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Lesson 9: Bonds

# The yield curve

The Yield Curve. Created by Sal Khan.

## Want to join the conversation?

• Assuming an upward-sloping yield curve, wouldn't it make sense to calculate the present value of each transaction and so one might come to see (at least in this example) that you could make more money by doing 1-month investments and then rolling them over versus locking up the same amount of money for thirty years? Obviously, the exact times and percentages affect this, but just saying in general.
• Yields rates of all maturities are always shown on an "annualized" basis, so if you just kept on rolling over 1-month investments, in this example your annual return would be 1%, as the example indicates. The longer the maturity of the bond, the more interest they have to offer to make up for the added risk, so the more money you make on an "annualized" basis. That is why in this example, a one year treasury earns you 3%.
• Is this the same thing as: yield spread?
• No the yield spread is the difference between two yields...For instance the yield spread of a specific bond could be measured as the difference of its yield to the yield of US Treasuries with same maturity...
• Why does this curve look logrythmic? Are Yield curves usually logs?
• This curve looks logarithmic simply because of how Sal drew it. It wasn't quite to scale. You can look up 'yield curve' on the treasury.gov site (or others I'm sure) and see the yield curve to scale.
• If you buy a 10 year \$1000 treasury bond at 3.5%, does that mean each year for 9 years you will get \$35 and then on the 10th year you get \$1000?

Or does it mean that each year you get nothing, but on the 10th year you get \$1035?

Or does it mean each year you get nothing, but on the 10th year you get \$1,187?
(compound interest)

If I buy a 30 year treasury at 4%, then do I get a 4% return each year? Or a 4% return at the end of 30 years which is like a .13% return each year?
• In your example, the interest is annual, so you would get \$35 each year for 9 years, then \$1035 in year 10.
The 4% Treasury will pay 4% each year, then the 4% interest PLUS the value of the bond. If it was \$1000, like your first example, you get \$40 yearly, then \$1040 in year 30. The return is based on how much you actually paid for that bond. This is a subject for another video, but you may have paid more than \$1000, less than \$1000, or exactly \$1000 (but that's rare). Those are called premiums or discounts, referring to the amount paid above/below face value.
• Is the best time to sell long maturity bonds when yields are low?
• If "best time to sell" means "get the highest possible immediate price", then yes.
• what's inversion of yield curve?
(1 vote)
• The typical yield curve shape is such that as maturity increase so to does yield which makes sense when you consider things like liquidity, time value of money, etc. An inversion of the yield curve is rather than an upward sloping yield curve, the curve slopes downwards indicating yields are higher for short term securities and vice versa.
• According to investopedia,
"When short term interest rates are higher, it typically results from increased demand for short - term credit"
By interest rates here, we mean the resulting interest rate that gets derived from these factors: bond maturity value, coupon rate, remaining time to maturity and current bond price?
So the interest rate at that point in time would be :
[(maturity value + remaining interest payments)/current bond price] - 1 ?

So if that's the case, why would there be an increase in interest rates if demand for short term credit increases?
Because if the demand increases, the bond price goes up, and the resulting yield or interest rate goes down... where am i wrong?
(1 vote)
• "Demand for credit increases" means there's more borrowing. That means more sales of bonds. Bond price goes down, not up.
• Does it make sense to draw a S shaped curve, as shown in the last part of the video Introduction to the yield curve?
(1 vote)
• looks like there maybe at some point there was an intention of doing a yield inversion explanation video. Though it would be a great add to the series.
(1 vote)
• steep yield curve what it means
(1 vote)
• It means the yield on short term bonds is a lot smaller than the yield on long term bonds.

When the yield curve gets steeper it means the difference between short term yields and long term yields is increasing. This can happen when short term yields fall, long term yields increase, or both.
(1 vote)

## Video transcript

If you were to borrow money for different amounts of time, you could imagine the person lending you the money might charge you a different annual interest rate depending on the perceived risk of having the money out there for that amount of time. And the same thing is true when people lend money to the federal government. So when you think about US treasuries, and US treasuries that have different maturity. And maturity just means when is the government going to pay you back, you could imagine that there are different interest rates, or there's different yields to maturity on that debt. So if we were to plot it-- so let's say that, and I'm just going to simplify here. Let's say that there's some treasury debt that's maturing in one month. And if you look at the price that you would have to pay for that debt versus the amount of money that the treasury is going to pay you when it matures, you see that the yield there is, let's say it is 1%. Let's say for treasuries that are maturing in three months the yield is 1.5%. Let's say the treasuries that are maturing in, I'll just pick some maturity dates here, let's say in one year the yield is 3%. Let's do a couple more. Let's say in 10 years-- you're essentially lending money to the treasury for 10 years now-- the annual interest rate on that, let's say it's, I don't know, let's say it's 3.5%. And let's throw one more up here. Let's say if you were to lend money to the US government for 30 years the yield is running at, let's say it's 4%. So here we have different yields for different maturities. And if we essentially plot this on a graph, we get ourselves a yield curve. And it's usually called The Yield Curve. When people talk about The Yield Curve they're talking about the plot for the US Treasury in dollars, US Treasury bills and bonds. You can have a yield curve really for any debt instrument, for any corporate bonds, or even government securities or corporate securities of other countries. But in general, when they talk but The Yield Curve, they're talking about US treasuries. So let me draw a yield curve right over here. So on this axis I will put maturity. Let me scroll down a little bit, so maturity. And we have a bunch of different maturities. We have one month. Let's squeeze it, one month. We have three months. And this will be completely to scale. Then we have one year, actually one and three month, let's just put one month right at the beginning. So one month then three months is a little bit further out. One year would be right over here one a year. Five years would be like there. I don't have five years, let's do a 10 years. So I'll extend my line over. So one year, maybe 10 years is over here, 10 years. And then you have 30 years. And I'll just draw 30 years as far as I can. It's not completely to scale, but it's my best shot. And then we plot the yield for those different maturities. So in one month, you have a 1% yield. So let me do up the percentages here. So this is 1%, 2%, 3%, 4%. So on one month maturity the yield is 1%. On three month maturity the yield is and 1/2%. So maybe it'll be like right over there. On one year maturity the yield is 3%. So you plot one year, this is 3%. Let me write it, this is 3% right over here. This is 1.5% right over there. And the first one right over there was 1%. And then at 10 years it's 3 and 1/2%. So 3 and 1/2% is right over here. And we want that to be 10 years. So I'm just plotting that point. And then that 30 years, it's 4%. So 4% is what we get at 30 years. And if we connect the dots and draw a curve we are giving ourselves The Yield Curve. I don't want to make it look like-- let me see how well I can draw it. You have a curve that might look something like that. Just by looking at this yield curve, you see that when you lend money to the treasury for a longer period of time, you're going to get a higher interest than you would for a shorter period of time.