Prof. Lo knows his stuff but as an MIT instructor that is implied. I'm just a retired old wrench twister who is trying to nibble at the education I wish I had acquired many years ago and I'm grateful for the prominent universities for making some of that possible through this platform. Prof. Lo does a remarkable job of explaining the evaluation of markets and how decisions are primarily based on those valuations which is more or less a fancy way of saying follow the money. My one hope as one who has observed what the capital markets have given us over the ages, both good and not so good, is that he can contribute to sending out the leaders and decision makers of tomorrow who will be making those financial decisions, with an instinct to take in more than simply the p/l statement and consider the other consequences of those decisions. People overlooked Arrhenius over a century ago and it's our grandchildren who will inherit those consequences. Thanks again.
This lecture is a time capsule. So interesting to have this level of conversation before Lehman Bros collapsed and to hear about the dead cat bounce when the fed backed Fannie Mae / Freddie Mac. When he describes the forest fire with hidden gas tanks exploding, he exactly predicted how it would unfold in the following year.
Exactly my thoughts! In these lectures he seems to be predicting to a T how the whole crisis went down. Just shows how predictable the whole thing was I guess.
This lecture is really hidden treasure and one of the best MIT product from Professor. Lo. I am amazing how we are lucky. People who are intersted in finance like us ,can learn this kind of high quality lecture through youtube.Whatever this lecture was 11 years ago, it still gives knowledgeable finance theories and how to imply in real world.Thanks to MIT and Prof.Lo.
To the people who say the beginning question and answer session is a waste of time are not really interested in Finance. We are lucky that these lectures take place as the 2008 financial crisis is unfolding. I myself am interested in finance theory because of those times and how the bankers along with SEC, AIG and credit rating agencies fucked over the American people and the global economy.
Absolutely nothing in this video makes me think waste of time. This course actually got me interested in finance to begin with. Since it took place during the recession my interest was sparked because of this. Everyone there in person should be so incredibly grateful that they had Andrew Lo as a professor. I recently purchased his book Adaptive Markets: Financial Evolution at the Speed of Thought and cant wait to read it once it gets here.
Back again to rewatch the series a year after my 3rd pass. Watched these for 4 years now every year and I will keep coming back to this series. Best professor!
After financial crisis 2008..people, institutions, banks, politicians learned a lot about CDS, CDO, MBS etc..unfortunately these students were the product of THE MIT at the time of financial crisis... Andrew Lo is really an influential professor whose got tons of patience.,and trying his best not to answer abt upcoming danger which i think he already knew ..by the way thanx to MIT, and Mr. LO
the most valuable attribute of a wise and knowleageble teacher is simplicity without reductionism. prof Lo is a zen master of finance, he needs to get his own university.
Cant believe how much free education there is today. Thanks MIT. Always wished i could go but I wasnt smart enough when I was younger. Look forward to taking more advantage of opportunities like this thoough!!! Great Teacher btw. Keep up the great work Mr. Lo
@@luisvazquez183 Its a Bitcoin enthusiast thing. Laser focused on seeing Bitcoin make it to $100k per coin. Technically it would only take roughly 1% of the worlds total assets to be allocated to crypto to see that kind of price. XD
Good instructor. Agree, we should use economic tools to solve economic problems and political tools to solve political problems. It seems we sometimes get mixed up and try to use economic tools to solve political problems and vice-versa. Agreed, it is not as simple as letting big institutions and countries fail, because someone else, who may be politically motivated, will step in to bail out if you do not.
Yes, firewall in forest is to keep the wild fire away from extensively engulfing the entire mountain range; on the other hands, applying this theory in financing world is kind vague without an intact "fire wall" to let those "forest" inside the ring to burn off and to keep the rest safe. That's a really interesting Zen to applying in the finance world that I never thought about using firewall theory at all. Excellent idea. But who needs to be blame? Another problem comes up.....STF......
*Any question ever asked* Dr. Lo: “Well, actually we will cover that in lecture 6137”, or “I’m hoping YOU will be able to answer that question yourself by the end of the semester”. 😂 Excellent content, and I’m enjoying the experience, just something I thought was funny.
11:42, I wonder what they edited out and didn’t want us to see or hear? Also weird he always says the interest rate comes from the market. The FOMC controls the short-term rates and can even control longer term rates based on what inflation rate they target and whether they are in QE or QT mode and how aggressive they are.
To students who are confused why PV for perpetually growing cash flow formula doesn't work when r < g When r < g, the terms get bigger and bigger as we move ahead in the series, therfore the infinite series is divergent meaning it does not add to a finite value... While in r > g case, as we move ahead in series the terms get smaller and smaller so it adds to a finite value, hence it's a convergent series.
thank you Mr. Lo. Such crisp and clear explanations. I am to start my MBA in July this year, n so good to have the understanding of basics of finance beforehand.
@@thatoneguy6725 I'm doing my MBA in the best business school in my country. But I'm supplementing my knowledge and understanding with this series of lecture.
- NPV change on currency (do in currency u care) assumption: it changes - risk is hidden (firewalls analogy) - political issues answered with political things, and economy things with economic - with higher interests/discoount, €1 is more valuable -> increasing interest rate, diminishes the NPV (that's why market matters in the mkt interest rate -- it's actionable, not theoretical; market is real) - PV=C/r --> it has 10 discount rate, because it gives 10 on return, so its priced because the return is the discount (it goes in a circle idea(
Warren Buffet sold Delta Airlines pretty close to its bottom shows me that calculating NPV is very difficult to get right, and it probably consists of guesses about guesses or something like that.
At 26:40 I don't fully understand how the values in year 1, 2 and 3 are 86.538, 83.210 and 80.010. I get 86.400, 82.944 and 79.626. Can someone please enlighten me?
That is a stupid question: the type of currency would not have an affect on the NPV. All future cash flows are based of of the initial investment. Unless you changed currency type in the middle of the analysis which would also be a mistake. Even as the professor explained that if there was a deprecation/appreciation of the currency - it may influence the NPV. This is also not true because NPV is relative to the discount rate at the time of analysis and currency rate is taken into consideration upon selecting the appropriate discount rate.
Can someone please help me understand what he meant when he said at 33:50. "If I have a piece of paper that pays 100 dollars a year forever, with a 10% interest rate, how much is that piece of paper"? How does the answer equate to 1000 ? With an interest rate of 5% how is the worth of the piece of paper doubled to 2000?
in addition to the numerical proof inside the lecture, the pv of principal goes to 0 when time goes to infinity. so you dont care about principle but only interest rate implied and coupon.
How do you figure the value of a crypto? Where the USA people can buy them for say $20, but Nigeria is going into hyperinflation, so nobody can afford a $20 item?
Can somebody help me? If u get the interest rate (r) from the market, then is the interest rate always te same for all the agents who want to value an asset?
Remember that we're using convenient abstractions, fictions which only model the real world to a certain degree. But yes, assuming that interest rates are always fixed, and that there is at least one market in existence (meaning that at all times there exists at least one agent willing to borrow money at that market's interest rate), then the price of any asset can be no higher than the future cash flows as discounted by the lowest interest rate that exists. This follows from our axioms - again, useful approximations - that presume (1) perfectly frictionless (free and instant) exchanges, (2) the rationality of economic actors, who would never pay more than the lowest price available.
+FCK YOU So the price can't represent the real value? It just reflects how much the participants think it is?If it's true, there comes another question: how can you see the real value? In another word, can you define real value and find a way to figure it out?
Watch the first lecture. This is it's "real" value. It's monetary value is how much participants are willing to pay for it. If you are talking about intrinsic value you are in the realm of ontology and its somewhat subjective. You also need to think about what you mean by "real". Can some things be more "real" than others. Our society reflects an object's value via the scale of money through the consensus of the market. That scale can be inflated of deflated i.e 1USD measures less than it did 50 years ago but this is due to the amount of goods vs money in circulation. Basically money actually is our attempt to quantify "real"value.
Also interest rate comes from the fact that in lending money (value) or investing the value the participant lending/investing it could be earning money by using this value elsewhere and takes a risk by parting with it and so needs incentive. Also as a borrower/investee, getting value now to payback later itself has value and is reflected in the interest rate, i.e the time value of money. This is still its "real" value, it's simply taking the complexities of the market into account.
The course textbook is: Brealey, Richard, Stewart Myers, and Franklin Allen. Principles of Corporate Finance. 9th ed. New York, NY: McGraw Hill, 2007. ISBN: 9780071266758. There are other readings available. See the Readings section for the list of books at: ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/pages/readings/. Best wishes on your studies!
For a more detailed list of topics covered in this course, refer to the Course Outline by Topic available in the syllabus at: ocw.mit.edu/15-401F08. Best wishes on your studies!
The people that lost the most money are not the ones who benefitted from taking the risks but the unsofisticated homeowner that were prayed on by the same financial institutions that were bailed out.
This is a beginning graduate class. See the course on MIT OpenCourseWare for more info and materials at: ocw.mit.edu/15-401F08. Best wishes on your studies!
Brealey, Richard, Stewart Myers, and Franklin Allen. Principles of Corporate Finance. 9th ed. New York, NY: McGraw Hill, 2007. ISBN: 9780071266758. See ocw.mit.edu/15-401F08 for more info and course materials. Best wishes on your studies!
Prof. Lo, Warren Buffett gets interest rates from the 10 year federal note when valuing a stock. What you think about this? Have you got interest rates from the 10 year federal note?
I wonder how this guy would analyze forex markets. No cash flows, yet there is quantitative information about relative values of the currency "assets" based on supply, demand, and central bank policies
Yup, I didn't expect that although I expected e somewhere in there. Is there a simpler way to find the answer? I took Taylor series of the log of the expression, and its limit got me r. Not that tedious, but didn't seem like an elegant way to solve this.
if r = g that would equal 0 C/0 is and ERROR make a Pearson's Correlation Coefficient Table. Then use the formula for "r" the Pearson Correlation Coefficient see how strong the relationship is between r and g.
(Assuming you're referring to the point when he said that *g > r* leads to a discontinuity.) Sure, zero is a number. But as soon as *r* hits zero, multiplying it by some number *g* has no impact, as *x * 0 = 0* ... leaving us with a final interest rate of *0%* at that point.
Prof. Lo knows his stuff but as an MIT instructor that is implied. I'm just a retired old wrench twister who is trying to nibble at the education I wish I had acquired many years ago and I'm grateful for the prominent universities for making some of that possible through this platform. Prof. Lo does a remarkable job of explaining the evaluation of markets and how decisions are primarily based on those valuations which is more or less a fancy way of saying follow the money. My one hope as one who has observed what the capital markets have given us over the ages, both good and not so good, is that he can contribute to sending out the leaders and decision makers of tomorrow who will be making those financial decisions, with an instinct to take in more than simply the p/l statement and consider the other consequences of those decisions. People overlooked Arrhenius over a century ago and it's our grandchildren who will inherit those consequences. Thanks again.
This lecture is a time capsule. So interesting to have this level of conversation before Lehman Bros collapsed and to hear about the dead cat bounce when the fed backed Fannie Mae / Freddie Mac. When he describes the forest fire with hidden gas tanks exploding, he exactly predicted how it would unfold in the following year.
Crazy, he’s a G0aT
Exactly my thoughts! In these lectures he seems to be predicting to a T how the whole crisis went down. Just shows how predictable the whole thing was I guess.
it was already unfolding when this was recorded..
@mclaren720 no it wasn't, they were still talking about saving lehman bros
This lecture is really hidden treasure and one of the best MIT product from Professor. Lo. I am amazing how we are lucky. People who are intersted in finance like us ,can learn this kind of high quality lecture through youtube.Whatever this lecture was 11 years ago, it still gives knowledgeable finance theories and how to imply in real world.Thanks to MIT and Prof.Lo.
If you're not interested in the Q&A session, you can skip to 21:20 to jump straight to lecture 3.
Life saver
Time saver! Thanks
hero
ughhhh twas grinding my gears
Views are dropping with each lecture. If you made it this far, keep going bro.
We got this buddy.
Mr.Lo's class is very informative. This is a classical MBA finance class.
To the people who say the beginning question and answer session is a waste of time are not really interested in Finance. We are lucky that these lectures take place as the 2008 financial crisis is unfolding. I myself am interested in finance theory because of those times and how the bankers along with SEC, AIG and credit rating agencies fucked over the American people and the global economy.
Absolutely nothing in this video makes me think waste of time. This course actually got me interested in finance to begin with. Since it took place during the recession my interest was sparked because of this. Everyone there in person should be so incredibly grateful that they had Andrew Lo as a professor. I recently purchased his book Adaptive Markets: Financial Evolution at the Speed of Thought and cant wait to read it once it gets here.
Back again to rewatch the series a year after my 3rd pass. Watched these for 4 years now every year and I will keep coming back to this series. Best professor!
13:00 Helicopter and firewall analogy for the 2008 financial crisis
19:15 Look at muti-perspectives: social, economical, political, etc.
Q&A till 21:10
Thank !you
Tysm
one of the best channels on you tube, thank u from the bottom of my heart❤
After financial crisis 2008..people, institutions, banks, politicians learned a lot about
CDS, CDO, MBS etc..unfortunately these students were the product of THE MIT at the time of financial crisis... Andrew Lo is really an influential professor whose got tons of patience.,and trying his best not to answer abt upcoming danger which i think he already knew ..by the way thanx to MIT, and Mr. LO
Man.. after the 2022 crisis honestly this guys teachings still hold true. True power to the people. GOAT
no words...best professor i have ever seen..thanks a lot Andrew Lo sir
krishna kishore
the most valuable attribute of a wise and knowleageble teacher is simplicity without reductionism. prof Lo is a zen master of finance, he needs to get his own university.
Thank you very much for these lectures, MIT and Professor Lo.
Excellent class and superb teacher! Wish I could get into Sloan! Thanks MIT for putting it on RUclips!
Cant believe how much free education there is today. Thanks MIT. Always wished i could go but I wasnt smart enough when I was younger. Look forward to taking more advantage of opportunities like this thoough!!!
Great Teacher btw. Keep up the great work Mr. Lo
@@luisvazquez183 Its a Bitcoin enthusiast thing. Laser focused on seeing Bitcoin make it to $100k per coin. Technically it would only take roughly 1% of the worlds total assets to be allocated to crypto to see that kind of price. XD
Good instructor. Agree, we should use economic tools to solve economic problems and political tools to solve political problems. It seems we sometimes get mixed up and try to use economic tools to solve political problems and vice-versa. Agreed, it is not as simple as letting big institutions and countries fail, because someone else, who may be politically motivated, will step in to bail out if you do not.
As a general principle, the public likes simple solutions for almost every issue, when actually every issue is unimaginably complex, even intractable.
Yes, firewall in forest is to keep the wild fire away from extensively engulfing the entire mountain range; on the other hands, applying this theory in financing world is kind vague without an intact "fire wall" to let those "forest" inside the ring to burn off and to keep the rest safe. That's a really interesting Zen to applying in the finance world that I never thought about using firewall theory at all. Excellent idea. But who needs to be blame? Another problem comes up.....STF......
No other course on Finance anywhere on the internet comes close to this. 10/10
top university, top professor, top learning experiences, just straight to success. I want to mit
what is going on? are u there?
Watching this lecture after recently reading Stress Test is very insightful. Mr Lo comes across as very prescient.
*Any question ever asked*
Dr. Lo: “Well, actually we will cover that in lecture 6137”, or “I’m hoping YOU will be able to answer that question yourself by the end of the semester”. 😂
Excellent content, and I’m enjoying the experience, just something I thought was funny.
I thought the same thing as I am just finishing the 3rd class…like WTF man.
"If Lehman Brothers go under..." hah
Yes, need to catch up with what AL said the prerequisite preparation in the lecture. That's it
@@arrowb3408 you failed to understand comment i guess
11:42, I wonder what they edited out and didn’t want us to see or hear? Also weird he always says the interest rate comes from the market. The FOMC controls the short-term rates and can even control longer term rates based on what inflation rate they target and whether they are in QE or QT mode and how aggressive they are.
To students who are confused why PV for perpetually growing cash flow formula doesn't work when r < g
When r < g, the terms get bigger and bigger as we move ahead in the series, therfore the infinite series is divergent meaning it does not add to a finite value...
While in r > g case, as we move ahead in series the terms get smaller and smaller so it adds to a finite value, hence it's a convergent series.
10:30 Lo predicted 2008's crash
I think it's very interesting to hear the Q&A I think it adds a lot
thank you Mr. Lo.
Such crisp and clear explanations. I am to start my MBA in July this year, n so good to have the understanding of basics of finance beforehand.
did ya get that MBA?
@@thatoneguy6725 I'm doing my MBA in the best business school in my country. But I'm supplementing my knowledge and understanding with this series of lecture.
same@@twinprime
- NPV change on currency (do in currency u care) assumption: it changes
- risk is hidden (firewalls analogy)
- political issues answered with political things, and economy things with economic
- with higher interests/discoount, €1 is more valuable -> increasing interest rate, diminishes the NPV (that's why market matters in the mkt interest rate -- it's actionable, not theoretical; market is real)
- PV=C/r --> it has 10 discount rate, because it gives 10 on return, so its priced because the return is the discount (it goes in a circle idea(
Excellent Professor Lo. I hope to see your name on the Nobel Economy Laureate for next year.
I hope the same
Warren Buffet sold Delta Airlines pretty close to its bottom shows me that calculating NPV is very difficult to get right, and it probably consists of guesses about guesses or something like that.
As for cnooc calculation,why the interest is being deducted from borrowing base, its not mentioned that this is a discount.
Brilliant explanation! Thank you, Andrew Lo and MIT
49:07-
55:10-How
1:04:50-Mortgage Payment , Loan Payment
At 26:40 I don't fully understand how the values in year 1, 2 and 3 are 86.538, 83.210 and 80.010.
I get 86.400, 82.944 and 79.626. Can someone please enlighten me?
90000/(1.04) instead of 90000*0.96
This course is awesome.
That is a stupid question: the type of currency would not have an affect on the NPV. All future cash flows are based of of the initial investment. Unless you changed currency type in the middle of the analysis which would also be a mistake. Even as the professor explained that if there was a deprecation/appreciation of the currency - it may influence the NPV. This is also not true because NPV is relative to the discount rate at the time of analysis and currency rate is taken into consideration upon selecting the appropriate discount rate.
Andrew Lo is a boss
Can someone please help me understand what he meant when he said at 33:50. "If I have a piece of paper that pays 100 dollars a year forever, with a 10% interest rate, how much is that piece of paper"? How does the answer equate to 1000 ? With an interest rate of 5% how is the worth of the piece of paper doubled to 2000?
c/r = 100 / .1 = 1000. if interest rate goes down to .05, then the pv of perpetual fixed income securities is doubled to 2000. you correct
in addition to the numerical proof inside the lecture, the pv of principal goes to 0 when time goes to infinity. so you dont care about principle but only interest rate implied and coupon.
the "Consol bond" ended in 2015. So much for forever
Thank you Mr. Lo, I have known the perpetuity and other before, but I never got a clear explanation as what you do.
What is practical application for understanding these concepts for normal individual
Conspicuously clear session
note to self, perpetuity is a convergent power series, hence finite.
37:48 can somebody tell me what is the answer , (the question is how to calculate the price if we have the ''r''), it is 5% am i right?
It must be 20% right? (1/5)*100
How do you figure the value of a crypto? Where the USA people can buy them for say $20, but Nigeria is going into hyperinflation, so nobody can afford a $20 item?
33:09 yes sir we did it and sum of all integers is 1/12 using that trick
do u want to work with me through this course?
@@sparshgupta4077 yes I am
@@himjanand2034 I'd like to
Gold is not an asset? has no CFs... tallking what is said in minute 24 :30sh
is there anyone who has access to "Principles of Corporate Finance" 9th edition ? Please let me know where can i get this edition 🙏
Can somebody help me? If u get the interest rate (r) from the market, then is the interest rate always te same for all the agents who want to value an asset?
Remember that we're using convenient abstractions, fictions which only model the real world to a certain degree. But yes, assuming that interest rates are always fixed, and that there is at least one market in existence (meaning that at all times there exists at least one agent willing to borrow money at that market's interest rate), then the price of any asset can be no higher than the future cash flows as discounted by the lowest interest rate that exists. This follows from our axioms - again, useful approximations - that presume (1) perfectly frictionless (free and instant) exchanges, (2) the rationality of economic actors, who would never pay more than the lowest price available.
@@asherreich9820 The Law of One Price...right?
Interest rate comes from the market. How do you pick it?
+Lin Cha market pricing determines the interest rates, auctioned by the market participants (by professionals who know what they're doing).
+FCK YOU So the price can't represent the real value? It just reflects how much the participants think it is?If it's true, there comes another question: how can you see the real value? In another word, can you define real value and find a way to figure it out?
+Lin Cha Interesting questions, I'd recommend that you look for this course professor email and hope for an answer.
Watch the first lecture. This is it's "real" value. It's monetary value is how much participants are willing to pay for it. If you are talking about intrinsic value you are in the realm of ontology and its somewhat subjective. You also need to think about what you mean by "real". Can some things be more "real" than others. Our society reflects an object's value via the scale of money through the consensus of the market. That scale can be inflated of deflated i.e 1USD measures less than it did 50 years ago but this is due to the amount of goods vs money in circulation. Basically money actually is our attempt to quantify "real"value.
Also interest rate comes from the fact that in lending money (value) or investing the value the participant lending/investing it could be earning money by using this value elsewhere and takes a risk by parting with it and so needs incentive. Also as a borrower/investee, getting value now to payback later itself has value and is reflected in the interest rate, i.e the time value of money. This is still its "real" value, it's simply taking the complexities of the market into account.
What about an interest free economy?
These MIT students are towering geniuses that I could never even comprehend.
price return and return, whats different exactly? got lost
How can I access the problems and questions that mr. Loo mentioned
The course materials are available on MIT OpenCourseWare at: ocw.mit.edu/15-401F08. Best wishes on your studies!
where can i get the maths problems from this course
Any of the materials that we have for the course are available on MIT OpenCourseWare at: ocw.mit.edu/15-401F08. Best wishes on your studies!
@@mitocw thank you
Very good instructor!
Whats the nam4 of the book prof leo keeps mentioning
The course textbook is: Brealey, Richard, Stewart Myers, and Franklin Allen. Principles of Corporate Finance. 9th ed. New York, NY: McGraw Hill, 2007. ISBN: 9780071266758. There are other readings available. See the Readings section for the list of books at: ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/pages/readings/. Best wishes on your studies!
Omg😮 thnk you 🎉😅😊 I cant belive mit replied to me ❤❤❤
Actual class starts at 21:15
Actual learning starts at 0:00
Did he assign any readings this time around? If so I must've missed it
For a more detailed list of topics covered in this course, refer to the Course Outline by Topic available in the syllabus at: ocw.mit.edu/15-401F08. Best wishes on your studies!
Maybe the textbook by Brealey, Myers and Allen
Is it legal carry out my own auctions?
The answer to the last question is e^r?
it's e^r - 1
questions stop at 21.15
AUDIENCE: [INAUDIBLE].
Andrew Lo: That's a great question!
WTF MIT
The people that lost the most money are not the ones who benefitted from taking the risks but the unsofisticated homeowner that were prayed on by the same financial institutions that were bailed out.
Is it an undergraduate course lectures or MBA? If it is MBA then these are very basic...I guess.
This is a beginning graduate class. See the course on MIT OpenCourseWare for more info and materials at: ocw.mit.edu/15-401F08. Best wishes on your studies!
1:07:10 Explication de chaque constante
slide 22, (31:06), wait, isn't this day to day job?
Does anyone know the textbook he is talking about?
Brealey, Richard, Stewart Myers, and Franklin Allen. Principles of Corporate Finance. 9th ed. New York, NY: McGraw Hill, 2007. ISBN: 9780071266758. See ocw.mit.edu/15-401F08 for more info and course materials. Best wishes on your studies!
@@mitocw thank you I appreciate it
Prof. Lo, Warren Buffett gets interest rates from the 10 year federal note when valuing a stock. What you think about this? Have you got interest rates from the 10 year federal note?
Prof Lo is so high up there in academia, it would be a miracle if he even looked at this comment section, let alone someone's comment.
I wonder how this guy would analyze forex markets. No cash flows, yet there is quantitative information about relative values of the currency "assets" based on supply, demand, and central bank policies
Cant believe I am watching MIT Sloan class while riding a bus.
19:56 Tell that to you-know-who
Problem and solution for Cooperate financial. Can we get a Download link for that ?
for the sake of free education.
we don't have free education in finance
old comment, but some problems and solutions were uploaded on the course page on mit ocw
Are these MBA students or undergrad?
By the number of likes, I can judge attendance rate goes down like crazy: 2k, 800, 380
anybody want to work with me through this class?
yes we can work on it
Sure!
Pretty informative and an excellent faculty teacher
Awesome stuff, MIT!
bookmark
37:05
(1+r/n)^^n when n go to infinite converge to e^r
exponential interest is used in option interest rate
Yup, I didn't expect that although I expected e somewhere in there.
Is there a simpler way to find the answer? I took Taylor series of the log of the expression, and its limit got me r. Not that tedious, but didn't seem like an elegant way to solve this.
"every now and again, you get your face ripped off." LAWL
if r = g that would equal 0 C/0 is and ERROR
make a Pearson's Correlation Coefficient Table. Then use the formula for "r" the Pearson Correlation Coefficient see how strong the relationship is between r and g.
r cannot equal g, as it's specified to be larger, r>g
36:27 he predicted the future.
I am also very much interested in MIT COURSE FROM RUclips
I love how at this point interest rates across the entire curve are headed straight to 0. 😂😂😂
THANKS FOR
AWARENESS
Isn't zero a number?
(Assuming you're referring to the point when he said that *g > r* leads to a discontinuity.) Sure, zero is a number. But as soon as *r* hits zero, multiplying it by some number *g* has no impact, as *x * 0 = 0* ... leaving us with a final interest rate of *0%* at that point.
wow theres a talk about leman brothers :D
Well session
Good Lecture!!
Fun fact:
Mr.Lo starred in the Big Short.
Super informative video.
Slide 24 has error...second formula should be continous sum
that was great! thanks prof. Lo!
1:30
This is really awesome sessions!
do u want to work with me through this course
Ok, now we need to learn calculus in a MBA program
1:04:15
so many qustions.