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Introduction to the yield curve

Introduction to the treasury yield curve. Created by Sal Khan.

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  • blobby green style avatar for user Connor Gower
    How does the rate change when investors sell to each other? Say, for example, there is high demand when a 1-month bond is auctioned by the gov. and the rate is 0.5%. If the market then became scared and investors tried to sell their bonds on, people would only buy them for a higher interest rate (say 1.5%). However, my question is: where does this extra interest come from as the US treasury can't increase its interest payments on the original bond as it is not involved in this 2nd transaction?
    (28 votes)
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    • blobby green style avatar for user snopanen
      You buy a new 1 year bond of $1000 that has a fixed interest rate of 0.5%. Now, if you hold it to maturity, you'll end up getting $1000+$5.

      The next day, new 1 year bonds get auctioned for 1%. If someone bought one of them and held it to maturity, they'd get $1000+$10. Now, noone would be willing to pay you $1000 anymore for your 0.5% bond as they can get better ones from the auction.

      You need the money, so you end up selling the bond in the secondary market for $995. The bond still pays $1000+$5, but now it would be comparable to a bond with a face value of $995 that would pay $10 in interest. So, the extra (or lowered) interest is due to the difference between the amount it was sold in the secondary market and the principal amount that gets returned to you at maturity.

      By scaling the secondary market value to $1000 (1.005*995 = 1000, 1.005*10=10.05) you can compare the bond to a new one (ignoring the fact that this bond would mature one day earlier). That is, the secondary market price of $995 compares to a bond with a face value of $1000 and a fixed interest rate of 1.005%.
      (60 votes)
  • blobby green style avatar for user Tage
    Why wouldn't all bidders at the auction bid really low, so as to receive a more valuable yield rate? It seems there are other influences that determine the yield of an issue at an auction. Any help or references?
    (9 votes)
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    • blobby green style avatar for user lu.runbo
      supply and demand... and also, if you and everyone else decided to bid low, and i KNOW of your collective intention to bid low, then I have an incentive to bid slightly higher, so that I would end up getting the bond, but at a very favorable price. Now since you and everyone else know that some people like me will try to take advantage of the collusion system AT YOUR DETRIMENT (because there will be fewer bonds for you to buy), or "cheat", then it makes no sense for you or anyone to collude for artificially low prices.
      (21 votes)
  • leaf green style avatar for user Paul Kïttson
    So if the US government has to pay for example 4% for a twenty year bond, does that ammount fluctuate after it is sold? Why i ask is because when the US's credit rating got downgraded they said the bad thing was thiei interest payments would go up. I wasnt sure if that was only for future bonds or currently issued ones as well.
    (4 votes)
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    • blobby green style avatar for user rossjordan21
      The answer to your question, minus the politics, is no the rate does not change. The price that the bond is sold at, at auction ( new bonds ), will fluctuate but the bond will continue to pay the " coupon amount " ( the stated rate of return on the bond ) Also, the " Face Value " of a treas. bond does not change. They will mature at par or 1000 per bond. The concern was that the yield it would take to get people to buy bonds would be much higher, costing the government more to borrow funds on newly issued debt.
      (8 votes)
  • piceratops ultimate style avatar for user Scottyboy1
    If the USA's credit rating has dropped then whyis the intrest rate still so low.
    (2 votes)
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  • blobby green style avatar for user David Barrett
    Just wondering, how come Bonds are seen as a safe investment, good for widows and orphans, when their price is subject to fluctuation?
    (2 votes)
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    • old spice man green style avatar for user TerryMHogan
      While their quoted price fluctuates day to day, their actual value does not change at all if held to maturity. If you hold a 10-year bond for 10 years, you will receive your full face value, exactly what you were expecting, when it matures. (that is assuming no defaults) However if you hold an equity for 10 years and then go to sell, the price could be drastically higher or drastically lower. Also the payments on the bond are known with certainty, while the dividends of an equity can fluctuate.
      (4 votes)
  • blobby green style avatar for user malsam.v2
    Hi Sal,

    I have a small doubt with regard to Yield Curve and fed fund rate. Fed lends money to US government at Fed Funds Rate and US government always tries to keep the fed funds rate as low as possible.. (Even below zero thru Quantitative Easing). It is because US govt. can reduce its liability of its Repayment to Fed. But my doubt is.if the rates are keep decreasing.wont it affect the global investors in Treasury Bonds?? Who will be willing to invest for low rates? Pls crct me if m wrng..
    (3 votes)
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    • ohnoes default style avatar for user Tejas
      The Federal Reserve does not actually lend money at the Federal Funds Rate. In fact, the Federal Reserve rarely loans money directly to the U.S government at all. It normally will go onto the open market and buy the Treasury Bills from those who already bought it from the U.S Government.

      The Federal Funds Rate is the rate at which the Federal Reserve wants banks to lend to other banks. Normally, the Federal Funds Rate is slightly higher than the rate set by Treasury Bonds, because there is more risk in loaning to another bank when compared with loaning to the U.S. Government.

      The rate set by Treasury Bonds is found using a reverse-auction. That means that the government asks for money and gives the bonds to those who are willing to accept the lowest interest rate. (The Federal Reserve is not one of these investors.) Therefore, the global investors are the ones deciding the Treasury rates, and they will always be willing to invest for the rates which they decide.
      (3 votes)
  • mr pink red style avatar for user Kamal Taghizade
    why is the quality so bad? :(
    (2 votes)
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  • male robot donald style avatar for user harry park
    Why does high demand for treasuries lower the interest rate?
    (1 vote)
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  • mr pink green style avatar for user Vinay Dwarakanath
    What is the meaning of yield curve flattening?
    (1 vote)
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    • male robot hal style avatar for user Andrew M
      It means that the long term interest rate and the short term interest rate are moving closer together.
      A "normal" yield curve has higher long term interest rates than short term rates, so usually a flattening of the yield curve is referring to the fact that the long term rates are coming down, although in principle it could be that short term rates are rising, or some combination of the two.

      (There are times when the yield curve is not normal but is "inverted", with long term rates below short term. It's unusual to talk about "flattening" in that context but if you did you would be referring to some combination of upward-moving long term rates together with downward-moving short term rates. )
      (2 votes)
  • spunky sam blue style avatar for user sivsamhitvadd
    In the primary market for the T bills when the government is holding an auction, wouldn't a lower bid mean the government has to pay back little on a fixed coupon rate? Also, is this auction the process to determine interest rates or initial price of the bond?
    (1 vote)
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Video transcript

Welcome back. Before we proceed further and get a little bit better understanding of why maybe some of these investors were so keen on investing in mortgage backed securities, essentially loaning this money to all these people who are buying these ever appreciating houses, I think we need to a few more tools in our tool belt. So I'm going to introduce you to the concept of the yield curve. You might have heard this before. You might have heard people on CNBC talk about it. And hopefully, after about the next five or ten minutes, you will know a lot about the yield curve. So when most people talk about the yield curve, they're talking about the treasury yield curve. And what does that mean? What is even a treasury? So these treasury securities, whether they're T-Bills, treasury bills, treasury notes, or treasury bonds. These are loans to the federal government. And these are considered risk-free. Because if you lend to the federal government and they're running short of cash, all they have to do is increase taxes on us the people and they can pay back your debt. So in dollar denominated terms, the treasury bills, notes, and bonds are about as safe as you can get in terms of lending your money to anyone. So when most people talk about the yield curve, they're talking about the risk-free yield curve. And they're talking about the curve for treasuries. So first, a little bit of definitions. What is the difference between treasury bills, treasury notes, and treasury bonds? They're pretty much all loans to the government. But they're loans for different amounts of time. So if I give a loan to the government for $1,000 for six months, that will be a treasury bill. So I will give the government $1,000, the government would give me a treasury bill. And that treasury bill from the government is essentially just an IOU saying that I'm going to give you your money back in six months with interest. Similarly, if it's three months, it's a three month treasury bill. Treasury notes are loans that are from one year to 10 years. So on this graph that we're going to make using the actual yield curve rates, from zero to one year-- and actually there's no zero year treasury bill. Actually, the shortest one is one month. This would be something like here on our graph. So from one month to one year, these are T-bills. And this is just definitional. Then from one year to 10 year, these are notes. Actually, I believe the one year itself is a note. Up to one year is a bill. Although, I might be wrong with that. Correct me if I'm wrong. That's just a definitional thing. From one to 10 year, these are called notes. And then when you go beyond 10 years, these are called treasury bonds. These are just definitional things to worry about. So with that out of the way, let's talk about what the yield curve is. I'll just give you a simple thought experiment. If I'm lending money to someone for a month versus lending money to that person for a year, in which situation am I probably taking on more risk? Well, sure, if I'm lending someone for a month, I know only so much can happen in that month. So I would expect to be paid less interest. Not just obviously in dollar terms, but even adjusted for time, I would expect less interest for that month. And this is actually an important point to make. When I say that I'm charging 6% interest for that month, that doesn't mean that after a month the person is going to pay me 6% on my money. It means that if I were to give that money to somebody for a month, and they were to pay it back. And then I were to give that money to, say, that same person, or another person, for a month, and I were to keep doing that for a year, then in aggregate I would get 6%. So that 6%, no matter what duration we talk about, whether one month, one year, five years, 15 years, when we talk about the interest rate, that's the rate that on average we would get for a year. It's the annualized interest rate. So going back to my question. If lend someone money, even the government, for a month, there's usually less risk in that. Because only so much could happen in a month versus in a year. In a year there might be more inflation, the dollar might collapse, I might be passing on better investments, I might need the cash in a year's time, while I have a lot of confidence that I don't need the cash in a month's time. So in general, you expect less interest when you loan money for a shorter period time than a longer period of time. And so let's draw the yield curve and see if this holds true. So I actually went to the treasury website, so that's treas.gov. And this is the yield curve. So they say on March 14, so this is the most recent number. And I'm going to plot this. They say, if you lend money to the government for one month, you'll get 1.2% on that money. And remember, if it's $1,000 it's not like I'm going to get 1.2% on that $1,000 just after a month. If I kept doing it for a year, this is an annualized number, I'll get 1.2%. And so for three months, I get a little bit less. And then for six months I get more. And then it does seem that the overall trend is that I expect more and more money as I lend money to the government for larger and larger periods of time. And this is a little interesting anomaly that you get a little bit more interest for one month than three months. And we'll do a more advanced presentation later as to why you might get lower yields for longer duration investments. That's called an inverted yield curve. So let's just plot this and see what it looks like. So you saw where I got my data. So they say for one month I'd get 1.2%. So this is one month. It'd be right about here. Three months I get about the same thing. For six months I get 1.32%. Maybe that's like here. One year, I get one 1.37%. Maybe it's here. Five years, I get 2.37%. So that's maybe like here. And these aren't all of the durations. I'm just for simplicity not going to do all of them. For 10 years, 3.44%. So maybe that's here. For 20 years, I get 4.3%. Like that. And then for 30 years, I get 4.35%. So the current yield curve looks something like this. And so you now hopefully at least understand what the yield curve is. All it is, is using a simple graph. Someone can look at that graph and say, well, in general what type of rates am I getting for lending to the government? On a risk-free free basis, or as risk-free as anything we can expect, what type of rates am I getting when I lend to the government for different periods of time? And that's what the yield curve tells us. And in general, it's upwardly sloping. Because, as I said, when you lend money for a longer period of time, you're kind of taking on more risk. There's a lot more that you feel that could happen. You might need that cash. There might be inflation. The dollar might devalue. There's a lot of things that could happen. So the next question is, well, what determines this yield curve? Well, when the treasury, the government, needs to borrow money, what it does is say, hey everyone we need to borrow a billion dollars from you, because we can't control are spending. And they say we're going to borrow a billion dollars in one month notes. So this is one month notes. They're going to borrow a billion dollars. And they have an auction. And the world, investors from everywhere, they go in, they say, well, this is a safe place to put my cash for a month. And depending on the demand, that determines the rate. So if there are a lot of people who want to buy those one month treasuries, the rate might be a little bit lower. Does that make sense to you? Think about it. If a lot of people want to buy it, there's a lot of demand relative to the supply. So the government has to pay a lower interest rate on it. Similarly, if for whatever reason people don't want to keep their money in the dollar, they think the U.S. might default on their debt one day, and not that many people want to invest in the treasury, then that auction, the government is going to have to pay a higher interest rate to people for them to loan money to it. So maybe then the auction ends up up here. And similarly, the government does auctions for all of the different durations. And duration, I just mean the time period you're getting the loan for. So they do it for one month, three months, six months, one year, two year, three year, et cetera. Once the government has done that auction-- You give the money to the government, they give you an IOU called a T-bill. Then you could trade it with other people. And that's going to determine the rate in the short term. So the government does the auction. But then after the auction, and a lot of people had demand, but then a lot of people get freaked out. And the public markets, when you try to sell that treasury, will then expect. a higher yield. I know that might be a little complicated now. And I always start to jumble things when I run out of time. But hopefully at this point you have a sense of what the yield curve is. You have a sense of what treasury bills, treasury notes, and treasury bonds are. And you have some intuition on why the yield curve has this shape. See you in the next video.