. Make sense.
What I’m talking here about, I’m talking about Icarus. Have you? Do you know Icarus Leyen?
Oh, this is again. Yes, this is again, yes.
Do you know the story of Icarus? Minotau.
There were two people, one father and one son, who went out of the.
Who is out of there?
Of the maze. They were inside the maze and they got a lot and Icarus went of the maze by putting.
Robe and follow in the room. Yeah, once they went out, they put.
They make wings with with wings, with wax, with wax, and what they do as Icarus is don’t get too close to the sun because if you get close to the sun, all the wings will melt.
went close to the sun.
Hi.
All the wings, yes. What is the idea? Careful with good ideas and trying to approach humans to the sun or to ghost or to try to go.
Do we now have something to make us fly?
And we use this match. We can feel warm. The sun is there and we can think, oh, we are like goats.
Is there AI there? Careful with approaching to match the side because arbitrage happens and you cannot have free branches for them.
You can have a free lunch one day, a free lunch two days, but.
You use AI without thinking, your wings will match. Make sense. What I’m saying is absolutely important. Absolutely important. Why? Because.
Because you are now in the university.
And what we are living nowadays with AI is crazy.
Did you connect? Love? You think so?
Come from all the exercises I am praying you to do.
I’m sure that most of the exercises I tell you to do or other teachers tell you to do can be immediately solved with a problem, yes.
Imagine that I tell you to run 10 kilometers. You know the exercise. You take a car instead of running by yourself.
You understand what I’m saying? No, I don’t want.
What is the point? What I want to tell you and this is absolutely important to understand.
The quarantine bean at university. The quarantine bean at university is not doing a lot of things.
Great. The point is doing small little things, routinely and making all these little things up.
The point is not be doing oh, I have prepared things, then then works. Oh, I have prepared 100 slides. With AI you can do it in seconds. The point is just doing things by yourself.
I repeat, I repeat, I repeat, I repeat same as push ups, same same as going to the gym at the end is mental exercise and also and also juicy a lot AR.
I will do. I will be using AI.
All the day.
Do you know why I why I am not using more AI? Because I don’t have time.
Like being the whole day using a day.
So, so arbitrage in finance theory and arbitrage is.
Define NASA 0 investment trading strategy that generates generates as soon profit.
No initial investment, no negative cash flows, a positive cash flow at some point, lower 3 lakhs without risk.
A certain game without risk and without investment.
Yeah.
OK, on Wall Street, arbitrage also often means.
What I have told you taking advantage of new information. If you take advantage of new information, you are assuming risk at.
Whatever. And so this at the end, careful because you can lose a lot of money with every tax.
And this is.
The name of the game that I have played with you when talking about market additions.
If there is an arbitrage opportunity.
The one that detective will get again will make market efficient efficient. So if there is an arbitral opportunity, someone will detect it will make market efficient, will make the arbitral opportunity disappear.
And MAR and arbitrage opportunities will not exist.
Makes sense.
I told you we’re talking about market efficiency with technical analysis and fundamental analysis and value investment.
Does it work or not? And what I told you is because it works, because technical analysis works, it doesn’t work.
Because it works. Because you can make money. Thanks to all these people making money, markets tend to efficiency in the week. Make sense.
So at the end, at the end.
This one one second. Talking about market efficiency, talking about a market that is efficient is the same as saying that no arbitrage is possible. Market efficient hypothesis is the same as.
No Rd. grads.
Congrats.
Condition. Yes, are the efficient hypothesis is equivalent to no arbitrage condition.
What are we going to do today? We are going to use the no arbitrage condition in order to calculate price of securities in order to calculate price of homes.
OK.
Tater 3 letters and at the end there is just one.
So important and so simple, two different securities will have same payoffs in the future.
These two securities should have same price.
So talking about.
The no work in France condition is same as talking about the law or of law of one price, same payoffs, same payoffs, same price and if not.
I mean drugs.
There are different we are going to see with three examples. Also due to the law of one price, we will be able to calculate the replicant portfolio, replicant portfolio and also then.
We will see that because of the low of what price, we can also calculate price of deliver. We are not going to use this deal.
This last statement in the end of the course when talking about the regards.
Now what we will do is now what we will do is just a quick sound, yes.
We are going to do 3 examples, one regarding the law of one price. This first example will be a warm up and we will see.
The example, the one that I want you to fully, fully understand and to repeat. And finally we will see one example.
We will proceed quickly, but I will not care too much about the last example, yes.
No.
So let me start with the highlights. Yes, cats and tigers.
Please.
These securities, these two securities.
This to exist.
CADS stands for a Certificate of Accurate Dressery is A and Tigers. I don’t know what Tiger.
I think I mean especially something regarding Christmas.
Where where are we straying you?
Treasury investment growth receipts. This is the planning for that. But what I want you to understand, what is a cat or what is a tiger? A zero upon bond.
Just a serum combo, yes, and the price of cats.
Is 94 going.
34 and the price of tigers is 95.24.
Make sense?
How much I’m going to get within a year by buying one or the other, I will get 100 yes.
I will get 100. I pay today. How will you calculate the deal of these two goals?
The yield is written there, 6%.
5% and present value is equal to future value over 1 + R rise to one yes.
So the yield is 5% games by with HBR.
Mutual value over present value. Hi, Jessica.
So 94.3495.24 makes sense.
Tell me yes.
Right here, each numbers are 4.24 and 5.24.
And take I’m going to get 100 a year, yes, take that.
This is.
It’s two separators. Make sense.
OK.
Here there is an arbitrage opportunity. How can we take advantage of this arbitrage opportunity?
How can we take advantage?
But talking about arbitrage, always we will buy the cheapest and we will send, we will sell the most expensive one. Yes, so.
So what I’m gonna do?
I’m gonna buy.
Want to buy one of these? Yes. So if I buy one of these, money goes out of my pocket. Yeah.
It.
I please.
Hello.
Yes, I’m gonna buy one of these.
So if I pay 94, I will get 100 within a year. Make sense?
And on the other hand, what I will do, I will sell one of these. If I sell this, this 95 comes into my pocket, yes.
95 comes out of my pocket. How much should I pay in a year? Negative 100 I can receive today. 95 in one year I will get the 100, yes.
What I will do?
What I will do, I will just send these cash flows. Yes, I send these cash flows.
And what I get today, I will get $0.90.
4/3.
Yep, to supply and demand law.
You remember the supply in the Mongo?
Well, the man look, you remember it.
What will happen with this price?
If a lot of people start buying it.
They will go up. What will happen with this price if a lot of people start selling it?
Rise will go down. Make sense what I’m proposing you to do by this to serve this. So a lot of people start doing this thing. What is going to happen with the arbitrage opportunity?
That it will disappear. Make sense? Those who will take this quickly will get the beginning $0.90 and then later this will tend to 0.
Make sense?
Or will you pay money? Bye.
Finding this.
I’m shorting this.
OK, suppose there are two that was paying 100 in one year. Yes, the price. How do arbitragers exploit the price difference? I’ve already.
Next step. Next step.
What about what if there are transaction costs?
But if there are transaction costs, there will be there are transaction costs for buying or selling. I need to pay a fee.
There will be one point that the fee will be higher than the gain I will get, so it will not make any sense to play arbitrage. Make sense.
Make our reference 2 our reference. Make sense.
For example, in this same example, both better, we still have a tiger. The cost of shorting is $1.00.
If the cost of shorting is $1.00, will it make sense?
To do to Will it make sense to pay $1.00 in order to to get $0.90? So this will make the arbitration opportunities appear.
What are the highest and lowest possible prices of tiger product to catch that prevent arbitrage? The difference is $1.00 Yep. And then what is the cost of shorting is $0.50 and the cost of buying is $0.50?
Save.
Make sense?
Stop.
First example.
What did I tell you regarding the first example? But I don’t care too much about the first example and he’s working with zero compound one time, so it’s simple.
Why did I call you regarding the second example?
That is the most important example exercise we are going to, we are going to see, we are going to do today. Makes sense.
So what do I need?
I have 3 serum compounds with.
Three different materials.
Thank you for what year?
If I pay 98 in one year.
I will get 100 if I pay.
96 three years I will get 100.
I’m good.
Make sense?
E.
One year, two years, and three. Any sense?
If I pay 98, I will get 100. If I pay 96, I will get 100. If I pay 93, I will get 100. Make sense.
What can I complete?
I can calculate the yields, the HPR of this year composed, yes, and analyze the HPR. What is the return that I will get? The yearly return that I will get?
For one year, for two and for three. Make sense.
And then.
Knowing this, I’m considering the arbitrage condition.
What must be the price?
What must be the price of a three-year annual cucumber?
These are 10% coupon rate and a free value of 100. Make sense.
Let me look for blue.
What is the price?
Yes, when they try so a born with.
10% of.
I am going to let you 3 minutes in order to write the cash flows of this ball. Yes, to write the cash flows, future cash flows, yes.