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you so what we want to talk about today is yields or interest rates let's start off with that basic statement I'll use this letter I to represent a yield or an interest rate not a number of dollars but a percent we can calculate a yield or an interest rate or rate of return or three different terms we could calculate that on various types of investments will mainly be talking about bonds in our particular applications but you could calculate that for stocks and in theory any other kind of an investment the way I stated this last time is we've got a standardized way of talking about interest and the standardized way that we have of talking about it is to say the return to the investor per $1 loaned or invested per one year and the reason for that is investments whether it's bonds or stocks are an investment in real estate or whatever investments are of all different sizes and for all different durations or terms and since there are all different sizes then we can't make any direct comparisons between yields or returns unless we do something to standardize that and so what we'll do is we'll divide it if it's a million-dollar investment will divide the return two million ways to get it down to per $1 worth and that way when compared to a $50 investment which we would divide 50 ways our return and say how much do I get per $1 worth of investment same thing about terms some are short-term investments some are long-term investment will standardize that and say for one year's worth of this investment hole would be my return and so on then if we get a number that says point zero four in our calculations that would mean we're getting four pennies four cents per $1 invested per one year okay and then we would express that as four percent and this way of course moving the decimal over and add in the percent now we'll build this up but this is just the interpretation and what I would add before we go on is we're gonna end up with a calculation with our calculators on punching buttons and the important thing that you know is this on in almost any kind of calculation when you were in grade school and things like that and you were learning mathematics just being able to do a calculation was the point of everything but now at this point in your life when you do a calculation nobody's given you calculation just saying hey can you punch those buttons and get this number now it's the interpretation that's so important being able to punch the buttons is the thing that you've already got that skill and now when you get that number it's how do I interpret that what does that mean and that is really what this is about at this point you're gonna have a number and you don't want to just say Oh point zero three eight six yeah what Oh point zero three eight six is what and you need to be able to say here's what that means to me now the way we do this is we have a fraction and in the numerator their fraction we put the annual return on the investment and in the denominator the size of the investment okay so all we've taken is this sentence the return of the to the investor per $1 alone per one year we took that sentence and turned that into a fraction which now we still need to flesh that out some but you see here where we've got annualized returns we've already you know when we go to our formula we're gonna have something annualized in the numerator and by dividing that annualized return by the size of the investment we will divide that down if it's a million-dollar investment we're gonna be dividing that return a million ways to get $1 worth if it's a $50 investment we're gonna divide by 50 whatever that return is to get it down to per $1 worth of investment and now on this and this annualized return we have two kinds of returns that investments provide us okay and one is just this and to go back to the bond we can generalize a statement but coupon interest per year I should say annual coupon interest okay plus annual capital gain that is to say a capital gain would be an increase in the value of the investment its market value and the size of the investment we're not going to change that and I'll write it slightly differently amount invested again we're just expanding each one of these terms when I say something about the return I want you to know there are these two components and now let's talk about that coupon interest I'll draw a bond okay we'll put a face value on it or a maturity value we'll put a coupon interest rate let's say 5% and we'll put a maturity date let's say five years hence so whatever today is plus five years okay so now from this example here's our annual coupon interest it's the coupon interest rate times the par value and so here would be point zero five times a thousand dollars equals fifty dollars a year that be our coupon interest okay how about our capital gain how much can we tell from this there's a missing piece of the puzzle here that week and I'm gonna fill in this missing piece of the puzzle or provided I should say but right now we can't because here's how we know five years from today here's what the bond will be worth a thousand dollars you'll cash it in know by cashing in you'll hand the bond over they will say here's a thousand bucks thank you very much but the other part of the story is how much you pay for it if you buy that bond today hypothetically by today for and just an amount of money let's say nine hundred dollars you purchase this bond you write somebody a check for nine hundred bucks right now now we have the information here's our capital gain it's the par value minus the purchase price right our par value is a thousand dollars our purchase price nine hundred I'll write that in a thousand minus nine hundred equals one hundred yes but annualized we've got to have an annualized return because that's what we're asking for here per one year if we buy this today for nine hundred and goes up to a thousand dollars between today and maturity that's five years to get that hundred dollars we don't get to a hundred dollars this year all right there's time today five years hence we pay a $900 for today it goes up to $1,000 here and each day there will be a fluctuation in the price but over time that price will move up along that line someplace sometimes a little above sometimes a little bit below but over time if we buy that here and in five years from today we have $1000 we've got a $100 capital gain but we it says here annualize that on an annualized basis five years and that's $20.00 a year so let's do our final calculation now our interest rate on this bond is the annual capital gain our annual coupon interest $50 our annual capital gain $20 and how much did we invest in this how much did we invest nine hundred dollars so we have seventy dollars income per year on average from a nine hundred dollar investment and that is well it's a very lucky number here point zero seven seven seven seven seven seven equals seven point seven eight percent I'm rounding home and so what that says is if I buy this bond today and hold it until it matures five years for today I buy it for nine hundred dollars it goes up to a thousand that I'm getting almost not quite eight cents per one dollar invested each year and this would be referred to as a yield to maturity because we're calculating it what's your yield what's your rate of return if you buy today and hold it till maturity now this is somewhat imperfect it's I wouldn't call it a rule of thumb but it is a formula that we can do in a fairly simple way the problem with this in real life is that when we talk about the amount invested how much is invested in that okay it's true that we invested nine hundred dollars on the first day we got nine hundred in the denominator but what's happening over time is that at any point in time we could sell this bond and so if on this particular day you could sell the bond for let's say nine hundred and thirty dollars on that particular day you say I could sell this for nine thirty but I'm leaving my money in there what you're leaving in there is nine hundred thirty dollars and so the amount you have invested that day is nine hundred thirty dollars and so it's really changing over time and so to some extent I mean this is a the math is correct and the the model is correct as far as it goes if we understand what we have well what we have is something that's a little bit imperfect here okay there's a more exact way of doing this but it's not an easy way of doing it and it's a lot easier to do if you had your calculator okay let me calculate present value equals and this will just be the formula you've seen this formula before we're gonna take the future dollars this generates $50 divided by 1 plus I to the first power plus $50 divided by 1 plus I to the second power and so forth if you are calculating the present value that's the way you do it and then over here on the left hand side because we know this here's the price today its value in the marketplace is nine hundred dollars right nine hundred dollars is the value in the marketplace and that value in the marketplace is all these future receipts that we're gonna have from the bond divided by 1 plus I to the T power there's only one unknown in this formula and the unknown is the hi and so what we could do we could spend some time with this with a calculator I could do it in a couple minutes with a spreadsheet but just through a sort of a hit-and-miss we could put in various interest rates or you know like 7% 8% sevens a little too low eights a little too high and then we just start trying different numbers and there will be a number and interest rate number that would make this statement true 900 equals all that stuff well that's not fast but that's exact but that's not fast it's not something you're gonna do like if you're just you know sitting down maybe at the bank or something like that or most of you're not gonna do this ever but it's more exact and so what we do instead is we use that formula that we've got down there for yield to maturity and that's the one we'll be using but I do recognize that there's it's a little bit of a fast method that's not right out to several decimal places but it's pretty close and that's what we'll do that's what a lot of people do most people do that are calculating these yields now here's how we would change this well I'm not gonna tell you how we would change it because I wouldn't change it till I get to the next formula or the next concept that we want to talk about anyway are there questions about this here's why that wouldn't work with a stock and I started to say hey how would this work with a stock with the stock you could say something about what's my annual coupon interest that would be like a dividend it's not coupon interest but what's my annual dividend payment and then with the stock you could talk about your capital gain but only over a certain period like hey I bought that stock three months ago here's where it is today or I bought it three years ago here's where it is today it's a game but it's not really calculated to a maturity date because the stock doesn't have a maturity date and by the way we made by a bond and not hold it to maturity and so that really is what leads us to this next idea what if I don't buy that bond and hold it for five years what if I buy this bond and I pay $900 for it but what if I only hold that for not five years but three years then what and so the concept that we have on this particular case is a holding period yield or a rate of return and we've got the same general things in this formula is our annual coupon interest plus annual capital gain and divided by the amount invested now in this particular story will all change as little as possible it's the same bond we're gonna buy it for $900 but let's say we hold it for three years and so it'll still have two years to go until maturity when we sell it and let's say that we sell it for sell for oh I don't know 960 dollars let's don't do that let's say 980 dollars I have a reason for changing and I don't want things to be too much like the case before and so now here's what we would do huh annual coupon interest what is our coupon interest on this $50 right just like before 5% of $1,000 hold it for three years sell for 980 what's our capital gain we bought it for 900 went up to 980 our total capital gain is $80 but annualizing that it's $80 over a three-year period see now why I didn't want to use what 960 to sell it I didn't want to be a $60 gain divided by three years 20 just right before so we're not doing that but anyway so it went up in value $80 over a three-year period how much is this anybody $26 and how much $26.67 the amount invested $900 what 76 67 over 900 eight point five two percent anybody get a different number I don't mean these to be you know two different formulas we sometimes use one term sometimes the other okay now we've used the same type of calculation as we did for yield to maturity and all of these are coming back and basically following this general statement that we have here but now we're not holding it until the maturity date it's a holding period yield just for that three years and sometimes that's called a rate of return you particularly would call this a rate of return it for a stock because there is no such thing as a maturity value on a stock you buy a stock and you sell a stock and then there's two kinds of return from a stock not coupon interest but a dividend that's the sort of guaranteed payment that they send you in the mail some stocks that's a zero they don't give you any dividend other stocks almost all of your return is dividend but this is if we were talking about a corporate stock this would be the dividend part and this would be the capital gain if it's a bond we get ahead an example bond it's a five-year bond but we held it only three years now something I want to emphasize and it's this you can calculate yield to maturity before you buy the bond you can go hey why buy that bond today and I hold it till it matures five years from now my rate of return be seven point seven eight percent because all those numbers are locked in those are certain it's like hey I'm going to get twenty dollars a year in capital gain if I buy it today and hold it for five years so this is an ex ante or before the fact type of a calculation I can calculate that that before I buy that bond and this kind of a calculation is xposed or after the fact this is looking back and said hey you know I bought that bond I paid $900 for it now I never knew when I was gonna sell it I bought that bond and maybe I sell it the next day maybe I'd sell it and maybe I hold it to maturity maybe I'd hold it for a year or two or three or five or 4.1 and I didn't know we never know when we're gonna sell these investments and we didn't know what the price was gonna be so this is after you sold it hey you call your broker I want to sell this month or I want to sell this stock and you sell the bond or you sell the stock for nine hundred and eighty bucks and then you go oh what was my rate of return and now we're looking back we're not looking forward looking backs and here's how I did are you with me and so these are fundamentally different and this would be this is the only way to do it with a stock you're always looking back at the stock you never know what they're gonna do with the stock for its price is gonna be and there is no maturity you can't say I'm just gonna assume I hold this to maturity there is no such thing so it's always gonna be a looking back thing no here's what you could do you could say hmm if I bought this bond and held it for three years and sold it then for 980 here's my return you can do that but those are just all what-ifs 3 years how'd you come up with that 980 where did you come up with that and if somebody told you you know I'm gonna buy some General Electric stock I'm gonna pay $20 for today I'm gonna sell it for $45 three years someday you just say ok let's talk about something else because you don't know what you're talking about nobody knows that so the concept with a bond something that's pretty safe we're pretty sure that it's going to mature at a thousand bucks this has some meaning this yield to maturity but for most investments that we are going to trade f
r all stocks and for bonds that you think I'm not gonna hold it for maturity this would be the way you'd do the calculation except on test day you've got to be able to do it either way there's one other yield I want to talk to you about and it's called current yield and this current yield is focusing on cash flow and so all that we do with this one just say how much do I get in that check they send me every year okay in this particular case you get a $50 check each year and you've put $900 off to buy this thing and so you're gonna get back about five and a half cents a little bit more five point five five percent five point five six or something you're gonna get a little over five and a half cents per dollar that you invested as a cash flow basis and so this is really coming back to this yield to maturity and just saying okay forget about that capital gain I know I'll get that someday but it'll all show up at that point is 100 bucks and what do I get in the meantime and the people who focus on that are the ones who would be buying this bond in order to pay their bills like if you were retired and you went out and bought a bunch of bonds and said hey I'm gonna get the interest from these bonds that coupons and I'm gonna use that to pay rent or house payments or take vacations or whatever mmm you can certainly do that what you can't do is go down to the you know to a car dealer and say I want to negotiate on a car I've got thousands of dollars of capital gains coming for years from today or five years for today can I buy a car they would say no can you make the payments and so can you make the payments that would be this kind of a current yield that would be talking about then and this is not particularly important to most people but there are people for whom this is very important it's the cash flow kind of income any questions about this yes no that one when you say that one you mean okay here's the thing you're getting 5% of that but you only put that much money out and so you're getting $50 not on a one thousand dollar investment that'd be a five percent return you're getting $50 on a nine hundred dollar investment and so that gives you an extra 10 percent of that it is coming back to you you put up its what this is saying to us is what is my and your coupon interest per dollar investment and this is the dollars invested okay that's the value of the day you bought it that was its present value the day you bought it hmm otherwise you weren't about it right or it could be less than its present value to you but it's not more because then you'd say no like you couldn't say present value for me eight hundred eighty dollars and they'd say nine hundred yard buy they go huh you should say no okay all right let's go on to one more topic then we're done with these interest rates let me give you one of those problems on test day where I put that formula up here and I said you can through trial-and-error hit-and-miss try to find that yield would you like to do that because because there wouldn't be time for the other problems on the test so you get three percent correct you know I mean that's you got that one but nothing else okay this last topic that we want to talk about we've just been talking about interest rates and yields here for the last few minutes there's been this word and all economists know about this word maybe you know about it but there's been a word that we haven't been saying because we know about it and we just think we economists hey let's don't just keep repeating this over and over we all take this for granted and the word we haven't been saying is nominal and by nominal we mean just an unadjusted interest rate just the kind of number you'd read in a newspaper see it reported on television if they say treasury bonds are paying five point one percent that's the interest rate but that's a nominal interest rate here's what we want to recognize lets us talk about and i'll use 5% as a number here let's just say that you own me a thousand dollars for one year and I say I'll pay you five percent to use your money that's the interest rate I'll pay so you give me a thousand dollars I do whatever for a year you do whatever for a year or a year from now I get back and I say here's your thousand dollars back and here's 50 bucks for letting me use your money and that's more or less the way a bond would work or a loan okay here's the additional twist though that we want to add to the story while I've got your money something else could be happening out there in the world for example there could be inflation right if I take your thousand dollars and let's just say over here at the McDonald's restaurant hamburgers are selling for $1 apiece if I take your thousand dollars today and go over to McDonald's restaurants say what will this buy me they would say a thousand hamburgers and I say well thank you give me those hamburgers I got a thousand hamburgers and then let's say that what happens over the next year is the price of stuff shoe shoes and socks and basketball tickets and cars and houses and hamburgers let's say the price of stuff goes up a lot and let's just say hypothetically it goes up a hundred percent prices double $100 pair of shoes two hundred dollars twenty thousand dollar car forty thousand dollars one dollar hamburger two dollars so a year from now I say okay let's get back together here's your thousand bucks back and of course the fifty but let's leave that to the side right now here's your thousand bucks back and say oh oh thank you you're an honest person you promised to pay me back and here it is if you go over to McDonald's and say hamburgers place they would give you 500 hamburgers not a thousand so inflation is eating up or destroying or some people would say taxing the purchasing power of money and so when you are thinking about this am I gonna loan money to that guy yeah you want to be paid interest you want to be paid a return on making a loan but what you'd like to have is dollars when they come back to you that are just as valuable as they were before yeah I'm willing no all my money for five percent let's say but I want a dollar to buy just as much as it does today so you give me five percent and dollars of equal value of equal value of equal purchasing power and so even though we don't verbalize this very much that's what we're going for you wouldn't have to verbalize it if people just said hey there's a hundred percent inflation and I said hey loan me a thousand dollars I'll pay you five percent you would just say no why not well because I can buy a bunch of stuff at that thousand dollars right now or I could loan it to you and if I loan it to you when I get it back it's this worth half as much it's still one thousand dollars but it just buys half as much stuff I'm gonna go buy that stuff you could go buy shoes for yourself or you could go buy whatever canned goods things you know that have some I mean things today and you could use those over time those shoes and so forth and they would not lose purchasing power I mean they would still a pair of shoes a pair of shoes but if you give me that dollar today and I give you back later when prices have gone up that dollar is not worth as much so when we are setting these interest rates in our lending process what we're really doing is this is we want some real interest I'm willing to loan you that money for 5% let's say but I also want you to pay me for a loss of the purchasing power I want both of those things so I'll tell you what yeah I'll loan you that money for 5% plus if we've lost what a hundred percent or a 50% of the purchasing power of this I want to be compensated for that too so anyway we've got this formula where that the interest rate that we observe in the market place and like I say we usually don't say in nominal we just say the interest rate but it really has two components to it and the real interest rate might be like five percent and if you say you know prices are going up a hundred percent they're doubling I want that inflation premium and by the way out let me jot that term down in this inflation premium it's not looking back it's looking forward so this is really the expected inflation rate over the life of the loan and by the way this rate is annualized everything about interest is annual remember we talked about that before the annual return per one dollar and so forth anyway so we're always talking about an annualized number here and so we're talking about an annual inflation rate what percent increase in prices is going to occur and so if you say I'm willing knowing for five percent but prices are going to double then what you say is I'll tell you what I'll do all on you that money for one hundred and five percent now you're protecting yourself right you're protecting yourself against me giving you dollars that are there you give me dollars out of this big when I give them back to you they're that big in terms of their purchasing power you've got to protect yourself and that's why you're doing would I be willing to pay that much yeah here's why I can go buy a thousand hamburgers today if I wait till next year to go buy those hamburgers I don't only buy 500 with that saying I want to beat inflation I want to get there before they raise the price so I'm willing to pay extra I'm willing to pay this little bonus to get that money if I want to go buy a house and the price of housing is going up thirty percent a year I'm saying oh my gosh I want to buy a hundred thousand dollar house if I wait till next year it's one hundred thirty thousand dollar house and so if you say to yourself I think there's gonna be thirty percent inflation I'm gonna attack that 30 percent on the interest rate I said okay I'll pay thirty percent more for that money because I want to buy that house and it's prices going on thirty percent if I wait for a year it's gonna be a hundred thirty thousand bucks okay so this is something that both of us now neither one of us are gonna verbalize this if you said to me hey there's gonna be a hundred percent inflation I would say you know you're just making that up we don't know that do we I'm guessing more like twenty percent and I'm negotiating now and I'm still thinking hundred percent but I'm not gonna say yeah you're probably right could be two hundred percent you're just going to charge me more so I say yeah you know I think you're a little bit crazy not a little bit maybe a lot probably maybe ten percent twenty thirty at the outside well and whatever you say if you say 30 I'd say 20 and if you say 20 I say 10 that's what negotiation is about right so anyway but when we see an interest rate and these are outrageous numbers that I put up here when we see an interest rate it's got an inflation premium built into it okay if we look over long stretches of time and this is how about this the interest rate in a non inflationary environment if we look over long stretches of time and find those periods where there's not inflation people not talking about it's not on the horizon and so forth what we see is that the Treasury can go out there and borrow money at about two to three percent it depends on the term to maturity but if we were just talking about a 1-year Treasury bill then around 2% 1-year Treasury bill and that's where the government is issuing not a bond but it's a call a bill but it's kind of like a bond it's a debt security but when the United States Treasury is borrowing money for one year at a time and we go back over the last 40 50 years then they're paying about 2% to borrow money on a real basis and then what happens as we tack on inflation and if what you have is an inflation rate of about well let's just say a 3% period and by the way over the last generation the inflation rate is approximately average 3% so over that generation what you would expect to see is that there'd be about a 5% nominal interest rate on those securities and the people who are lending their money for 5% they don't think oh I'm getting ahead 5% what they're thinking is this I loaned my money for five I'm gonna lose 3% because by the time I get my money back prices have gone up and I'm losing purchasing power I'm just gonna end up a 2% everybody okay on this and this is what's important to us the real interest rate now there's only one problem with this and n we will be done here's the problem nobody knows what that rates gonna be that expected inflation rate is a forecast can be right can be wrong what's the inflation are gonna be from today for the next year I don't know I can guess but I don't know I've guessed before been wrong in fact I'm always wrong when I guess because when I guess I put some decimal point on like two point one four percent well it's not two point one four it's a 2.2 or it's a 2.0 eight or whatever so anyway this is always a guest and so but this is the theory of it and I'm gonna write it down here is the nominal interest rate equals the real interest rate plus the expected inflation rate that's in theory how it works now in practice how this is applied is and by the way I use the term before here is ex ante makes ante is before the fact looking forward forecasting inflation what some people will do is look back the ex post situation and what they might say is something like this hey I want my money for 5% it turned out that the actual inflation rate was let's say 4% we lock this in this is the agreement here's nominal interest rate I loaned you the money we have an agreement we shook hands we wrote it in a contract in a story and then at the end of the year you pay me back we look back when we say hey look over the last year there's been 4% inflation and so then after that we calculate the ex post real interest rate and it's just the difference between these two things it's the it's guy I mean whatever makes 5 and 4 balance out would that be one that's what it is it's the last thing we calculate now the ex post this is after the fact looking back here's how we turned out and that ex post rate 1% is not equal to the ex ante rate maybe of 2% because we were wrong in our forecast so there's two different ways of looking at this real interest rate idea nominal interest rate equals a real rate plus inflation is it actual inflation or is it forecasted expected inflation okay this is known as the Fisher equation and it's named after a guy named Irving Fisher it was a US economist and I'm not exactly sure what year he wrote this but about 1907 I'll put a question mark there but sometime along in that period about a hundred years ago okay I got a couple minutes so let me introduce the next topic are there any questions about this about Irving Fisher Irving Fisher was a very smart economist wrote a lot of articles invented things there used to be a Rolodex kind of thing that secretaries will keep on their desks it's all plastic thing or probably metal when he invented it with a lot of little cards around it you know and people would write down their contact information for different people and kind of spin it around and I'm like you know here's Bob and here's Steve and here's Sally and so forth anyway he invented one of those products and did a lot of things became very wealthy and then the Great Depression came along and I think kind of wiped him out stock market crash and all that sort of thing Tata I believe Yale University here's what we want to talk about now we just talked about interest rates about how to calculate and calculate them 4% 6% 8% how to calculate it but the real question or the next question we want to talk about is why or interest rates whatever they are why our interest rates 4% or 6% or 8% and so what we are going to do is and I've already kind of alluded to this previously we're going to develop a supply and demand model we're gonna put the quantity of the good that we're talking about on the horizontal axis the good is credit dollars for loan and what we're going to put on the vertical axis is the price of borrowing those dollars and there's gonna be supply and demand and so that why our interest rates four or six percent supply and demand is of why so what we will do is we'll talk about the components of supply and we'll talk about the components of demand then we'll put all that stuff together we'll talk about supply a
d demand independently then put them all together and get an interest rate and that's next and I'll see you next time
