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today we want to continue our discussion of these interest rate differentials where we talked about an interest rate on a specific loan and we said that it is comprised of two things one is this general interest rate environment that is shared throughout the economy and that came from this supply and demand situation that we discussed earlier the loanable funds model plus then what we have our interest rate differentials associated with the specific loan okay and so a real estate loan is different than a car loan and the short term loans are the different than a long term loan risky loans different than say phones and so forth and so that's what we're talking about now are these differentials what will happen is this is that over time interest rates will move as a family and so if the interest rate environment that climate that everybody shares if it's causing interest rates to go up and down over time then other interest rates will move up and down with it in more or less the same pattern but at different heights and so this might be the interest rate on riskier loans and this one might be interest rate on less risky loans and there will be others on shorter term loans versus longer term loans but they're all following this general pattern from the interest rate environment and that is that loanable funds model that we had okay and so anyway what we talked about already is the impact of risk or default risk and you remember we talked about last time about the the credit ratings from Moody's and Standard & Poor's and then they were then the credit scores I looked at that also the credit scores for individuals ranges from 300 - was 8:50 and so anyway but those would be applying more to an individual versus these triple a double a single a and so forth that would apply to corporations and government borrowers so anyway that's what we talked about last time this time what we want to do is we want to talk about term to maturity and the impact term has on interest rates okay now there's a simple answer to this there is no simple answer to what impact term has on interest rates it depends it varies over time if we go get a bond page from The Wall Street Journal or New York Times will say Treasury bonds what we'll see on that table there's different maturities like one month from now that would be a maturity on a treasury security and it will carry a yield so let me put here term and then yield and it'll carry a certain yield and let's say 1% and I'm using hypothetical numbers there will be other terms and by the way there are dozens and dozens and dozens of different issues of Treasury security and different maturities and so as we just go down here there will be two months three months four months and so forth let's say six months maybe it'll be one point five percent and maybe 12-month maturities there will be a two point five percent I'm two year maturities or 24 months four percent five years six percent mmm ten years six point five percent where am I getting these numbers just making them up thirty years eight point one percent now here's the thing about all of these securities if we're just looking at Treasury securities they all have the same amount of default risk right which is minimal there's always a chance that humanity as we know it would be destroyed or that I don't know Mexico would conquer the United States and abrogate all the debts and so forth there's chances that stuff can happen but very unlikely and so it's pretty likely that the government is going to honor its and the federal government is going to honor its obligations so the same amount of default risk on all of these and in terms of the market ability the trading market the markets open every day for these securities and there's an active market for all these securities there's really not much difference in these securities except for one and that one main difference is term to maturity and so you know there's this term economists always using ceteris paribus other things being equal here other things are equal between all these securities and term to MIT and the only thing that varies this term to maturity otherwise these are the same and so if we came and got these numbers here's term that we'll put on our horizontal axis if we came and got these interest rates then what would say is one month and it looks like oh there's one percent and put a dot up here and I'm not gonna try and get all these dots out there let's look at one year and it looks to me like two and a half percent put a dot out there remember our term basis points what we're saying is here there's from one month out to one year it's plus one hundred and fifty basis points right this rises by a percent and a half well let's say five years and then this would be what the numbers were using here here's six percent how many basis points so next are three and a half percent it's three hundred fifty basis points these are huge gaps that I'm talking about here 3a plus three hundred fifty basis points that's a lot and then reality you seldom would ever see that and let's just take the last one thirty years and 8.1% how many basis points 210 right and put a dot out here now in reality there are as I say dozens scores I don't even know maybe a couple hundred I'm not sure how many different issues of Treasury securities and so in reality we would have so many dots out here that it you know they wouldn't there wouldn't be these big gaps but these dots kind of trace out a relationship between turn to maturity and yield and this thing is called a yield curve Wall Street Journal and other publications they've got software and basically what you see with that software is just all kinds of dots out there there are so many of these different securities and what they'll do is their software will trace a line through there that is the closest fit and usually curved anyway and we get a you curve and this tells us the relationship between term to maturity and yield and what this says is longer-term loans and investments have a higher yield a higher interest rate than shorter term loans and investments that's what it says then you know if you go get the newspaper let's say for the next 1,000 days what you're gonna find is that out of probably 900 or 950 probably not 950 but 900 out of the next thousand days you're gonna see an upward sloping yo curve and this is the most common relationship between term to maturity and yield there's a positive relationship longer-term loans higher interest rates shorter term loans lower interest rates and that doesn't just apply to Treasury securities it also applies in general to home loans for example or car loans in general if you go in and price some car loans call up two or three banks and say hey how much for a car loan with the three-year maturity a four year five years six year and you find out that hey the longer the term to hire the interest-rate you go on price a bunch of home loans 15-year 20-year 30-year and you'll find out generally no longer the term and by generally I mean you'll find that out today but if you do this you know once a week for the next 10 years 20 years you're gonna find out that it's almost always that way longer term loans higher yields higher interest rates but it's not always that way here's what we sometimes see sometimes we see a horizontally occur it's flat there are times that we see a yield curve with a little bit of a hump in it sometimes it's just a yield curve that has a negative slope so it's not always upward sloping sometimes downward sloping and the truth of the matter is there is no general rule it has to look this way or has to look that way what happens is people observe something you know like I say nine hundred times out of a thousand and then they come to that conclusion hey that's what it looks like well not really because there are things that affect that and in fact that's why we're here today is talking about what is it that will determine the shape of the yield curve okay and don't forget we're interested in talking about factors that influence specific interest rates and so now what we want to do is talk about not risk but we want to talk about term so how does term to maturity affect interest rates and the answer is usually it's a positive relationship but not always and so since it's not always the same then we need to kind of have some understanding of why it varies over time this is a pretty interesting subject at least from my perspective here is something called the expectations theory that is pretty important it's theoretical but also it's got a foundation in the real world here's what it says is that the interest rate let's say the long-term interest rate is an average of today's short-term interest rate and short-term interest rates expected to prevail in the future and I purposely added one more word in here but kind of threw it off to the side into the relevant future I don't mean to say for thousands of years out or any sort of random future but over a relevant period now I make that clear what I mean in just a minute and I've underlined a few words here that maybe you want to focus on I'm gonna focus on it in my discussion long-term interest rate here's what this says the long-term interest rate isn't doesn't have an independent existence you see that this doesn't say though there is a long term credit market it's got its own interest rate that's not what this says it says the long-term interest rate is dependent on short-term interest rates it says the long-term interest rates that's gonna be an average of the short-term interest rate today and the short-term interest rates that we expect in the future and so let's just talk about a simple example here's today and let's talk about a simple example of two years a two-year period a two-year period of course is two one-year period so add it together huh that's math and so if we just kind of said hey what's the interest rate on a two-year loan an answer is we don't know yet according to this expectations theory if today a one-year alone has an interest rate of let's say four percent and then we expect that a one-year hence one year from today we all got together and said hey you know what's the interest rate gonna be at that point that would be another one-year loan today we have an expectation of what that rates gonna be doing no no nobody knows anybody who knows can just become the wealthiest person on earth by speculating in bonds anybody knows what that rates gonna be that would be like if somebody said to you hey I know what the price of general electric stock will be a year from today well if you do you can get rich well if you knew what interest rates are going to be a year from the day you can get rich from that you can speculate in those markets you remember the idea of interest rate risk right if you know if interest rates are going up or down you know what's going to happen to bond prices they're going to move in the opposite direction so we don't know here's what this says though expect when do we expect it today today's expectation of the one-year rate one year from today and let's just say that I can snap my fingers and everybody in the United States everybody in the world suddenly say hey you know what I think one year from today interest rates will be let's say 6% on a one-year loan as soon as I snap my fingers everybody thinks it's 6% you know today there are 4 percent but I think there will be 6 percent in the future then here's what the expectation theory says it says that the 2-year interest rate two-year rate let's say today's two-year rate standing right here 2-year interest rate today would be 5% an average of today's short-term rate and the short-term rate we expect in the future now why an answer it's applying to man of course supply and demand answers everything doesn't it supply and demand let's just say it weren't today's rate is 4 percent and we do expect 6 percent we're not gonna mess with that but let's say that this interest rate were seven percent hypothetically on a two-year today's interest rate two year loans 7% and now we'll have some mutual fund company or some pension manager some insurance company they're sitting over here with a billion dollars and they're gonna lend this money out and what they would say what their billion dollars is hmm let's see I couldn't loan my money out short-term on a billion dollars I get 4% that would be 40 million dollars in the first year of interest I think that when that loan is up and I get paid back I'll have another billion dollars I think I'll get 6% then 6 percent of my billion dollars would be 60 million so if I would loan my money out for one year plus one year this is my long-term loan to short-term loans I would get 40 plus 60 I get 100 million dollars hey that's pretty good 100 million dollars but then this same pension manager insurance executive and so forth they say hey I got a billion dollars what if I loan that out for two years I get seven percent I get 70 million dollars this year 70 million next year I get 140 million dollars you know what that sounds better I think I'll do that and so what they would do is flood the market with these this two year loans there would be like no no more one-year ons to year to year to year then there'd be a huge increase in the supply and by the way we were doing this last time I don't wanna over emphasize at this time but where we were talking about you know the impact of risk and I was showing the supply of credit shifting well what we would have in this case is the supply of credit would shift away from one year oldest or two year ons and in that massive influx of new credit new supplies of credit would bring down those long-term interest rates so you just cannot have a long-term interest rate that's different from this average suppose it's the other way around suppose that this was 3% supposed today's 2-year rate is 3% and then today's one your rates for and we expect what 6% next year at this time then we'd say oh I've got a billion dollars get four plus six I get a hundred million dollars if I loan for two years I get thirty million 30 million 60 million Oh Oh nobody would loan long term in this situation the supply of credit would be withdrawn from the long term market and that reduction is supplied credit would cause the price to go up the interest rate and so what's going to happen is these massive flows we are talking about credit markets now we're billion dollars investments are not huge there are hundreds of investors in the world that have a billion dollars to invest and so to move a billion dollars around that's not a big deal and so if you think that this rate right here the long rate is not an average of today's short road rate and the short rate we expect that future if you think that's not true you move your money one way or the other you either move it into the long market if this rates too high or you move it out of the long market in the short rate market if this rates too low and then what's those dollars of stop moving once suppliers say or lenders ok I'm comfortable with this they stopped putting they say I don't really care I could flip a coin I'm okay with long term or short term I don't care and that would be if it's 5% here's on average then what happens is you got a billion dollars you go well you know I'm gonna get 40 million dollars here I'm gonna get 60 million there that's a hundred-man or I get 50 plus 50 that's a hundred now I don't care and at that point the massive flows of credit stop and it is then it's a what we'd call an equilibrium situation so in equilibrium the long-term interest rate is an average of today's short rate and the short rate we expect in the future okay now let's say we look at this situation just the way I've got it written down what's the yield curve look like in this picture first of all that yield curve that I drew a few minutes ago that yield curve is actual interest rates that are observable it's not in our heads not what we expect what we observe and in this little picture I have right here we've got two interest rates that are observable today's short-term interest rate one-year rate and today's two-year interest rate and so if we draw a yield curve term to maturity here and interest rate here if we
raw you curve what we see is this one year yields 4% two year yield 5% so now we have an upward sloping yo curve let's look at this rate the five-year I'm sorry the 2-year interest rates 5% this is an average of four I'll say average of four plus something and that's five percent right what is that something that's got to be six right four in something average five that's something six so if we have an upward sloping yield curve if the long-term interest rate is above the short-term interest rate it must be because that's something is higher and that four so if we see an upward sloping yo curb then that can only be caused under this explanation under this story it can only be caused if lenders expect short-term interest rates to rise in the future above today's levels if we don't expect that if we thought the short-term interest rate did stay where it is today four plus four don't average five four plus something bigger than four that's what creates at five and so the only way to get an upward sloping yo curve is for us to expect higher short-term interest rates okay suppose we had a downward-sloping yo curve I put a case of that up a moment ago that let me go back and do this again what one year interest rate maybe is 4% two year interest rate maybe a 3% we pick up the newspaper it says to us this 1-year Treasury securities are yielding 4% 2-year Treasury securities yielding 3 how can that be well this rate the long term interest rate is an average of today's short-term interest rate and the short-term interest rate we expect in the future four plus something average 3 that something's got to be less than 4 if that were a 4 4 + 4 average out to floor so 4 4 and something to average out 2 3 then this something has got to be below where it is today so we expect short-term interest rates to go down in the future - where - right so the only way to get a downward slope and this is a negatively sloped yield curve the only way to get that is if lenders expect short-term interest rates to decline below today's levels now I don't want I don't want to the next thing - you can go in your notes if you want but I'm not going to test you on it because it's a complication that if you were an investor it would make a big difference if you had a hundred million dollars or a billion dollars to invest but for you to understand the theory of it this is what you need to know but I'm going to tell you one more thing and it's this what I'm telling you right now is not strictly true but it's kind of true but not strictly true and here's why not let me go back to the story I had a minute ago hey I've got a billion dollars if I invest whatever I had here before let's put this as well I'm only then at five if I've got a billion dollars I'm not really indifferent between these two approaches if I've got a billion dollars I say look I get 40 million dollars interest in the first year I'd get 60 million dollars of interest in a second year that's a hundred if I go through the longer term approach I get fifty fifty would you rather have the 40 million in the first year and 60 million in a second or 50 million in each year they both add up to 100 when do you want your money sooner or later sooner so really we're not indifferent here but the story is best if we leave it at that point and this is what we would call wherever I wrote this down where I said it's an average the way I've told the story I've said this is an arithmetic average that's the way I'm telling the story where five is an average of four and six and five is an average of four and six if you do the math the way you learned in grade school but when we allow for compounding when we allow for the time value of money to enter into this then 40 million plus 60 million is not as good as 50 million plus 50 million and so what you would do in that case to actually be accurate 100% accurate as we would use something else called a geometric mean or average rather than an arithmetic mean or an average and so I'm just telling you that even though it seems like I don't know any difference different between these two I do know the difference and I do know that what I'm telling you is not exactly true but it's pretty close if somebody said would you rather have four dollars plus six or five dollars plus five you almost don't care but when we start talking about millions and millions and stuff and with the rates it doesn't make any difference of this four and six or five and five versus 40 60 50 50 the percentages that doesn't make any difference but in terms of how much do you care not much if we're just talking about a few dollars ten dollars and so forth anyway but to allow for the compounding this is really it's a more sophisticated approach we would be doing one plus the interest rate in the first year multiplied by one plus the expected interest rate for the second year equals one plus the two year interest rate this is where we start getting the compounding in there don't put this in your notes unless you know unless you just enjoy having a bunch of trivia in your notes but I'm just saying to you that the way you would do it with an arithmetic mean I 1 plus I 2 e equals R 2 and well I guess it would be divided by 2 and then you'd be done that's arithmetic mean but here what the geometric mean it's all more complicated and so I'm just saying to you that the way we're telling the story here is the simplest possible way and it's not a hundred percent accurate but the theoria but the idea of it is exactly right and that's what you should focus on and we will always like on tests and stuff like that we'll be using the arithmetic mean where four plus six average five and that's the end of the story but in reality four plus six don't average 500 about this geometric mean it would be a little bit different than five it might be four point nine seven percent or some number like that okay what about a 30-year loan well let's just say a three year on we've got an interest rate that's three years and what I'm saying is that that would be an average of three things it would be an average of today's short-term interest rate it would be a second item would be the short-term interest rate that one your interest rate that we expect to prevail prevail one year from today and then another short-term interest rate that we expect to prevail two years from today and so we've got this three-year period okay and we've got a short-term interest rate today let's say it's four let's say that we expect a short-term interest rate to be six two years from today and then we expect the short-term interest rate to be I don't know let's say seven did I say two years four percent today we expect that one-year rate to be 6% one year from today we expect the one-year rate to be 7% two years from today and so then the alternative would be make one long-term loan for three years so 17% divided by three is how much five point six seven percent and that would be using an arithmetic mean that would be the average that would be our three-year interest rate okay what's our yield curve look like one year four percent what's our 2-year interest rate anybody anybody Bueller that's from Paris Bueller's Day Off what's a two-year interest rate here five how'd you know that four and six average five okay so five what's our three-year interest rate five point six seven right let's go out another year let's say on this day that would be three years hence three years from today we expect that short-term interest rate to be I don't know let's say 6% again so what do we have we have twenty three divided by four equals six point seven five five point seven five help me out here I added six point twenty three five point seven five right okay yeah I had one more for let's say that one two three four years from today we think the short-term interest rate would be four percent now 27 divided by five equals what would this be four five point four and so now if I trace my yield curve out there's a yo curve that rises and it starts to drop off this is what we see today this is the one-year yield one year hence two years has three years hands and then four years hands and so our expectations about the future would tell us that oh now we have a yo curve that rises for the first open to be three years out of four years out and then starts dropping off and you see what happened really was this is that we really thought that after what two years out that interest rates short-term rates would start dropping off right but ru curve continued having a positive slope on it all the way out for four years do people have expectations about interest rates three or four years away and the answer is yeah of course they do those expectations have a different nature though if you just ask me what I think interest rates will do over the next six months I'll be thinking a lot about the current policy and what's the economy doing today we talked last time about a procyclical pattern and interest rates right or I might think about what's happening overseas what's happening to the value of the doll or the economies overseas I might think about things like that but if I start thinking about what our interest rates gonna do in 3 or 5 or 10 or 15 or 20 years who knows what's gonna happen with those things then we start thinking about institutional types of issues it's like what's the Federal Reserve committed to what's happening with physical policy the President and the Congress and what kind of things are they doing now that maybe will have a lasting impact for the last couple of decades the Federal Reserve has been committed to fighting inflation keep an inflation down and not every day every month but at least trying to bring it into line with one to two percent inflation that has been their commitment their number one commitment and so what I say is this as long as the Federal Reserve has that commitment as far as I know legislation hasn't changed that would influence the Federal Reserve and make them commit to some other inflation target the people who work at the Federal Reserve the top officials they have PhDs in economics they're sort of being brought up being trained the same thing at different universities but more or less the the evils of inflation so what I say is you know I kind of think the Federal Reserve's committed to inflation over the long-run one or two percent and if I think that then that's going to shape my expectations of what's going to happen - right the Fisher equation tells us how inflation figures into this whole interest rate story so that kind of figures into what I think interest rates are gonna do five or ten years down the road twenty years down the road and so our expectations are different and maybe you never think about it but on the other hand you're neither an economist nor a person who manages a hundred million dollars of money but if you started having to manage a hundred million dollars worth of money and somebody said to you hey what are you gonna do with this long term money you'd start forming expectations about the future why cuz you have to you don't have a choice somebody who does think about those things will get your job so then you will think about them but the point is that once you start thinking way down the road you'll build other things into your thinking not just what's going on today if somebody asked me about the stock market what's gonna happen to stock prices over the next 10 or 20 years you know right now I might be thinking is there a recession or is the economy strong what our corporate earnings doing that kind of stuff what's the latest headline is there Warner middle east our oil prices going up or going down stuff like that could influence what I think stock prices will do over the next few days few weeks few months but if somebody said to me hey what about stock prices ten years so now I started thinking about huh is this economy fundamentally sound what's our competitive position relative the rest of the world are we passing laws that make it impossible to do business the United States or are we passing laws it would encourage people to do business and so we form expectations but they are of a different nature and then according to this expectations theory and if this doesn't work then supply and demand doesn't work people aren't trying to get rich but according to this then those expectations will shape our y ou curve and that's not the end of the story though but it is what gives these little Wiggles and twists and turns to the yield curve the way I drew that first when I was just making up numbers and so forth but yo curves are you know sometimes it will be very steep and then just flatten out on you why expectations now there's something else to be put in the story here and it's working at the same time as expectations and this goes by different names the second theory that I'm going to talk about I'm gonna call the quiddity preference well what it comes down to whatever theory or whatever label you attach it comes down to avoiding interest risk or interest rate risk I used to turn them last time when we were talking about default risk I said that people are risk averse well we are averse to interest rate risk you remember this idea of interest rate risk I drew the little picture before and then we've got here's interest rate then over here is bond prices and this is not only bond prices but loans can be sold in the marketplace so it's the value of the loan in the marketplace but I drew this and then I showed that if interest rates go up the value of these loans and securities goes down remember that and then also turn to maturity where the loss is small for short term securities and loans and large for a longer term remember all that discussion well that's the second thing that's operating here and so the attempt to avoid that interest rate risk stability is what we like okay liquidity is an attribute assets have liquidity is the most liquid of all assets a dollar bill you know what it's going to be worth one dollar but the thing is if we get a 30-year bond what's it gonna be worth I don't know the prior interest rates fluctuate a little bit in the market and a 30-year bonds price goes way up and way down it's not very liquid it's not very much like cash and so people don't feel good they've got a preference toward certainty and stability and so what this says is people will try and avoid these 30-year loans and try to focus on the one month to 12 months they'll try and focus on shorter term there's a preference for that and so if we had here supply and demand to graphs if we started off here's one year loans and here's 30 year loans and let's say they're both paying 5% to begin with 5% 5% and then if we come in and say hey what about this preference for liquidity this avoidance of interest rate risk then what we'd see is this is people go yeah this makes me nervous 30-year bonds that makes me nervous and so then the supply of funds would start moving to avoid that kind of risk and then what we would have is this greater supply of funds here s two less supply of funds here s two and then maybe this interest rate to go up to five point seven percent and maybe this one would go down to four point one percent and now when we draw our yield curve just considering this one factor alone one and thirty would I have four point one five point seven upward sloping yield curve now here's the final point the real yield curve that we see is both of these theories put together and so this is always with us regardless of our expectations about the future if we think interest rates are going to stay exactly where they are today short-term rates are not going to change there's no expectations built in this we're gonna have an upward sloping you curve and then when we superimpose the expectations on top of that we'll get a yield curve that may look a little bit Wiggly or may even slope downward but it would be because of expectations on top of that liquidity preference or that attempt to avoid that interest risk it's both of those theories working together that's it for today we will finish up this material on interest rate differentials next time so long you
