the following content is provided under a Creative Commons license your support will help MIT OpenCourseWare continue to offer high quality educational resources for free to make a donation or to view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu these are the financial highlights of Lehman Brothers as of the end of 2007 now you can get more recent hilum from looking at their SEC filings their 10k and 10-q S which are accounting reports that they provide to the SEC on a quarterly basis but I just thought we'd take a look at the annual financials of this business at the end of 2007 the net revenues for Lehman Brothers was 19 billion dollars this is a firm that earned 19 billion dollars in revenues in 2007 we're not talking about a little small little shop here this is a major financial institution and if you look at their their profits their net income four billion dollars of net income in 2007 and 2007 was not a great year so four billion dollars of income is a pretty impressive number and if you look at their long-term capital the capital base we're looking at a hundred and forty five billion and if you take a look at their their assets under management the assets under management in billions is two hundred and eighty two billion dollars of assets under management now at the end of night 2007 would anybody have forecasted that a company like this could be gone nine months later gone I mean just obliterated twenty eight thousand five hundred employees so we're talking about major disruption to the New York workforce a number of people are going to be looking for jobs now a number of jobs are going to be created as you know a consequence of these dislocations I'll come to that in a minute but this is an extraordinary set of events and one key to what's going on and why this might have happened is this number right here the net leverage ratio that net leverage ratio tells you something about how much exposure Lehman Brothers had relative to how much capital they're actually managing and let me give you an example of what I mean by that and I'm going to give you a personal example they're going to come back to we talked about mortgages last time and I told you all that you got now had the power to compute mortgage payments well you know that a mortgage is a loan right you're borrowing money from the bank to buy this beautiful home that you want to live in does anybody know how much money you typically have to put down when you buy a home yeah 20% is the typical number although in recent years it's much less than that for example when I first bought my home way back in 1988 my first home when I moved here to Boston I actually only had to put 5% down because I was able to get a jumbo loan and in addition purchase mortgage insurance so that the bank was willing to lend me quite a bit more than they usually would now let's take the 20% down as the standard number because that is absolutely industry standard if you put down 20% for let's say a $500,000 home which in the Boston area is a little starter home I'm afraid a half a million dollar home you put down $100,000 and the bank lends you $400,000 the value of your total assets is of course five hundred thousand right you've got a hundred thousand of your own money four hundred thousand of the bank's money and with that five hundred thousand you give it to the other party to buy the home and now you are the happy owners of a five hundred thousand dollar home what kind of leverage ratio do you have in that circumstance anybody calculate that quickly close but no cigar five to one right five to one in the sense that you have five times leverage your total exposures 500 you've got 100 it's five to one now what does that mean five to one leverage that sounds scary that sounds like you are really levered up well it's only scary if the value of the assets swings around a lot for example let's do a simple back of the envelope calculation suppose house prices fall by ten percent that's only ten percent right that's not a huge number it's significant but it's not huge what's the return on your investment how much have you invested in the home hundred thousand dollars if the value of the home falls by ten percent how much has the value of your assets fallen by fifty thousand right of that fifty thousand how much does the bank lose none right because they've lent you money and they expect you to pay it back they're not equity holders they're not looking to take on any downside risk they just want their money back with interest so the bank doesn't care what the value is they still expect you to pay back their hundred thousand the four hundred thousand dollars that they lent you with interest so that 50 thousand dollar loss it's all yours and you put down a hundred thousand and you've lost 50 half of your assets just got wiped out with only a ten percent move in the value of the home now instead of putting twenty percent down as a standard what if you did what I did which is you put down five percent so five percent of five hundred thousand dollars is $25,000 right the bank lends you four hundred and seventy-five thousand so this is not a conforming loan it's say you've got to buy insurance and it's subprime so on and so forth five percent is your investment twenty five thousand dollars now suppose housing prices go down 10% what's the return on your capital well you've lost everything right the $50,000 loss is still there but you only put in 25 so you've now lost all of your capital and on top of that you're in the hole for another 25 so you've actually lost not only all of your wealth but actually you've lost more than all of it you've lost minus 100% of your wealth or your total return your net return is minus 200% so if you're a major financial institution and you're leveraged 16 to 1 and the value of that portfolio declines by 10% or 20% you can go through capital very very quickly now let's do a back-of-the-envelope the amount of capital that they have let's go up and take a look at this the amount of capital that Lehman had is something like total long-term capital 145 billion okay if you leverage that 16 to 1 and then you ask the question with that leverage amount of capital if it drops by I don't know 10% 5% 7% of that total asset base you can see how you can go through 105 billion of capital pretty quickly with leverage now you might ask why on earth would anybody do this why would you leverage 16 to 1 well why would anybody buy a house in New England with 5% down that's just as crazy what's the leverage ratio if you put 5% down 2020 so I was a proud leveraged investor that had 20 to 1 leverage I beat Lehman Brothers why would I do that is that insane well yeah well yes I that's a that's a very polite way of saying it yes I would tie up too much capital if I didn't do that the fact they didn't have the capital so so thank you for being kind but but why wasn't it nuts yeah exactly if the value goes up then I earn that kind of money those same kind of money though so if housing prices go up by ten percent then at twenty to one leverage I look like a hedge fund manager right make a ton of money but that's not the only reason that I'm willing to do that because you're saying that I want to take that risk what if I why would I do that yeah Michael why exactly the risk of 20 to one leverage is only a risk if the amount of housing price fluctuation is such that it could actually wipe me out but up until very recently housing prices have done nothing but this they've gone up and not only have they gone up they've gone up in a very smooth and orderly fashion you know if house prices went up by fifteen percent a year every year you might be thrilled but also a bit scared that's not what happened housing prices have gone up maybe I don't know eight percent ten percent seven percent five percent six percent it's been relatively smooth and so the volatility the volatility of those kinds of investments were low enough that the leverage didn't scare me at all and in fact I didn't lose money I held that house for about you know five or six years and bought another one and and it was fine it was fine because that kind of leverage is not a problem as long as the volatility of the of the overall investment wasn't out of hand what happened over the last two or three years is that the volatility has gotten out of hand we're going to talk about that Wednesday at that Pro seminar I'm going to give you a concrete in not only of how it got out of hand but how financial engineering and the design of derivative securities to expand the housing market and provide people with these loans exacerbated the problem on the downside but of course do the purpose of it was to help people on the upside is exactly looking at the investments going up in thinking that gee they can never come down yeah question right that's a that's a very important point the mark to market what is mark to market me anybody know we've never used that term in class so far yeah that's right when something that may have a book value gets marked to a reality check in terms of market price so for example the first lecture where I auctioned off that little bot tiny box that you had no idea what was in there it had no market value beforehand at least not till any of you but we marked it to market we marked it to market at 45 bucks and so it established a market price now the question is who cares what the value of the house is you're living in it you're enjoying it so what's the big deal well that's right it's not a big deal if you enjoy living in the house and you can afford to pay the mortgage and you're okay and millions of homeowners are exactly in that situation so we can't forget that that said that the subprime mortgage has enabled literally millions of homeowners to become homeowners who never could have but there what if there's a problem in terms of interest rates going up and your mortgage payment going up because you ended up getting a very low teaser rate for your mortgage you've got an adjustable rate mortgage because they said gee you can buy this house with virtually no money down and you've got plenty of resources to be able to pay for it because your payment is only you know $300 a month and then a year later that mortgage payment is $1,000 then it's a real problem okay then you got a decision the decision is are you going to keep paying all of your income and have a hard time making ends meet for a house that you'll never get the money back it's literally taking your money and burning it because you've lost your equity and you've lost so much more beyond your equity that in order to make money you'd have to hold on to the house for 20 years and you can't afford the house anyway do you do that or do you put the key in the front door and move out and say you know what bank it's all yours I'm moving on that's what's happened across the country it's the fact that people can't afford these mortgages because they got in at low teaser rates and now the rates have come up because the interest rates have been going up now something very significant going to happen tomorrow tomorrow the Fed is almost surely going to cut rates because they want to reduce the pressure on the system for these exactly these kinds of issues they want to reduce the the kind of default rates and by doing by keeping interest rates low they actually are going to be able to encourage liquidity and reduce the kind of pressure that we've been seeing yeah question the house goes down say 25% it's been only you know a year you feel like the happen again it's never going to come back up and you literally just go to the bank you saying well that depends on what you signed when you got your mortgage from the bank most mortgage contracts are known as non-recourse loans meaning that they've got your house is collateral but that's all they got they don't have your firstborn they don't have you know your pinkie finger you know and depending on where you borrow in some cases you may have to give that up but no the fact of the matter is the most they can do is take your house away and sell it and a lot of homeowners are saying great it's all yours I'm moving out of Stockton California I don't need the house I don't need to have these mortgage payments where I'm throwing in good money after bad that's that's there that perspective yeah so your credit score would go to hell so you're waiting so you'll wait five years or seven years and then you'll you know be back again there's a finite limit on you know how long they can keep those kind of credit scores and beyond a certain point you will have a clean record but even with that bad credit score I mean don't forget that's how the subprime mortgage market got created you saw the TV ads right doesn't matter if you're in default doesn't matter if you have no credit doesn't matter you don't have a job will still give you a loan now that's not true today or not as true today but at some point when the market recovers we're going to see that come back again and so you will be able to borrow again okay yeah yeah actually interest rate and home yeah has it changed right exactly that goes with well yes and no I mean I think that the subsidization that you're talking about really happens very very indirectly the fact that there are large numbers of defaults ultimately may mean that it's harder to get a subprime loan so the folks that are actually good credits but don't meet the prime borrowing rate criteria yes they will suffer but in equilibrium by equilibrium I mean when supply equals demand the price is the price is the price so you know it depends on you know what kind of a borrower you are but whatever whatever type of borrow you are if you can signal that that's the type you are you will be able to get that appropriate kind of credit alright so in that sense you know it's not as if taxpayers are footing the bill for the particular interest rate ships that are going on taxpayers may end up footing the bill for what happened with Bear Sterns what happened with Fannie Mae and Freddie Mac and that's one of the reasons why over the weekend when when the Fed was approached by Lehman Brothers and say hey you know you got to help us out here the Fed said you know what we're done with that you know sorry but we can't ask the American taxpayer to foot this bill either otherwise there's going to be tremendous backlash and so when Lehman Brothers was left with without backing from the Fed they went to a number of private organizations like Barclays Barclays said that they would be willing to do it if the Fed was able to provide some kind of backstop the Fed was not willing to provide a backstop so Barclays said thanks but no thanks and at that point Lehman said we have no choice because we cannot close a sale within a matter of you know 24 to 48 hours from this point on and we've got some notes coming up we've got to do something so they filed for chapter 11 yeah yes we're actually going to talk about that in the next lecture in this next segment inflation if the Fed cuts rates what one could argue that the reason we're in the mess that we are is because the Fed had kept the Fed Funds rate so low for so long that even after the stock market crashed with the internet bubble bursting the housing market continued on with its bubble because it was still so cheap to borrow and and I'm sure I mentioned before that when I was an assistant professor at the Wharton School back in 1986 looking to buy a house the 30-year fixed was at 18% 18% for a 30-year fixed mortgage I didn't do it because I couldn't afford it at the time but think about that versus today mortgage rates are maybe at a recent high of six seven eight percent that's not bad relative to historical historical standards okay so yes I mean I think that's that's the concern that if we keep interest rates too low that's going to encourage inflation and inflation will have its own cost anybody who's from a kind of any latin-american country will know the ghost of inflation is tremendously frightening and we don't want to let that get out of hand if you remember back to the 1970s we had some inflation in the u.s. that was a real problem so we're going to talk about that in just a couple minutes any other out yes absolutely yes do I think it's reasonable um you see you you're not allowed to ask that question to an economist or rather an economist it's not allowed to answer that reasonable is relative and there are moral and ethical overtones that economists don't like to get involved in it's human nature is it human to suffer from fear and greed well yes and I don't think I'm going to change that anytime soon nor are you going to be able to change that anytime soon so that's one of the reasons why we we study finance is to develop an intellectual and discipline framework for thinking about these issues because if you don't if you don't have a framework for thinking about this then you're left responding to fear and greed right now we are in the absolute grips of fear those of you who aren't in financial markets if you read the papers my guess is you'll start getting scared anyway and if you're in financial markets I promise you this is the scariest time that we've been in including August of 98 October 87 94 you know 2001 all of the kind of periods of market dislocation is trumped by what's been going on over the last few weeks and it's exciting from the point of view of being a finance student because you actually have the opportunity to understand and do something about this but but it requires a certain discipline to do that yeah and good what does exactly mean because everybody if I I guess it's not a retail man but if I could if I have some money deposited there will they give it to me because I am a liability well that's exactly the problem the answer is I don't know and that's one of the reasons why there is this dislocation nobody knows because nobody knows how large the losses could be and part of the thing is that the losses at Lehman and other financial institutions including Merrill Lynch Merrill Lynch in some ways has bigger exposure than Lehman the difference is that Merrill Lynch has other sources of revenue that are able to let it get through this situation a bit more gracefully but the broader problems we don't know because we don't know how the value of these large assets are going to be valued if you value them at zero then they're in deep trouble and not only are the shareholders going to get wiped out but a lot of the creditors are going to get wiped out if you value them at what they're valued now well then they're going to be some hiccups along the way but a number of people should get out without you know outrageous losses something now yes wait till things get better well my Latin American experience yes yes I mean that's exactly what filing for bankruptcy does when you file for bankruptcy you basically go to the courts and say I cannot make good on my IOUs and I recognize that this is a problem so I'm going to ask the court to appoint a conservator or a supervisor to oversee the disposition and dissolution of my assets in order to make an orderly transition to pay off all of the creditors and you know who's last in line the shareholders that's right so most people think the shareholders are going to get nothing which is kind of astonishing because take a look at their closing price in 2007 the closing price of Lehman Brothers stock sixty two dollars a share at the end of 2007 nine months later it's worth zero zero from sixty two dollars a share that's a huge destruction of value and you know what part of that loss in value is really due to the loss of brand and the loss of business viability it's intangible assets it's not it's not like all of a sudden the Lehman investment bankers and proprietary traders and asset managers all of a sudden they they have brain damage they're a lot stupider than they used to be they're just as smart just as savvy just as experience just as knowledgeable as ever they were the problem is that because of the magnitude of their exposures there's general concern about their viability as a business and when you don't want to do business with them when everybody doesn't want to do business with them when nobody wants to do business with them they're not a business and the value of their business goes to zero and so there's a chicken and egg problem and the bottom line is that you know irrespective of whether it's the chicken or the egg when the egg breaks you know you're done yeah yes yes what happened with Lehman is quite similar to what happened with their except that with Bayer there was a rush on it there was a panic that was triggered by what seems to be some kind of a rumor not necessarily large exposures coming to bear stearns actually had funds that were engaged in these kinds of subprime mortgages CDOs and CDSs those funds went under during the summer but Bear Stearns as a business collapsed because individuals really didn't want to do business with it because of this kind of a risk and the same thing happened at Lehman except Lehman's exposure was much larger they have much larger exposure these markets they're one of the biggest players in these particular kinds of securities okay let me just uh because we're running out short on time I'd like to just take one more question and then let me go on with our lecture and believe it or not we are going to cover material exactly related to this when we start talking about fixed income security so this is very much apropos yeah Ronnie yeah great question yeah absolutely so this is a great question I'm actually going to talk about that specifically Wednesday evening but let me let me give you the short answer now the short answer is that within the next two or three months Wall Street will be frozen I though there going to be a deer caught in the headlights they won't know what's going on they won't know what their hiring plans are they won't know the number of slots they have they won't know if there's resumes flying back and forth so it's going to be a bit of chaos for the next two or three months it's not clear that that's can affect you because internships still have to be filled entry-level positions are actually the least of least concern to businesses because those are the ones that they want to fill because the new generation are hungry and and smart ready to do anything take on anything and cheap that's right I didn't want to say that but you said that so but good value let me put it that way your good value and so what's going to happen is it'll be virtually impossible for a senior managing director from one firm to easily get a job at another firm within the next two or three months until things settle down at the entry-level job market I suspect that there will be some disruption for example just a simple indication of that today after my four o'clock section I was supposed to meet with the CFO of Bank of America Joe price as many of you know we established a relationship with Bank of America just recently the laboratory for financial engineering of to work with B of a to do some interesting research and get access to their tremendous database and we were going to launch that set of discussions today with Joe price not surprisingly at 3 in the morning I got an email from a B of a employee saying that he will not be coming to MIT today after all he's a little bit tied up by the way B of a also looked at Lehman over the weekend so over the weekend B of a folks were pretty busy shopping shot they looked at Lehman but again when Lehman when the Fed wouldn't guarantee any kind of a backstop for Lehman a B of a passed as well so that's an example of the kind of dislocation I'm talking about there'll be scheduling glitches and things like that going forward though after the two or three months I actually think this is a fantastic time to get into the industry because when you have these kind of dislocations opportunities get created and opportunities for people that are smart that are hungry that are willing to work hard I mean that's exactly the kind of situation that you want to be in when things are going well they don't need you they're going to hire people just to be clerks and you know to get people lunch but now is the time where you can actually have a big impact so rather than be discouraged I think all of you had perfect timing in terms of being in school now in two years time you'll get out that's when all of the businesses are going to be recovering and certainly doing quite well I suspect and even within the next six months you're going to see that number of firms are going to be hiring and by the way the dislocation we're talking about is on the broker-dealer side on the asset management side hedge funds pension funds asset management companies foundations endowments non-financial corporations they're hiring and they need people with financial expertise to deal with these kind of market dislocations so I think that the job prospects are actually quite bright for this class and the class after the folks that are going to be in a little bit of a tough bind are the second years who will be interviewing for their jobs in the next two or three months they may end up having to wait a little bit longer and I suspect that you know they will take a little bit longer to settle on their jobs but even then MIT students end up having a bit of an advantage over other MBA simply because of the expertise that we bring to the table okay so sorry about taking up so much your time but I think this is a relevant and it were useful for what we're going to be talking about next let me now turn to let me let me turn to what we ended with in the last class which is the inflation topic last class you recall we talked about the two formulas that you're going to know very well by the end of this course perpetuity z' and annuities and compounding and where we ended with was this notion of inflation how many of you already know what inflation is and you've talked about it in macro okay some of you so let me go over it briefly and I think you'll see very quickly exactly what the idea is it's really meant to capture the fact that the purchasing power of your money can vary over time irrespective of the time value of money and let me explain it this way at a particular point in time let's say time T you've got a certain amount of wealth WT and the value of the kinds of things that you like to buy is given by an index call it I sub T so you can think about that as the price of the basket of goods that you enjoy okay so this only include consumer items food clothing and what as well it to include other items leisure entertainment and so on and the fact that you have a certain amount of wealth doesn't really tell you how happy you are it's really how much you're able to consume how you use that wealth that tells you how happy you are so economists really like to focus not on total wealth as a measure of your standard of living but how you're able to consume that wealth so we're going to come up with a basket of consumption goods and call that price of that basket I sub T all right now let's move from time T to a different point in time T plus K so k periods from now you're going to have a different amount of wealth hopefully bigger and presumably you're going to be able to consume more well that's presuming that the prices of what you like to consume don't change but if those prices do change then in fact you might not be really better off in any way and so in order for you to tell whether or not you're better off or worse off you need to know not only how much wealth you have but how much that wealth can buy you in terms of the stuff that you like to consume so the idea behind inflation is to measure the purchasing power of your dollar and that's completely different from time value of money time value of money simply says that people are impatient and they prefer money now the money later but inflation is a comment about the purchasing power of that dollar now versus later and it can go either way in other words it's possible that a dollar next year will buy you more than a dollar today because if prices decline as they have right now for energy for example energy is below $100 a barrel just a few months ago it was at 130 dollars a barrel so if we had a winter a few months ago that would have been really bad because home heating oil would have been a lot more expensive than it looks like it's going to be however it's still going to be more expensive than it was two years ago when oil was at $40 a barrel so you need to know what you're going to consume in order to get a sense of whether you're better or worse off and that's what we measure by this price index I of T plus K so when you're looking at your portfolio you might ask the question what's my return on my portfolio and the way you calculate that return is look at your wealth at time T plus K divided by your wealth at time T subtract one from it and that's your return right that's often called the nominal return because it's a name only meaning it's the actual number of dollar bills that your wealth will grow to so if you've got a thousand dollars this year next year you've got $1100 your nominal return for your wealth is 10% that's the number of dollar bills you have more than you had this year 10% more now if you want to know how you're doing in terms of your level of happiness your purchasing power your cost of living your standard of living you've got to look at what's going on with the cost of living increase I sub T plus K divided by I sub T and we can write that as a fixed growth rate PI per year 1 plus PI to the K so let's suppose that all the prices of the things you love and enjoy they go up by 10 percent as well well then have you made any money have you made any progress you've made money but you haven't made progress you've made 10% in terms of your return on your initial thousand dollars but the stuff that you like to eat and and buy and use that's also gone up by 10 percent so in fact you can't do any more consumption next year then you could have this year because while your wealth went up by 10 percent the cost of living went up by 10 percent so from a from a real perspective real meaning what you really care about you haven't really made any progress inflation is a measure of how much progress we've made and so when you engage in analysis of these kinds of present value problems you've got to ask the question whether or not you're focusing on nominal returns or real returns okay and ultimately as a consumer what you all care about is real returns you want to know whether you're getting better off in terms of what you can really consume so how do you do that well first of all you have to change the units oh sorry question yeah why that letter oh no no no I'm sorry yeah this is a thank you for pointing it out no by PI I just mean a variable name called PI I don't mean 3.14159 only at MIT when I get that question I've taught at other universities and they ask me what that funny-looking symbol looks like but so yeah sorry about that this is just a Greek letter that deter that denotes a variable is like it's like R or something all right thank you so here what I've done is to define a variable called your real wealth at time T plus K real meaning this is what you really can do with your money in terms of consuming what it is is your nominal wealth divided by the rate of inflation so in the case of the example I gave you where your nominal wealth goes up by 10% and your inflation rate goes up by 10% when you take your nominal wealth and you divide it by that growth rate in inflation what do you get you get a thousand dollars in other words your wealth hasn't changed in real terms okay so in the example I gave you your wealth went up by 10% your inflation rate for a year is also 10% so if you divide your total wealth by that that index you're basically going to get back to your original amount of wealth right so here's the general the general framework your real wealth is going to be your nominal wealth divided by the rate of inflation you're dividing by it because you're using as your units of comparison today's consumption basket right and so the way you can look at your real return which is denoted 1 plus R real to the K power your real return over K years is equal to the real wealth at the end of UK years divided by your wealth today that's your real rate of return right because it's how much real dollars you have at time k that's just given by your nominal rate of return of your wealth and then divided by the rate of inflation okay so this is the expression that is the the basic relationship between real and nominal consumption goods and then we approximate this ratio with this very very simple relationship here the real rate of return is approximately equal to the nominal rate of return divided by or minus the inflation rate naught divided by anything that's the approximation so getting back to my example my example of if you have a 10% nominal growth rate for your investment and you got a 10% inflation rate then in that case there's no approximation in fact your inflation rate your real rate of return is zero right 10 percent minus 10 percent is 0 where the approximation happens is when you have something a little bit different for example suppose the inflation rate were 10 percent and suppose your nominal rate of turn was 15% according to this approximation what's your real rate of return 5% right it's not exactly 5% because if you take 1 point 1 5 divided by 1.1 oh it's not exactly 5 percent but it's approximately equal to that okay what this says is that you ought to think as a consumer not just about the total dollars that's growing but the purchasing power of those dollars okay for the purposes of doing NPV calculations I want to just mention one rule of thumb that will do you in good stead no matter what kind of calculations you do and that is simply to keep track of whether you're using nominal or real cash flows and then to use nominal or real discount rates to match in other words nominal cash flow should be divided by nominal discount rates and real cash flow should be denominated by real discount rates most of the cash flows that you will get in your analysis will typically be nominal nominal meaning that's the actual number of dollars you will see on those dates but occasionally you may get a forecast that is made in real terms in in terms of purchasing power and in that case you have to just be careful to use the right interest rate when you're doing your discounting you have to take into account inflation nominal gets discounted by nominal real gifts discounted by real that's all you have to remember okay any questions about that we're now done with lecture three and we're moving on to lecture four which is fixed income securities and this is the focus of much of the dislocation in markets today so this is very topical and something that I think you know you'll find very useful when we start trying to understand exactly what's been going on in these markets let me start with a little bit of an industry overview and the industry overview will will give you a sense of why these markets are so important as well as so large okay so we're going to start as I said with an overview of markets and the participants and then I'm going to talk about valuation of fixed income securities it turns out that all of the hard work that we've done just over the last three lectures are going to be able to get us through all of valuation for fixed income securities in other words you now know all that you need to know to price virtually any fixed income security without default without uncertainty remember we said no uncertainty right until lecture 12 but that's pretty it's a pretty significant accomplishment because there are lots and lots of securities out there that are fixed income securities and you now have the tools you don't know that you have the tools yet but you do believe me you have the tools to price them all so we're going to go over the valuation principles and apply them to discount bonds and coupon bonds and then I'm going to talk to you a little bit about uncertainty I want to bring in interest rate risk in a very simple way I want to simply talk about the fact that interest rates do change over time and that change can actually cause some concern as well as some opportunities I want to discuss what those opportunities can and concerns are and then I'm going to conclude by talking about default I'm going to talk about corporate bonds and I probably won't talk about the subprime issues in this class because I want to focus on the material that's required but I will talk about it in this pro seminar which is optional so you're welcome to come on Wednesday and we'll go over that material and if you want you can take a look at it yourself it's pretty self-explanatory so I think you'll you'll see how it goes for readings I'd like you all to read chapters 23 through 25 Aubrey Lee Myers and Alan you'll have three lectures to do that lectures four five and six will all be focused on fixed income securities so let me talk to you a bit about the industry now the name fixed income securities means exactly what it says what we're going to do now is to focus on pieces of paper where the payoffs are fixed and known in advance unlike a stock where you buy a stock and you don't know whether it's going to pay off at all and the cash flows the dividends or repurchases or capital gains are uncertain you don't have any idea what the cash flows may or may not be in contrast to those securities fixed income instruments have fixed incomes so they have very very clearly stated payoffs that you know in advance so from a pricing perspective these are probably the simplest kind of securities that could possibly be constructed right it couldn't be simpler than a piece of paper that says every year on this date I will pay you ten thousand dollars of nominal currency right that's a fixed income security examples are anything from Treasury securities securities issued by the United States Treasury and other foreign Treasuries to federal agent securities we know about those now right Fatih Mae and Freddie Mac securities to corporate security securities issued not by the government or by government-sponsored entities but by private corporations and public corporations and then municipal securities these are securities issued by local governments and then mortgage-backed securities securities that are payoffs of pools of other securities including mortgages and then and the whole mix of collateralized debt obligations collateralized loan obligations credit default swaps and other complex instruments that's a lot of securities and to get a sense of how many securities we're talking about let me show you the market this is as of the end of 2006 because that's the only data that I could get that is as timely at the end of 2006 the US bond market consisted of just tremendous tremendous amount of assets so six point four trillion in mortgage-related securities twenty four percent of the market two point three trillion in municipal x' four point two trillion in Treasuries two trillion and asset-backed securities three point eight trillion money market two point six trillion in federal agency securities and so on these numbers they dwarf the stock market so we're traditionally focused in financial financial analysis on pricing stocks and analyzing stocks and we get all excited when Google tries to take over Yahoo and so on but the size of the markets the size of equity markets are dwarfed by fixed income securities and again you know these are apples and oranges and I'm just saying that there is a hell of a lot more apples and there are oranges you could you can figure out what you want from that but these are really big markets and on this slide I show you the evolution of these markets how they've grown over time from 1985 to 2006 and what you'll see is that the mortgage-related market has just you know grown by tremendous tremendous amounts as well as federal agency securities that's Fannie Mae and Freddie Mac and asset-backed markets was nothing in 1985 it didn't exist in 85 and now we're talking about a two trillion dollar market here so a lot has happened in the last 20 years it's been exciting times for financial markets and right now we're in the midst of some market turmoil because of that unbridled growth now this is the amount outstanding this chart shows you the issuance that is the amount of debt that's being issued at any given point in time so the first was an example of the stock of debt at any point in time and now I'm talking about the flow of debt year by year and you can see that as of 2006 mortgage related bonds were the fastest growing segment by far and that continued up until 2007 and then the breaks started being put on to that market okay and you can see over time the growth of these various different markets and the fact that federal agency securities grew but mortgage-related securities probably was the fastest growing a subject to the asset back to market as well which is related yeah mortgage related specifically about mortgages asset-backed could be any asset so for example consumer credit card loans you can package that up and sell claims on that and that would be under asset backed securities not under mortgages so but they're related obviously okay so these numbers will give you an idea of what's out there what's significant and what's not this gives you a sense of the amount of trading that goes on while these securities are large in size and large in flow they are not that large in terms of transactions so unlike stocks that trade all the time we don't have an organized u.s. bond exchange like the NYSC where people trade bonds every minute of the day there are bonds being traded every minute of the day but they aren't typically the same ones whereas I would argue that Microsoft and Google are traded every minute of the trading day so typically bonds do trade but they don't trade unorganized exchanges and that makes them less liquid even the very very safest and most liquid bonds are do not trade as frequently as equities and futures so the liquidity characteristics can be very very different for these instruments and these complex securities like collateralized debt obligations mortgage-backed securities they trade even less frequently because they are highly complex and it's not that easy to figure out what their prices are from minute to minute every day now the fixed income market participants that we're going to be focused on fall into three groups its intermediaries and investors issuers of course are the end-users of these instruments they include everything from government's down to foreign institutions these are the folks that you pieces of paper that are io u--'s and they get cash in return for that to finance their operations and in return they pay interest okay the investors of course are the folks that are buying the paper or essentially providing loans so every once in a while when I go out with my colleagues for lunch in the Finance Group one of my colleagues will say can I sell you a bond I didn't go to the cash machine today and I need you to help me finance my lunch these are how finance professors speak and and unfortunately the idea about buying somebody's bond is you're lending them money right so instead of saying can you lend me five dollars we have to say well I'm going to issue a bond can you can you buy my bond the investors are the ones that are loaning the money to the issuers okay and these include as I said government's pension funds insurance companies banks hedge funds and so on in the middle of all of this are the intermediaries primary dealers other kinds of dealers investment banks the credit rating agencies the credit enhancers what are we mean by credit enhancers folks that help credit markets by providing insurance to the credit like private mortgage insurance and liquidity enhancers these are the counterparties that try to bring buyers and sellers together to increase the liquidity of the markets the dislocation has been going on in the intermediary sector and of course the issuers are having some difficulties now because they're going to have to make good on these kind of claims and the people that are going to be hurt ultimately will be the investors who are holding pieces of paper that may not be worth as much as possible and so the efforts now at trying to shore up the finances of Fannie Mae and Freddie Mac Gleeman Merrill and all these other institutions is really aimed at trying to help out a combination of the intermediaries and the issuers because if you don't help out group then what happens is that this group is going to get hit so Lehman Brothers for example is an intermediary they are one of the biggest dealers in these kinds of securities Merrill Lynch is also one of the biggest dealers in these kind of securities as dealers they end up taking exposure on their own books that's not a great idea in general because the best of all worlds is your the toll collector that's collecting tolls for traffic going back and forth and back and forth you don't take any risk but if not everybody wants to go back and forth and back and forth and back and forth you might stand ready to do one side of the business and let other folks do the other side of the business but if you're not careful in laying off your exposure you can end up getting hurt pretty badly an example of this that happened in equity markets in 1987 was when the stock market crashed that was a very serious event on October 19 1987 where in one single day the US stock market lost approximately 20% of its value in one day now that's a serious dislocation we're going to talk about that this Friday when we run this trading game I'm going to have all of you engage in trading over a very short period of time so you're going to be under tremendous pressure as well you tell me how easy it is to think on the fly what happened in that morning of October 19 1987 is that the specialists the dealers who are supposed to be making markets their job is to buy when everybody wants to sell and to sell when everybody wants to buy they got it there in the morning at 9:30 and we're overwhelmed with everybody wanting to sell so they ended up buying the specialists and they bought and as they bought what happened to the price kept going down that means more people wanted to sell so they kept buy and as they bought what happened price kept going down and it kept going down all the way so the stuff that they bought in the morning was worth 20% less in the afternoon and these market makers will also use leverage so many of their capital bases were wiped out by that 20% in a day because they were just doing their job in fact it was a story about the floor of the New York Stock Exchange was literally packed I mean it was it was tighter than a Tokyo subway train during rush hour okay it was packed I mean literally you know you were elbow to elbow against others unfortunately one of the market makers had a heart attack around 1:00 or 2:00 o'clock and he wasn't able to fall to the ground until the market closed at 4:00 because he was propped up by everybody else desperate to try to transact and he died and somebody who was near him said you know look I knew the guy was in trouble but what was I supposed to do I was a hundred thousand shares long and I had to unload my in my portfolio I mean they would they were trading that's how desperate it was on that day so this kind of intermediation can be extraordinarily high pressure and when you're engaged in an unwinding of portfolios dislocation can occur so we're seeing that right now play out and it's a little different because we're dealing with fixed income security so I'm going to come back and talk about that okay that's the background to what we're going to study these fixed income markets and fixed income instruments I'm going to ask you to read really admire so that you can get up to speed on institutional details and there are quite a few so I would urge you to please do that reading and make sure that you understand the basic terms of these markets what I want to talk about though is the framework I want to give you a framework for thinking about valuing fixed income securities and really as I said it's a framework that you already know you already have that in your mind I've already changed the way you think about financial markets by asking you to focus on cash flows and timing and the time value of money that's all you need in order to value fixed income securities the rest is just institutional detail which while very important is not something that we need to worry about in class but I'll leave to you to focus on so let me give you an example of valuation how to do it it'll be a very short one you all know how to do this we've got a cash flow a sequence of cash flows for a particular security that I'm going to call a bond and in particular I'm going to call this a coupon bond now with a coupon bond there are two things you need to know you need to know what the coupon is and you need to know the maturity how many dates that it pays off one of the institutional details that you'll need to know is that coupon bonds typically pay semi-annually some coupon bonds can pay quarterly but most of them as a matter of convention pay semi-annually but that changes depending on the market so you'll need to learn a little bit about those kind of conventions I'm not going to worry about that and I'm going to abstract from that and simply say that here's a three year coupon bond that has a principal of $1,000 that's the typical principal or face value that a bond comes with so this piece of paper is an IOU and it says I owe you a thousand dollars at the end of three years okay but I'm not going to pay you just a thousand dollars at the end of three years I'm going to pay you fifty dollars every year for those three years so the coupon is a five percent coupon so when you hear of a coupon bond that's at five percent three year bond that term that I just uttered means that it pays off a thousand dollars at the end of three years and in the interim it pays off fifty dollars a year as its coupons why is it called a coupon bond in the old days the bond was actually a piece of paper and on the bottom of it were little coupons and you'd clip the coupons and mail them in and once a year when you mailed them in or twice a year when you mail them in you get back $50 okay nowadays it's all done electronically so first thing you do in order to value the cash flow draw a timeline okay we're here sitting at date zero that's today and you've got three years to go one year two year three years at the end of three years you get paid your principle $1,000 plus the coupon there are three coupons for three years and so at the end of this bond when the bond matures you get paid a thousand and fifty and then fifty-fifty and here we are at day 0 question what is this worth yeah right yeah right if the interest rate is 5% it's worth thousand dollars today if the interest rate that's par but if the interest rate is worth less than that right and if it's worth it right exactly so in general how do you figure out the price of this thing yeah well no I was asking some a different question which is how do I figure out the market value of this bond today time zero yeah compute the net present value NPV that's one answer but I was that was the correct textbook answer what's another answer of how do I figure out the market value exactly auction it off how many people want to pay me a thousand dollars for this today no a thousand and one thousand whatever we can auction it off and figure out what the price is from the market but in fact what we're doing by doing so is computing the present value and the way we're doing it is by figuring out what the price of a dollar is in date one today what the price of a dollar in year two is today and what the price of a dollar is in year three today getting those exchange rates and then converting all of those different currencies to dollars today right we know this we've done this many times so the way that you figure out valuation whoops the way that you figure out valuation is by using discount rates that we get from the market and applying them to compute present values right very simple so really the components of valuation for bonds if there's no uncertainty you already know we've done it that was last lecture and for special cash flows like annuities and perpetuate ease we've got closed form solutions formulas you can program up and Excel to figure out the kind of risks that we're going to focus on later on in this lecture and in the lectures after we talk about uncertainty is inflation risk we talked about that right the fact that when you buy a bond or you sell a bond if the purchasing power changes that's going to introduce a new kind of unknown that we need to grapple with credit risk that's a major form of risk that we're dealing with in financial markets today and that we're likely to be dealing with for years to come you might like to borrow from me or lend to me but what about credit issues how do you know that I'm still going to be around a year from now or two years from now timing which will come back to a little bit later on liquidity and then of course what currency if we're doing international borrowing we have an extra dimension of risk which is fluctuations in the exchange rate okay so for the next couple of lectures I want to keep life simple and talk just about riskless debt risk lists in terms of default so in particular I'm going to be talking about US government bonds alright and I'll come back to risky debt later but for now let's just focus on the debt that will not default because you can always print up dollars to pay off your creditors right those dollars may not be worth as much as you would like them to be if you do too much of that but for now we're not going to focus on default okay so the first kind of bond that we're going to try to price is what's called a pure discount bond this is a bond that is different from a coupon bond in the sense that there are no coupons so it only pays off one payment at the end and the reason it's called the discount bond is because it is what it sounds like the price of the bond today is going to be at a discount from the face value if the face value is a thousand dollars and there's nothing in between then the price of the bond today can't be greater than a thousand dollars right because money today is worth more than money next year so the price today is going to be lower than a thousand dollars it's going to be a discount over a thousand dollars hence the term pure discount bond now there are pure discount bonds out there US Treasury bills are examples where there's one payoff at the end and nothing in between but a while ago financial engineers came up with a rather brilliant idea which you may not think is so brilliant because it's so painfully obvious the government issues coupon bonds as well and typically for longer maturities like you know five years fifteen and thirty years there aren't no pure bonds for those longer maturities when the government issues them they issue them with coupons but you can imagine a situation where somebody would like to have a discount bond for 30 years and so some clever financial engineer said hey here's what I'm going to do I'm going to buy up a lot of these treasury coupon bonds and I'm going to issue discount bonds that match exactly the coupon payments from my Treasury bonds in other words I'm going to take the coupons and strip them and offer them up as separate securities and I'm going to call these strips and these strips which stands for separate trading of registered interest and principal securities created a huge market for essentially what our government bonds but had that have been pre processed in a in a relatively simple way now this didn't happen that long ago maybe I don't know 15 or 20 years ago they created strips so this is why I'm so excited about financial markets and why I think all of you have tremendous opportunities it's because there are so many ideas that may seem obvious to you but are not obvious to the market and you know there's no patent on good ideas there's no monopoly on good ideas you can actually create tremendous value by coming up with what you might think of it's so simple a solution but that solves problems for very large financial institutions now how do we price these things well this is just what a one-liner the price of a discount bond is simply equal to its face value discounted to the present by the appropriate interest rate that's it pure and simple we're now we're now done with pricing pure discount bonds there's nothing else to it okay it turns out that this is a really wonderful relationship because if you've got two of these three variables in this equation you've got the third if I tell you what the phase value is and what the interest rate is you've got the price if I tell you what the price is and what the face value is you've got the interest rate and if I give you the interest rate of the price you can actually figure out what the face value is all right so this relationship is going to be very handy when we look at the prices of these instruments and we want to now infer what that says about what's going on with interest rates in fact what I'm going to show you next time is that when we look at the newspaper and we take a look at the prices of discount in coupon bonds implicit in those prices is a forecast of the future this is as close as any of you are ever going to get to a crystal ball I'm serious by looking at prices you can tell the future you can't do it perfectly but you know neither can gene Dixon or any of the other astrologers right the point is that this is our way of figuring out the collective intelligence of all market participants and what they think about what's going to happen and because of that because of that kind of of market knowledge I can tell you that with 99.5% confidence tomorrow the Fed will cut its interest rate now how do I know that I don't know that the Fed may not but if you look at financial markets today if you look at Treasury prices today if you look at the Fed Funds futures today all of those prices if you know how to read them if you can decipher those tea leaves it will tell you that tomorrow the Fed will cut rates so I want you to watch tomorrow to see if I'm right okay we very embarrassing and potentially catastrophic if I'm wrong so so listen carefully any any questions yeah yeah that's right in other words if they cut rates tomorrow then they're going to be shooting a one of the very few remaining bullets that they have the question is you know if a bear is charging at you and you've got one bullet left you're probably going to use it anyway right so why don't we return to this issue on Wednesdays is we're out of time all right thank you