8. Theory of Debt, Its Proper Role, Leverage Cycles

published on July 13, 2020

We're talking about the theory of debt and interest rates so I want to talk about a number of technical topics first I'm going to start with a model Irving Fisher model of interest and then I'm going to talk about present values and discount bonds compound interests

Conventional bonds the term structure of interest rates and forward rates these are all technical things and then I want to get back and think about what really goes on in debt markets I have there's two assignments for this lecture one is

The several chapters out of the Fabozzi Adele manuscript and then there is a chapter from my forthcoming book that I'm currently writing but that is the most meager chapter that I've given you yet so the book is not done and so I

Think the real reference for this is the Fabozzi manuscript at this point and then of our Oliver will give a TA section that will clarify I think some of the points so anyway what we're talking about today is interest rates

The percent that you earn on a loan or that you pay on a loan depending on what side of it you are and interest rates go back thousands of years it's an old idea typically it's a few percent a year right the first question we want to try

To think about is what explains that why why is it a few percent a year and why not something completely different so the and why is even a positive number ever think of negative interest rates well these are basic questions so I

Wanted to start with the history of thoughts and an economist from the 19th century oregan from boom ba Varrick who wrote a book on the theory of interest in the late 19th century actually it was 1884 and he is a long a very verbose

Account of what causes interest rates but basically he came up with three explanations why is the interest rate something like 5% or 3% Hertz 7% or something in that range and he said there's really three causes one of them

Is technical progress that as the economy gets more and more scientific information about how to do things things get more productive so maybe the 3% is or the 5% whatever it is is the rate of technical progress that's how

Fast how fast technology is improving but that's not the only cause that boom Bava talked about another one was advantages to roundabout honest that must be some translation from his German but the idea is that more roundabout

Production is more productive this isn't technical progress but you know if someone can ask you to make something directly right now you gotta use the simplest in the most direct way to do it if you're going to do it right now but

If you have time you can do a more roundabout way you can make tools first and do something else that makes you a more efficient producer of this and so maybe the interest rate is a measure of the advantages to roundabout Ness and

The third cause that boom valve Eric is time preference that people just prefer the present over the future they're impatient it's a this is behavioral economics I suppose this is psychology that you know you've got a

Box of candy sitting there and you're looking at it and you're saying well I should really enjoy that next year maybe it would spoil by next year next month but somehow you don't you have an impulse to consume now so maybe the rate

Of interest is the rate of time preference that maybe people are you know why is the interest rate 5% it's because people are 5% happier to get something now than to get it in the future so he left that train of thought

For us this was not mathematical economics it was literary economics but the next person I want to mention in the history of thought is Irving Fisher who was a professor at Yale University but he

Wrote a book in 1930 called theory of interest and it is the all-time classic I think on on this topic so herbing Fisher is that he's talked about in your textbook by fellows Ian talked about in many textbooks he graduated from Yale

I mentioned that since your Yale undergrads he was a Yale undergrad graduated maybe it was in 1885 and he got the first economics PhD at Yale University in the 1890s and he just stayed here in New Haven all his life

And if you were living in New Haven in the early 20th century you'd know him because he was a jogger nobody else jogged he would exercise his and run around campus so everyone would see him in the nineteen teens or

Twenties nobody did that but he did it was a health nut among other things but I'm not going to talk I could talk a lot about him he's a fascinating guy I'll tell you one more story about him he would invite students to his house for

Dinner and he would explain to them before dinner that he believed that proper eating required that you chew every bite a hundred times before you swallow it so he would tell the students to do that and it slowed down

Conversation at dinner a great deal that's not what he's known for what he's known for is among other things his theory of interest so this is what's talked about in your textbook and I wanted to start out because with the

Irving Fisher because by the way I don't know when this room was built does anyone know since he died in 47 he probably lectured from the same blackboard right so I don't know the same slate it could be right he could go

Back to that time so I'm going to put back on the board what he had on this board I'm assuming in some time in the 1930s so well what your author your textbook author Fabozzi emphasizes for a theory of interest is something that

Came from Fisher both very simple and he says the interest rate this is faux Bozize distillation of Irving Fisher the interest rate is the intersection of a supply and demand curve for savings so I'm going to put saving your s on this

Axis and on this axis I'm going to put the interest rate call that R I don't know why we commonly use R for interest it's it's not the first letter it's in the middle of the word and the idea is that there's a supply of saving at any

Time that people then wish to put in the bank or someplace else to earn interest and the theory is that the higher the interest rate the more people will save so we have an upward sloping supply

Curve now this s means supply whereas this s down here means saving okay and then there's a demand for investment capital right the bank lends out your saving to businesses and the businesses want to know what the interest rate is

The lower the interest rate the more they'll demand so we have a demand curve for saving and then the intersection of the two is the interest rate well it gives the interest rate on this axis and the amount of saving on the other axis

That's very simple story and that's what Fabozzi covers in your text but I wanted to go back to another diagram that Fabozzi et al did not include in their textbook but it also comes from the 1930 book theory of interest and that that is

A diagram that shows a two period story and the thing I like about this two period diagram is that it brings out the boom valve or causes of interest rate in a very succinct way so this is the second curving Fisher diagram and I'm

Going to do a little storytelling about this you remember the book Robinson Crusoe was written by Jonathan Swift in the 1700s it was the story of a man named Robinson Crusoe who was marooned on an island all by himself and had to

Live on his own with no health this is a famous story called a Robinson Crusoe economy there's only one person in the economy so of course there's no trade to a little bit of trade but I'm just telling you a story of the raita there

Will be a rate of interest on Robinson Crusoe's Island okay so so here is I'm going to show here consumption today and on this axis consumption next year all right and let I don't know what I don't remember the novel I proud did anyone

Hear me you must have read somebody must have read Robinson Crusoe huh but I'm not going to be true to the story the story I'm going to tell is that Robinson Crusoe has some food that's all that the whole economy just

Is let's say it's green I know how he got that on the ham he's got drain and he's deciding how much to eat this year and how much to plant for next year so the total amount of grain he has is right here okay

So that is his endowment of grain and he could eat that's the maximum he could eat but if he eats at all there won't be any grain to plant for next year okay so he'd better not eat at all okay or he'll starve next year now in a

Simple linear production with tactical technology that's linear he can choose to set aside a certain amount of grain which is the difference between what he has and what he's consuming and then that will produce grain next period so

I'm going to draw a straight line that's supposed to be a straight line these are all supposed to be straight lines here okay okay and that is his choice set under linear technology I'm growing it with no no

Decreasing returns the idea is that for every bushel of grain that he plants he gets two bushels next year or whatever it is okay and so if if he were to consume nothing this period he would have if that's if I drew this thing with

The right slope of minus two he would have twice as much this is the maximum he could have next period okay and so he could consume anywhere along this point this line okay this would be the simplest Robinson

Crusoe economy now in fact so what does he do remember from elementary micro theory he has indifference curves between consumption today and consumption tomorrow remember these these are like contours of his utility

We typically draw them like this okay so what does he do he maximizes his utility and chooses a point that with the highest indifference curve touching the production possibility frontier this is the PDF the production possibility

Frontier and that determines the amount that he consumes and the amount of place he consumes this amount here and the difference between his endowment and his consumption is his saving and then next period he consumes this amount

Alright that's simple micro Theory that's familiar to you now so in this case the interest rate the slope of this line the slope is equal to minus 1 plus R where R is the interest rate okay so in this case I've told a very simple

Story it has only one boom Bhavik cause roundabout Ness well maybe maybe there's technical progress – I don't know it has maybe a couple of his causes if as time goes by Robinson Crusoe figures out better how to grow grain there could be

A technical progress component but preferences don't matter in this story right the Preferences are represented by his indifference curves and as since I've got a linear production possibility frontier in impatience doesn't matter

The interest rate in this case is decided by the technology the slope of the curve so we don't have all of boom valve ik scauses yet ok next step that was the that was the simplest Irving Fisher story the next step is let's

Suppose however that there are diminishing returns to investment in grain alright that means for example maybe when he when he grows a little bit of it he's very good at it and he does produce as a big crop but as he tries to

Grow more grain he gets less productive maybe he has to do it out in the worst land or he's running out of water or something is not going right then we would change the production possibility frontier so that it concave down ok

Something like that do you see what I'm saying diminishing returns to investment produce as you keep trying to add more and more grain to your production as you save more and more we get less and less return so now we have a new production

Possibility frontier that that that is more complicated so now what happens suppose forget this this straight line which I do first and now consider a new production possibility frontier that's curved downward well what does Robinson

Crusoe do well Robinson Crusoe picks the highest indifference curve right that touches the new this production possibility here so that means he finds an indifference curve that's tangent to it

And he chooses that point okay now okay do you see it so this is what Robinson Crusoe would do now the interest rate is the slope of the tangent e between the indifference curve and the production possibility frontier it's the same for

Both and this was the insight that boom valvert maybe had a little trouble getting there's two different things determining the interest rate one of them is the production possibility frontier and the other one is the

Indifference curves now it's we have all of them valve X causes we've got roundabout miss we have technical progress and we have impatience well the impatience would be reflected by the slope of the of the indifference curves

So let me put it this way suppose Robinson Crusoe really wanted to consume a lot today he was very impatient that means that his indifference curves now did you give me colored chalk no we have a little

Yellow all right suppose Robinson Crusoe is very impatient he wants to consume now he doesn't care about the future then his indifference curves might look I'll just draw a tangent see his indifference curve might look different

They might look like this okay so he would have a tangency further to the right consuming more today and less in the future okay now the slope here is different than the slope here right because I haven't changed the production

Possibility frontier but I've moved to a different point on the production possibility frontier so you can see that if Robinson Crusoe becomes more impatient his interest rate goes okay now you understand that the

Interest rate in the Robinson Crusoe economy is not just about Robinson Crusoe it's about all even though there's only one person in this economy it's about all of the organ from bomba werkes

Ba boom ba verax causes the technology is represented by the technical progress and the roundabout Ness and the Preferences are represented by the indifference curves and you can see that the actual rate of interest in his

Economy is is determined by the tangency beat now on the other hand suppose Robinson Crusoe were very patient and really wants to live for the future then the indifference the highest indifference curve that touches the

Production possibility frontier might hit up here right now that's another Robinson Robinson Crusoe with a different personality who is more patient then the tangency would be up here and the interest rate would be much

Lower because the interest rate would be the slope of the line that goes through that tangency point tangent to both the in indifference curve and the production possibility frontier so this is just one person economy is this clear so I've

Drawn a lot of line maybe I should start all over again we've now we've now gotten all of Burma vyx causes of interest and we've got we've got an interest rate we've tied it to production and the technology that

Were represented by the production possibility frontier and taste represented by the indifference curve but now I wanted to add a person to the economy let me start all over again a second there's two Robinson Crusoe okay

In this island and let's start out with autonomy they haven't discovered each other yet they're on opposite sides of the island okay they have the same technology they have the same production possibility

Frontier but they live on opposite sides of the island and they don't trade with each other so let me start out again this is the same diagram and we have consumption today and consumption next year again and we have a production

Possibility frontier that's the same curve that I do before and the technology is the same for both of them okay and let's suppose they have the same endowment but let's suppose that Crusoe a is very patient and Crusoe B is

Very impatient so crew saw a his utility is indifference curves form a tangency down here so this is a and Crusoe beans and difference curves are up here this is B okay and so they are planning to plant that means that Crusoe a will be

Saving very little I mean will be consuming a lot but I say was the a is the impatient one the way I've drawn it consuming a lot now and not saving much for the future but is maximizing his utility that's what we have the highest

Indifference curve shown here which is tangent in Crusoe B is picked Crusoe B is the very patient one and it's consuming very little this year and it plans to consume a lot next year so let's say they're about to plant

According to these tastes and then they find each other okay now they realize there's two of us on this out now we're getting a real economy with two people okay so what should they do well the obvious thing is that there are gains to

Trade and the kind of trade would be in the loan market what they could do is it's the you know this Crusoe B is suffering a lot of diminishing turns to production so you know he really shouldn't be planning so much

Grain because he's not getting much return for it where is this other guy on the other side of the island has very high productivity he can produce a lot for a little bit of grain so he should so it said sell tell true so yeah you

Should plant some of this grain for me so because you're getting you out you are more productive because you're not doing as much well in short what will happen is they won't they'll do it through a loan I will loan you so much

Grain there's no money B wants to a wants to consume a lot so B will say I'll instead of planting so much we'll strike a loan so allow you to consume along your taste and what will happen in the economy is we'll find an interest

Rate for the economy that looks something I'm going to draw a tangent e like that's supposed to be a straight line and on this tangent line we have Chris OB has maximized his utility subject to that tangent line constraint

And Crusoe a maximizes utility subject to the same constraint and it has to be such a way that the borrowing market is shown over here clears and we have that kind of equilibrium you can see that both a and B have achieved higher

Utility than they did when they didn't trade so this is the function of a lending market okay so so a who wants to did I say that right a who wants to consume a lot this period the production point is here and B lends this amount of

Consumption to a so that a can consume a lot you can consume this much and be since he's lent it to a consumes only this much this period but you see they're both better off they've both achieved a higher indifference higher

Utility and what is the interest rate in the economy the interest rate is the slope of this line well the slope of this line is minus one closely interest rate so that is the Fisher theory of interest and now it's much more

Complicated you can see how all avoidin from Vaughn vivexx causes play a role but it's not you know the interest rate is not something you could have read off from any one person's utility is not just impatience we have we're both

Complicated people we both have a whole set of indifference curves and it's not necessarily easy to define whether or how much how impatient am I it interact with the production possibility frontier in a complicated way to produce a market

Interest rate so this is the model for the interest of the economy that that Irving Fisher developed and so I wanted to just take that as a given now when you put it this way it all looks indisputable that the loan market is a

Good thing right nothing there's no I can't think of any criticism of the two Robinson Crusoe's is going together and forming making a loan there's nothing bad about this loan right they're just both consuming more

As a result but I want to come back to criticisms of lending at the end of this lecture because I again part of this I want to try to make this course into something that talks about the purpose of Finance and the real purpose of

Finance and this story is not the whole story about real people and how they interact with the lending market but before I do that though I want to do some arithmetic of finance so is it and that's

Let me move on to what I said I would talk about namely different kinds of bonds and present values the the Irving Fisher story was very simple and it had only two periods so that's that's too simple for our purpose and so what I

Wanted to talk about now it is different kinds of loan instruments and the first end of simplest is the discount bond okay when you make a loan to someone you could do it in the form of a or between a company or between a government and

Someone a discount bond a discount bond pays a fixed amount at a future date and it sells at a discount today it pays no interest I mean it doesn't have annual interest or anything like it merely specifies this bond is worth so many

Dollars or Euros as of a future date and why would you buy it because you pay less than that amount so let's say that it's worth $100 okay in key periods two years you know there's there's something big you 'ti about I'll say t years and I

Made that our capital T because well so what is a discount bond worth today and now we have an issue of compounding which I want to come to in a minute but let's assume first of all that we're using annual compounding and T is in

Years okay then the the price of the discount bond today the price today is equal to $100 all over 1 plus R to the T power where T is the number of years to maturity T years to maturity okay and that's that's the

Formula okay in other words 1 plus R to the 10th power is equal to 100 over P so 100 over P is the is the ratio of my final value to my initial investment value if I invest in the discount bond and I want to convert that to an annual

Interest rate so this is the formula that allows me to do that so the R is also called yield to maturity because the maturity is T the time when the discount bond matures so it says if it's paying an interest rate R once per year

40 years and we can infer an interest rate on it even though it the bond itself has a price not an interest rate I mean we can calculate the interest rate by using this formula now Fabozzi likes to emphasize now let me come back

To compounding I mean maybe I just talked about this is elementary but let me just talk about putting money in the back here so compounding if you have annual compounding what that means is that it and you have an

Interest rate of are that your and you put your money in the bank with annual compounding and the interest rate is R that means you don't earn interest on interest until after a year you put your money in today half a year later if you

Put in $1 today half a year later you'll have one plus R over two dollars right with an interest rate R three-quarters of a year later you'll have one plus three quarters are dollars and then a full year later you'll have one plus r

But now after one year you start earning interest on the one plus R so a half year after that you would have 1 plus R times 1 plus R over 2 okay and then two years later you'd have 1 plus r squared and so on

That's annual compounding but the bank could offer you a different formula they could offer you every six-month compounding twice a year compounding then here's the difference after half a year you'd have one plus R over 2 as

Before but now after three quarters of a year you would have instead one plus R over 2 times 1 plus R over 4 and so on okay now what Fabozzi likes to do is compounding every 6 months this is what might make the textbook a

Little confusing because it we naturally think of annual compounding because a year or seems like a natural interval but in finance 6 months is more natural because by convention a lot of bonds pay coupons every six months so for Bo's he

Uses the letter Z to mean R over 2 and his time intervals are 6 months long okay so that means that the formula that Fabozzi gives for a discount bond once it assumes a different compounding interval the phobos e assumption he

Writes p equals a hundred all over 1 plus Z to the lowercase 2t where a lower case T is 2t and so that's the Fabozzi formula for the price of a discount bond of course it only applies at every six-month interval he's not showing what

It is at six and a half months or something like that so that's okay is that clear about compounding and about discount bonds okay now a fundamental concept in finance is present discounted value if you have a payment coming in

The future so I have a payment in T years or two T six months because a semesters then the present value depending on how I compound the present value let's talk about annual compounding the present

Discounted value of a payment in two years is just the amount the amount which is X dollars divided by one plus R to the T or if you're compounding every six months it would be X all over 1 plus Z to the a little bit lower case T all

Right lower case T equals 2t depending so whenever we ask a question about present values we'll have to make clear what the compound au niveau we're talking about by the way there's also I shouldn't say by the way it's

Fundamental there's also continuous compounding I talked about compounding annually or twice a year I can do it four times a year I could if I do it four times a year that means I pay one quarter of the

Interest after three months and then I starting earning interest on interest after three months and so on this what if you compound really often not every you can do daily compounding and or that would mean you would pay every

You would start earning interest on interest 365 times a year the limit is continuous compounding okay and the formula for continuous compounding is e to the R T where e is the imaginary is the natural number 2718 r is the

Continuously compounded interest rate so your balance equals the initial amount what did I say $1 times e to the RT let's continuous compounding okay now if you have a number of the unfortunate thing is that

Present value is allow us to compute present values in different ways depending on what kind of compounding I'm assuming but if I have a sequence of payments coming in the present discounted value of the sequence and

Suppose they come in once a year then it'd be natural to use annual compounding and then the present discounted value P DV is the summation of the payments and what am i calling them here X sub I over 1 plus R now I

Say X of T over 1 plus R to the T from T equals 1 to infinity and that's the present discounted value for annual compounding of annual payments and if suppose the payments are coming in every six months as they do with corporate

Bonds then it might be natural to do compounding every six months so then we do PV is equal to summation T equals one to infinity X of T over one plus R over two to the key and as limiting if I want to do continuous compounding suppose

They have payments that are coming in continually then the present Dallas discounted value would be the integral from zero to infinity of X sub T e to the minus RT DT and that would be a continuously compounded present value

For a continuous stream of payment so if someone is offering me a payments over time then the payments of the payments then have to be sum2 somehow into a present value and this is in finance it often happens that people

Are promising to pay you something at various future intervals over time and you have to recognize that payments in the future are worth less than payments today just as a discount bond it's worth $100 in five years but it's not worth

$100 today it's worth a hundred all over one plus R to the T appropriately compounded so the interest rate and that's true generally anything in the future is worth less so present discounted value is one of the most

Fundamental concepts in finance that whenever someone is offering me a payment stream in the future you've discounted to the present using these formulas so for example if you are lending to your friend to buy a house

And the person is promising to pay you over the years then you've got to figure out well what is that payment worth right now and you would take the present value of it there's a few present value formulas that are essential and I'm

Going to just briefly mention them the present value of a console or perpetuity the perpetuity or a console is an instrument that pays the same payment every period forever okay named after the British consoles that

Were issued in the 18th century they were British government debt that had no expiration date and the British government promised to pay you forever a a amount okay what is the present value

Now we'll call the amount that the console pays its coupon okay and let's say the coupon were one pound per year if it was paying one pound per year and we're using annual coupons an annual compounding then the present discounted

Value is equal to one pound okay over the interest rate that's very simple because this this bond will always pay you one pound and so what is the interest rate on it it's going to equal your one pound is equal are over

The present discounted value so the price of the bond should of the console should be the payment divided by the interest rate another formula is the formula for an annuity okay an annuity is a different kind of payment stream

It's a console for awhile and then it stops it can't an annuity pays a fixed payment each period until the expiration of the maturity of the so the formula for the so it pays let's say X pounds let's not say one pound if it pays X

Pounds every year then the present discounted value and it takes X pounds from T equals one to capital T and then it stops capital T is the last payment then the formula is x over R times 1 minus 1 all over 1 plus R

To the teeth power so that's the constantly annuity formula and that's very important because a lot of financial instruments are annuities the most important example being a home mortgage a traditional home mortgage you

Might take out a 30-year mortgage when you when you buy a house and the mortgage will generally say in the United States not so common in other countries but in the United States it will say you pay a fixed amount well

Usually it's monthly well let's say annually for now okay a fixed amount every year as your mortgage payment and then you pay that continually until 30 years has elapsed and then you're done no more payments okay the final thing I

Want to talk about is a corporate bond or a conventional bond which is a combination of an annuity and a discount bond and so a conventional corporate bond or government bond pays a coupon every six months so a conventional bond

Pays coupon C and I'm out C in dollars pounds or whatever currency every six months and principle plus C plus C at the end so that means that you it's really an annuity and a discount bond together right and so the present

Discounted value for the conventional bond would be the sum of the present discounted value for the using the annuity formula for X equal C plus the present discounted value of the principal which is given by the would be

This one where we have R over 2 because it's every six months and then the final I think it's the final concept I want to get out before talking a little bit about other matters they want to talk about forward rates and the term

Structure of interest rates now at every point in time there is there are interest rates of various maturities quoted and we want to define the forward rates implicit in those maturity formulas this is covered carefully in

Your textbook Fabozzi I'm just going to do a very simple exposition of it and so the forward rates are the concept of a knot the concept of a forward rate forward interest rate is it is due to Sir John Hicks in his 1939 book value

And capital and value and capital about 20 years ago I was writing a chapter for the handbook of monetary economics about interest rates and I was trying to confirm who invented the concept of forward interest rate so I'll build a

Little story around this but I thought it was Sir John Hicks reading his 1939 book and I couldn't find any earlier reference so I asked my research assistant can you confirm for me that the concept of a forward interest rate

Is due to Hicks and my graduate student looked around and tried to find earlier references to it and he could not and then one day the graduate student came to me and said this is like 20 years ago a graduate student said why don't you

Ask Hicks I said wait a minute this book was written in 1939 is that man still alive and he said I think he is so I wrote to the United Kingdom – I found his address I forget Cambridge or Oxford I forget and I said did you invent the

Concept of forward interest rate and then six months went by and I got no answer then I got a paper letter they didn't have email in those day from Sir John Hicks and it was written with trembling hand right

And he said my apologies were taking so long to answer my health isn't good and but he said to answer your question he said maybe I did invent the concept before for an interest rate but he said well maybe it wasn't you maybe it was

From Coffee Hour at the London School of Economics where he was visiting in the 1920s okay so there we go Sir John Hicks is reminiscing to me about what happened in coffee time at the in the 1920s so he said we were

Thinking about so I'm just trying to convey what he told me they were thinking at any point of time you open the newspaper and you see interest rates quoted for various maturities that's called the term structure of interest

Rates and the term structure of interest rates for example you will find you'll find Treasury but you'll find one-year rates quote will be a yield on one year bonds little bit yield on two years there will be a yield quoted on three

Year bonds right let me tell you right now for most of the world today if you want to borrow money for one year it's really cheap in Europe or UK us over much of the world it's like 1% us it's less than 1% I mean the the present who

You are what your borrowing rate will be depending on your credit history but if you have excellent credit one year interest rates are really low but if you want to borrow for ten years it's more like three and a half percent it's

Higher right so and if you want to borrow for thirty years they might charge you four or five percent okay this is the term structure of interest rates and it's quoted every day in the newspaper well I should say I'm thinking

In 1925 in 1925 you'd go to the newspaper to see it now you go to the Internet to see it so newspapers don't carry this anymore but we're I'm still in the mode of thinking of Sir John hooks a hick so we're in 1925 so you

Open up the newspaper in 1925 and you get the yield to maturity or the interest rate on various maturity all for today the thing that's quoted in today's paper is an interest rate between now today

And so many years in the future the one-year interest rate quoted is the rate between now and one year from now right and the two-year interest rate quoted is the rate from now to two years from now and and so on so Hicks and his

Coffee are people were saying well it seems kind of one-dimensional because all the rates that are quoted are rates between now and some future day but what about between two future dates and then they thought about this at coffee ahora

And someone said well it's kind of unnecessary to quote them because they're all implicit in the term structure today and this is where the concept of forward interest rate come and it's explained in Fabozzi but I

Thought I'm going to just try to explain it in the simplest term once you get the concept it's easy and I'm going to assume annual compounding to simplify things but in Fabozzi they being a good finance financier doesn't six-month

Compounding so okay so now words in the air is 1925 okay and we're in coffee hour and we're talking about okay suppose I expect to have I'm just trying to get my 100 pounds to invest in 26 okay it's 25 now this is a whole

Year from the 1926 okay and I want to lock in the interest rate now okay is there any way to do that I mean I could try to I could try to go to some banker and say can you promise me that you'll give me an interest rate in 1926 for one

Year the banker might do it you know but I don't need to go to a banker to do that I can once I have all of these turn all of these bonds available and if I can both go long and short them then then I can lock it in so here's what I

What I want to do this is what they were discussing at coffee I buy in 1925 two year bonds in an amount you got to buy the amount right you've got to buy one plus R sub 2 which is the 2-year yield squared all over 1

Plus R 1 bonds discount bonds they'll mature in two years okay and then I have two short in 1925 1 1 bond okay suppose I do that worth 100 that matures at 100 pounds okay so suppose I do that what happens after one period

Well after one period I owe 100 pounds right because I just shorted 100 a one period bond and so I pay a hundred pounds that's like investing 100 pounds at the end I get this amount I get one I get this amount times 100 pounds right

Because this is a number of bonds that I bought so what is the return that I get the return that I get is the ratio well if it's gives me the we call that the forward rate between 26 and 27 as quoted in 1925 and so that forward rate will

Say 1 plus the forward rate F is equal to 1 plus r2 squared all over 1 plus 1 plus r1 it's just the amount that I get because I see this is what I would get if I bought this number of bonds I get a hundred pounds times this number in two

Periods in 1927 but I put out a hundred pounds in 1926 so the ratio of the amount that I got at the end to the amount that I in 27 then I that I put in in 26 is given by this so that's 1 plus the interest rate I got on the bond so

You can compute forward rates for I'm just shown it for a 1 year ahead forward rate for a one-year loan but you can compute it for any periods further in the future over any maturity and this is the

Formula given it's on page 227 of Fabozzi I'm not going to show you the general formula the expectations theory of the term structure is a theory that I'll write it down expectations theory says that the forward rate equals the

Expected spot rate so you see what I'm saying here in 1925 I open the new open the London Times and right there I have printed the whole term structure today and I can then compute using forward rate formulas the implied interest rates

For every year in the future even out to 2010 they could have computed input if they had bonds that were that long I think they had a few C 1925 some bonds go out a hundred years if you wanted to do the one year rate from in 1925 for

The year 2011 you'd have to find a pair of bonds one of the maturing in 2011 and another one maturing in 2012 and if you did that you could get an interest rate for this year so that's that was kind of the realization but that Hicks got that

The whole future is laid out here in this morning's paper all the interest rates for maybe not out to 2011 I've had two out to a long time in the future and so what determines those interest rates so Hicks in his book wrote the simplest

Theory is the theory that we just these forward rates are just predictions of interest rates on those future dates so we could go back and see what were they predicting for they weren't thinking so clearly definitively about 2011 but they

Must have been because they were trading these bonds and so you could test whether the expectations theory is raft whether people are forming rational expectations by looking at those forecasts and seeing were they

Right okay now there's a lot was a huge literature on this but Hicks said that I just stopped with this Hicks said that there's a there's a those forecasts the expectations theory doesn't quite work because there's a risk premium that the

Forward rates tend to be above the optimally forecasted future spot rate spot meaning as quoted on that date because of risk and people are uncertain about the future so they demand a higher forward rate than they expect to see

Happening in the spot rate so I I will stop talking technical things so I wanted to say something I have so much more to say about but I'll have to limit do the time I what I've laid out here is a theory of interest rates and I've done

Some interest rate calculations and I've pointed out the remarkable institutions we have that have interest rates for all intervals maybe a hundred years and so it's all kind of like the whole future is planned

In these markets it seems impressive doesn't it but the question is is everything really and when I told you the Robinson Crusoe story didn't that sound good like when when the two Robinson Crusoe's discover each other

Aren't they obviously doing the right thing to make a loan from one to the other and I like that I think basically everything I've said here is basically right but I wanted to say that one of the themes of this course is about human

Behavior and behavioral economics and I wanted to talk a little bit about borrowing and lending and how it actually plays out in the real world and how our attitudes are changing our regular regulatory attitudes are

Changing so let me just step back and you know I think this literature that Irving Fisher and boom vive work and many others who've contributed to the understanding of interest rate is very powerful and important and it supersedes

Anything that had been written in the last thousands of years they had interest rates for thousands of years but that simple diagram that Fisher diagram came just a short time ago it's hardly long ago at all but I wanted to

Step back and think about what people said about interest rates going way back in time and so I was going to quote the Bible okay there's there's a Latin word you know this word you know what that means in Latin well actually our English

Word use comes from it so I know how to pronounce it Essaouira in Latin means use and it means also interest because what is interest you're giving someone the use of the money you're not giving them the money they're getting the use

Of the money and they had other words for interest but this ancient word had a negative connotation it sounded that it kind of meant something immoral okay and so we have a word called usury you know this word this is English now it's just

There's a mm it goes back more than two thousand years so the Bible I actually have it here in Latin I'm just curious about these things but I can't pronounce it right but it was for must been written in Greek or Aramaic or something

Original it uses the word yessiree ooh Sara but the quotation it says in Exodus if they lent money to any of my people that is poor by thee thou shalt not be to him as an usurer neither shalt thou lay upon

Him usury now what does that mean because you Sura could mean both interest and excessive interest though it's not clear what the Bible is saying about lending it sounds like it's telling you you can't lend you can lend

Someone money but don't take any interest that's what it seems to be saying but it's ambiguous and I was going to quote the Koran I don't speak Arabic I think there's a similar ambiguity in Arabic so so and I'm

Quoting an English translation of the Quran o you who believe be careful of Allah and give up the interest that is outstanding so or you Sura I that has been interpreted by modern Islamic scholars as that charging interest is

Ungodly and it was interpreted by Christian scholars they go back and they try to figure out what was meant and they couldn't figure it out either and times changed over the centuries but for for thousands of years the Catholic

Church how maybe not thought I don't know the whole history of this depends of which century you're talking about but for many centuries the Catholic Church interpreted this as do many Muslims today that interest is immoral

And therefore the only people who were allowed to loan were Jews because they weren't subject to the even though it's actually the book of Exodus it should be but they weren't subject to the same interpretation so it was considered

Immoral and wondered why is that why is it immoral because we just saw the logic of it now the the Robinson Crusoe story I had two different men on the other side of the island and I had one of them wanting

Consumption today and one of one of them wanting consumption later your first question is you know maybe they were wrong to be different maybe they they should both be doing the same thing why is one of them different than the other

The guy who's going to consume a lot today maybe I should have a word with this guy you know don't do it you're going to be really hungry next year why are you doing this so instead of forming a loan between the two we should advise

Them and maybe they don't need a loan so this comes back to what are we doing with our loans and are we giving people good advice and our or do we have a tendency in the financial world to be usurious are we going after and

Victimizing people by lending the money and that see that I think that there is a problem and this thousands of years of history of concern about usury has to do with real problems that develop so just in preparing for this lecture on

An impulse I got onto Google and I searched on vacation loans ok I found 16 million websites that were encouraging you to take out a loan to go on a vacation ok now is that socially conscious I was wondering about that is

It ever right to borrow money to go on a vacation I mean I I've thought about and I remembered Franco Modigliani who is one of the authors of your textbook and he was my teacher I still remain I remember these moments from classroom

And he was teaching us about these subject and he said he was thinking about examples of investments and he said you know what one of the best investments I can think of is a honeymoon

When you get married you go on a vacation now why are you doing that is it for fun probably not in fact I have a suspicion that most honeymoons are not fun I don't know I think it's just people are too

Uptight and tense from what what have we just done and I bet I bet that's right so why do you do it well you do it as an investment right you want this photograph album and you want the memories your kind of bonding I think

He's absolutely right you should go on a honeymoon so I did another search I searched on honeymoon loans okay and I got 17 million hit beat vacation loans so there are many lenders ready to lend and you should do it okay if your money

If you're just getting married and you don't have any money go to the money the Ussuri you're serious guy and and ask for the honeymoon loan so I'm not sure whether it's bad this is a question I I think that there are abuse and I want to

Just close with Elizabeth Warren who I first met her just a few years ago I actually I remember her book she wrote some important books about the react she is a harvard law professor who wrote books one of her books was published by

Yale called the fragile middle-class and it's about people who go into bankruptcy and she points out that in the us even in back in the old days when the economy was good we had a million personal bankruptcies a year this is because of

Borrowing you don't know how many bankruptcies there are because people are ashamed when they declare bankruptcy and they try to cover it up from as many people as possible there are as many personal bankruptcies

In normal year as there are divorces but you don't hear about them that you hear about all kinds of divorces people are ashamed of divorces too but they can't cover them up because everybody knows but they can pretty well

Cover up a bankruptcy and so they don't talk about it so what Elizabeth Warren is saying she thinks that the lending industry is victimizing people it's then it's advertising for a vacation loans and the like and then they don't tell

People about the bad things that will come so she wrote an article and this is interesting it was in Harvard magazine and that's a magazine that I suspect none of you read anyone read Harvard magazine okay

It's the harvard alumni magazine it goes out to all graduates of Harvard so you don't read it and you probably will never read you will be a reader of the Yale alumni magazine which will start arriving in your doorstep after you

Graduate and it will also include your obituary in the next century where that comes but the Harvard alumni magazine published this wonderful article by Elizabeth describing all of the abuses that happen in lending in the United

States I think it's an I don't know how I ended up reading it I think it was just such a nicely written piece that it just became one of their success story most people don't read that magazine but I read it and a lot of people read it

And she was so successful in convincing the pub this is just two years 2008 three years ago she was so successful that she got a Consumer Financial Protection Bureau inserted into the dodd-frank bill and we now have a

Regulator a new regulator that's supposed to stomp on these these usurious practices so it's it's kind of an inspirational story but the downside of it is she got too carried away criticizing the lending industry in that

Nice article it makes them sound worse than they really are and so Obama could not appoint her to head the Consumer Financial Protection Bureau because it would be too politically controversial so she is now the

Person trying to find someone to head her Bureau but I think that this is just another step and it's happening in Europe and other places the financial crisis has made us more aware of bad financial practices and so usury is

Again on our my usury is abusive lending that's taken without concern for the person who's borrowing and I think that what it means to me is that we will come back to talk about regulation in another lecture but that the original Irving

Fisher store in Bern barbarac story about interest was right and even vacation loans especially honeymoon loans are right but they we need government regulation to prevent abuses is otherwise and we do still have abuses

In the lending process so I'll stop with that and I'll see you on Monday

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