Alan Cring Productions in association with Emergent Light Studio presents the Illinois State Collegiate Compendium Academic Lectures in Business and Economics.
This is Business Finance, FIL 190 for spring semester 2024.
Today, Bonds and Bond Yields.
This is sort of a finish up.
I'm going to clean up some work from last week and from a little before that and then
carry it forward to this current chapter on bonds.
Now, this is the last chapter before the midterm exam.
I want to emphasize that on the final exam, on the midterm exam, on the midterm exam I
am not going to ask you any mathematical questions about bonds, bonds themselves, chapter 7.
I ask some general questions, definitional questions, concept questions.
Yeah, that's fair game.
But I don't like having you have so little time to get it together with respect to calculating
bond yields, bond prices, and all that kind of stuff.
I really don't want to put you in that situation as we are getting that close to the final
exam.
Why do I keep saying the final?
I'm looking ahead to the midterm exam.
So this is what I do with bonds today and on Wednesday is entirely the just, I'll show
you the math, fine.
But I will not hold you responsible for being able to do the math on the midterm exam.
Want to emphasize that.
We do have a surprise quiz today and that will begin at 10.35.
So look forward to that.
And you should always consider these quizzes as mini-preps, miniature study guides for
the midterm exam.
So definitely this one is right in that area.
Oftentimes, and I will cover the midterm exam in the review next Monday, but always consider
that those quizzes, sometimes I'm very lazy.
I'll just copy a question from a quiz and I'll paste it into the exam.
Or just change the numbers.
They're very similar, those quizzes are, to the way I ask and the questions I ask on the
midterm exam.
So always consider this, that there's a bright side to suffering through these quizzes that
makes you much stronger and that's why I have such good scores on the midterm exams.
This is because I've prepped you for them.
Enough of that, let's have a look at the numbers.
And we have on deck today, it's a bull day, but it is barely a bull day.
It's a barely bull day, as it were.
You can see that the Dow is up a lousy 0.15%.
And the standard of pores, it's up 0.01%, performing worse than the Dow.
And the NASDAQ is also up, but a lousy 0.21%.
And as you can see from the spark charts, everything started out happy today, but the
spark charts are showing that the bears have sort of come back in in the last 10, 15 minutes
and they're really tearing up.
They've dragged the S&P 500 down from a good start into almost negative territory.
As a matter of fact, it looks like a dip negative there for a couple of minutes.
But it's just not a good happy day on the street right now, on Wall Street, on the street
we say.
So we go over here and we have a look.
Crude is in nice, right in its trading band there.
I noticed the price of gasoline came up a little bit at the retail level, but it's nothing
major.
But the price of crude, you notice it, it had been down through the night and into the
early morning.
And then it had a bit of a spike here in the last 10 minutes or so.
Well, it was actually about 20 minutes ago it started running upward and I don't know
what its thoughts are, but it's nothing to be concerned about unless there's something
happening over in the Middle East I don't know about.
Gold is taking a toilet break, which is good news because if gold is rising that means
that there are concerns about stocks and bonds.
So we don't have that happening.
Gold and silver are both down.
Moving over here into the bonds, there you go.
Well we've got a little bit of a spike in the yields.
That would mean that there's something of a sell-off in the bonds, drives the price
down and therefore that will cause the yields to rise.
It's nothing much though, two and a half basis points isn't anything at all.
So right now bonds are kind of having a stable period around two and a quarter percent on
the 10-year benchmark.
So now remember that when I do this on purpose, remember that an interest rate or a yield
as it were is going to have the risk-free rate of course plus the three, the default
premium, the maturity premium and the illiquidity premium.
And of course the risk-free rate has the real rate plus the expected inflation premium.
Okay, with any interest rate is going to carry R sub F. All interest rates will carry that
one.
Where the action happens on a given interest rate is in this risk premium as we call it.
Now the default premium does not, isn't part of a treasury of any kind.
A three-month, a one-year, a 10-year, a 30-year.
Default premium you can ignore it, it's just not there.
However, and of course the illiquidity premium, you can sell any treasury debt instrument
in a blink of an eye.
They don't have any illiquidity.
They are easily transferred to whatever other assets you want.
The one that is interesting though, so with government, is there won't be any risk of
default, no risk of illiquidity, but this one is going to be there.
It grows as the time to maturity.
So with a very short-term treasury bill, it has very little maturity premium.
There's very little, tiny probability that interest rates would shift on the lender.
However, as time goes on, that thing gets long, that thing begins to grow.
A five-year treasury would have a bigger maturity premium than a one-year.
A 10-year would have a bigger maturity premium than a five-year.
A 30-year would have a bigger maturity premium than any of those.
Now there's something interesting here going on because of maturity premium.
Let's say 10-year maturity premium.
That should be the same whether it's a government debt instrument or a corporate debt instrument.
It should be the same because that is a macroeconomic thing.
So when we see this maturity premium right here, this will be shared by all debt instruments.
Government, corporate, private, they'll all carry the same maturity premium.
At least we hope they would.
There's an interesting thing that we can do with the maturity premium.
I'll bring that up in just a minute here.
But let me make a point here.
Suppose that I had a government yield, a 10-year T-note, treasury note, and its interest rate
was, let's say, 4.50%.
Now suppose we also, at the same moment, we had a AAA, very high-grade corporate note,
10-year note.
And suppose that it was going off at 4.62%.
Look over here.
These two different debt instruments will carry the same risk-free rate.
They will carry the same illiquidity premium.
They're both quickly, easily sold.
You can get rid of a AAA in the blink of an eye.
And they would also have the same maturity premium because they're both 10-year.
The only difference between these two instruments would be that the government debt instrument
would have no default premium, but the corporate debt instrument would have a default premium.
So in other words, if I look at it this way, and I'll put it in government, government,
and the yield on the corporate, they'll have R sub F plus R sub D plus R sub M plus R sub
I illiquidity.
The corporate, and R sub F, I'll put it in here.
The government default premium, the government, and the government.
This would be the R sub D of the corporate plus the R sub M of the corporate and the
R sub I L of the corporate.
Now I'm going to subtract these upward.
Well these will be the same, so when I say this minus this, I'll get a zero.
The R sub M's are the same, so that'll be a zero.
And the illiquidity premiums will be a zero.
The only difference will be this minus this, but this one is zero because there's no default
premium.
So in other words, the difference between them would be exclusively the default premium
on the corporate debt.
That would be the only difference between them.
That would be the only thing that could change, that could make them different.
We do this all the time because this tells us that the default premium on the corporate
debt is 12 basis points.
We know that.
And we can track it.
We can watch that default premium if it moves upward, that's a bad sign for high quality
corporate debt.
The markets are putting a higher default premium on it.
If that number right there, that 12 basis points were to contract, we know that this
is good times.
The markets are not putting as much of a default premium on high quality AAA corporate debt.
So we can create a chart going through time to see a hidden whispering sentiment of the
market about default probabilities.
And we can do this for double A's, single A's, because, well, it gets a little bit tricky
when you get below the A range because the illiquidity premium starts to fuzz it a little
bit.
You see what I mean?
There wouldn't be that, the two illiquidity premiums subtracting, canceling each other
out because they're the same.
They wouldn't necessarily be the same if the corporate debt is of low enough quality.
It might be a little harder to unload it very quickly.
But in general, though, the more important point here is that this is a way that we can
track the sentiments of the market about the probability of default in high grade corporate
instruments.
And so this is, and it is used, it's used quite a bit to just keep an eye on what's
going on in the market.
Now what is it right now?
It's been, it's contracted a little bit, maybe down to the difference right now is maybe,
I think I saw a point, 48, it was 48 basis points, and it had contracted a little bit.
This is a little bit extreme on this example.
It's usually a little bit more than that default premium is.
But I can look at the yield on a 10-year corporate bond, a AAA corporate bond, the yield on a
10-year treasury bond, and I can take the, subtract the two, and all that's going to
be showing is the default premium on AAA corporate instruments.
And then I can do it for double A's, and I can do it for single A's.
And like I said, once you get down to the B range, then it gets a little bit, a little
bit more speculative down there.
But that's useful for us to know.
Now there's another thing that gets us into the fun part of this lecture
for today, that maturity premium on bonds.
It should be about the same whether we're talking about treasury or corporate.
The maturity premium for 10 years from one instrument to the other would be about the
same.
The maturity premium for a 20-year, for a 5-year.
So taking that as our basis, taking that as our basis for this.
There is an animal called the yield curve.
Now I'm going to come over here, and I think I've put this up for you to see.
I'm going to have to check to see in your files folder in Canvas if it's there.
But let me look at something here.
Google.
It's not saving the bookmarks that I want.
It saves bookmarks that I'm not asking for.
But let me do it this way.
I'm just going to write yield curve.
Now the site here I'm going to use is the U.S. Department of the Treasury par yield
curves.
And let me do something here.
I want to do the time period for 2024.
Now I want you to look at something.
Look at, we usually, I mean we can look at this ultra short one month.
But do you see how these are moving around and changing from one month to six months
to a year to two years to three years?
That should be only the maturity premium.
Now it would be really great if I were able to show you what a normal yield curve looks
like.
A normal yield curve does nothing but take the maturities of a certain type of debt instrument
against their yields.
So this axis would be time to maturity on the horizontal axis and on the vertical axis
would be the yield of it.
Now what should happen, what is normal to happen is that you have a nice pretty
upward sloping curve.
The maturity premium gets greater the longer the maturity.
It builds through time.
That's what it should do.
And it usually does that.
Except that there is our times.
But let me show you a couple here.
This is the normal one.
It swoops upward pretty, very smooth, nice thing.
Let me show you one that would be the end of the world.
This one you don't ever want to see this one.
That's a descending yield curve.
That would be essentially the only way that could happen is if the hell of a depression
were coming in.
That would be about the only time you would see that.
So we pretend that that one, we won't see that one in our lifetimes.
However there's a mini version of it.
Now every time we've seen what I'm about to show you, either a recession or a pause has
happened.
Usually a recession.
Historically this one has always predicted correctly a recession.
Every recession has been preceded by an inverted yield curve.
There's an inversion that happens somewhere in the maturities.
Every recession has had an inverted yield curve before it.
Occasionally we've had where we saw an inverted yield curve and it didn't lead to a full blown
recession.
It just led to a place of flat economic growth.
The economy slowed down but it didn't go into negative territory for the two quarters that
are required to count as a recession.
So we did not, we've seen that a few times.
But an inverted yield curve is always a warning shot that things are going to get bad.
They could get really bad or they could get just a little bit bad.
But an inverted yield curve has always warned us of a recession coming.
I'll give you an example from my time as an economic and finance writer back in the little
earlier days of the internet.
Back in the early 2000s, well I think I actually started it in 1999.
I wrote a blog that became very popular, it was called the Dark Race Forums.
And I talked about economics, I did some little lessons in it and all that.
It was in the earlier days of the internet as you know it today.
Eventually long after that, back in 2011, 2012, my website was destroyed by hackers
and I suspect that they were from that scumbag group called Anonymous.
I had said some bad things about them and they attacked and they wiped me out.
They destroyed the backup servers and everything.
However, you can still find my work on the Wayback Machine.
The Wayback Machine is a website that archives everything that it has ever found on the web.
Very cool and I appreciate them for that.
But anyway, in the period from about 2005, I started writing about difficulties that
the economy was having that were not being discussed.
Manufacturing levels were sliding down to a third of what they had been in the Clinton
administration and the economy was having suffering severe, what were starting to be
severe economic treasury deficits.
We had been in treasury surpluses.
We had been closing the deficit all through the Clinton administration and in 1997, I
believe it was, we went into surpluses.
First time in half a century probably, we had actually had budget surpluses, one after
the other after the other.
And then of course we had some fun things happen.
In 2001, during the early years of the Bush administration, first we had a representation
that we were going into a terrible recession, which we weren't.
There was no recession coming.
But that gave the impetus for Congress to pass the longest, deepest tax cuts in American
history up to that point.
So we had deficits just returned big time and then we had 9-11, so we had a theater
war start up in Iraq and in Afghanistan.
We had a pair of theater wars, so we were driving into major deficit territory.
But 2005, 2006, things were looking bad in the economy and I was writing about it.
Come about 2008, here's what the yield curve was starting to look like.
It was starting to look like...
It was starting to flatten.
That's not an inverted yield curve.
Article inversion was not there in early 2008.
By the time we got...
I just kept writing about it, writing one article after another, because it was trying
to flatten in the five to seven, five to seven year maturity.
In other words, the seven year was trying to go below the five, but it was not.
It just kept hanging.
And then I can't recall what day in May it was.
We had a technical inversion just briefly and then it recovered.
But that's all it takes.
If it technically inverts, that's what has always led to a recession.
It's always been the predictor, not led to, but it's been the predictor of a recession.
Even it was like three basis points.
The seven year was below the five year.
And I called it.
I just put it on my website.
We have a technical inversion.
We're going to go into a recession.
Well there were a couple of other analysts like me and we were also talking about the
insane situation with the banks, the ten largest banks in the world, nine of them, their financial
statements, they were gone.
They were dead.
And yet they just kept going on.
And for some reason we couldn't figure it out why these dead banks, including Citigroup,
Citibank and BOA and all of these others were corpses according to their financial statements.
What you guys can do now.
But they kept going.
So I said we've got multiple crises coming down.
We're going to have something bad happen.
September 15th of 2008.
That was the morning that the entire world almost came to a financial apocalypse.
And I'll bet you don't know about it.
It started out on the East Coast.
As soon as the banks started opening, vast sums of money were being withdrawn from the
money market accounts along the East Coast.
It was just staggering along the lines of several billion dollars in each of the withdrawals.
We couldn't figure out where they were going.
They were going into shadow accounts and dark accounts.
But we figured where they would end up, we would just look for something that was spiking
in price.
Gold, silver, oil, something would be where those funds were going.
You can find any price spikes anywhere in the world's financial system.
It was vanishing.
By 10 o'clock, the Federal Reserve Board of Governors had called an emergency meeting
to their analysts, their tech people, the ones who watched the world's situation.
Where is this money going?
Who is withdrawing this?
We didn't have the financial disclosures in place then that we have now.
What the hell is going on?
Well, by that time, at 10 o'clock, $550 billion had been withdrawn from the money markets
along the East Coast and then along the Midwest.
The Federal Reserve put an immediate lockdown on withdrawals from money markets.
They said no more withdrawals.
They ordered the banking system to stop letting money be withdrawn.
If they had not, by noon, it would have been over.
The illiquidity, the banks would have had no money to honor your paychecks, your cards
at the store, or anything.
It would have been gone.
But the Fed got in front of it pretty well, amazingly.
And then later that little afternoon, Congress was called into an emergency session.
And the doors were closed and locked.
It was a secret session.
They called the Treasury Secretary, the Federal Reserve Chairman at the time, and a bunch
of others to find out from them what was going on.
At one point, a representative at the time, kind of a crazy guy, but he was right.
He asked the Secretary, rather the Speaker of the House, who was Nancy Pelosi at the
time, he said, Madam Chairman, are we under martial law?
And she just walked away from the podium.
No, we weren't, but Congress was.
They had US Marshals outside the doors to keep people from going out until they solved
it, until they answered the question, what's going on here?
There were some members of Congress who saw this.
They said, I smell a rat.
They were the ones who believed that 9-11 was a conspiracy.
And they said, this is another conspiracy.
Not only have you now taken away our privacy, now you're taking away our banking system.
You get that kind of stuff.
But one way or the other, yeah, we went into a hell of a recession.
We call it the Great Recession.
It was the worst one since the Great Depression.
And a few of us called it.
We saw it coming.
We thought it was going to be bad for other reasons, the collapse of the banking system,
because of its internal rot.
What we didn't know at that time, and we found it out by accident in 2011, there was a lawsuit,
Freedom of Information Act lawsuit, that was filed by a media group against the US Treasury.
And they accidentally released the memo that included in it what was really going on with
the banks.
The banks were being kept alive by back-channel money that was being fed to them through the
Treasury and the Fed to the tune of trillions of dollars.
We didn't know it.
It wasn't on the financial statements.
The SEC was involved in it.
They knew it was there.
Those financial statements were a lie, because they did not include that backdoor money.
At the time, a federal judge, the Federal Reserve and the Treasury joined the banks
in asking a federal district judge in Washington, D.C. to quash that memorandum and not allow
it into evidence.
To her credit, that federal judge said, go to hell.
Everyone needs to see this.
So it was released, and no one cared.
At this point, how much money? we can only guess, because it's still a secret.
Probably on the order of $35 to $45 trillion is being funneled into those banks, backdoor.
And the SEC lets it go.
So they were like, we're supposed to have them back?
No.
It was money.
It was just literally, that's something we don't know.
We got the memo.
We saw what was going on.
We could backtrack and figure out how much had gone in, but we don't know the mechanisms
by which it was going in.
We know how much it was.
Was it just trucks driving up?
Was it some kind of repost set up?
It was certainly not open market operations.
We would have seen those a mile away.
But there you go.
So as much as you can trust the SEC and disclosures and all of that, when it comes to banks, none
of us.
I was one of those idiots in 2008 who was screaming bloody murder, sell your bank stocks,
they're going to go to hell.
There were other investment analysts who were saying the same thing.
We looked like idiots, because the banks didn't collapse.
It was only in 2011 that we found out that we were idiots, because we didn't think.
How could those banks still be alive if they're in this bad of shape?
I was going to say, can't they not collapse because they were always getting bailed out?
Well that's just it.
This is the largest bailout in human history, in the history of civilizations.
But that's just the way it is.
Now getting back to this story here, going back to the yield curves, I'm just sharing
that with you as the intrigue that goes behind what we deal with in the world of finance.
We can't always believe what our lying eyes are telling us, but we have to rely on it
anyway.
And here's the kicker.
You are living in a very strange, I mean a strange-ass time.
Let me take you back to the time period 2023.
Apply.
Look at this.
That's not just an inverted yield curve.
That's an inverted yield curve from hell.
These numbers should be going up, up, up.
But right here, you see from the six months to the one year, you see from the one year
to the two year, two year to the three year, three year to the five, the seven, the ten,
the thing is inverted not across two.
It's basically that yield curve at the beginning of 2023 and it actually was before that.
The longest inversion of a yield curve any of us have ever seen.
Of course we were all saying, oh, recession.
Oh my God.
OMG.
We didn't go into one the first time.
We didn't even go to zero GDP.
Now a recession is technically, again, two consecutive quarters of negative economic
growth.
It didn't happen.
And now let's go here.
This thing has been inverted.
Let's go to 2024.
Let's go to the one from yesterday.
Look at that son of a bitch.
It's still inverted.
And it's still inverted way out there.
That should be a recession coming within six months.
That's about six to nine months for a recession to hit after an inversion, a technical inversion
of a yield curve.
It's not happening.
How in the hell the economy hasn't dodged a bullet.
It's dodged a nuke.
It just keeps going along like, now we're talking about the economic recovery is underway
and all this.
How?
An inverted yield curve never has had this happen.
Yeah?
Government spending is not that significant.
The budget deficits have been getting controlled, even with bad tax rates, and the Fed certainly
isn't printing money to feed the economy, to make it feel good, like chicken soup when
you have the flu.
This is something else.
It is the first time, and you are actually coming into your professional lives in something
that, and there's argument, well, why is this now?
Why not in another inverted yield curve period of time, in the 40s, 50s, 60s, 70s, 80s, it's
never happened before that we've had an inverted yield curve, and it did not lead to a recession.
It's never before happened that we have had a yield curve that had that much of a distance
going down in the yields.
How?
You got me.
I mean, you can see it right there.
See the inverted yield curve?
Even now, you saw what it was.
It's still inverted, clear out here to where it was at the beginning of 2023.
It's inverted clear out to the 20 year, and it shouldn't be.
We shouldn't have an economy doing as well as we do.
It's not a fantastic economy, but it is sure a decent economy.
We've been in an economic recovery long enough that I would argue that we're now in a full
blown economic expansion, and yet here we are with an inverted yield curve.
So there you are.
That's a little of the history of yield curves and near apocalyptic situations in the country.
That's above my pay grade.
I'm just a stupid old school professor.
I let other people worry about this.
There are different theories, or different hypotheses I should say, but none of them
really are satisfactory, although a couple... You see, as I had said before, the Federal
Reserve has a lot of different ways.
When we hear that the money supply was being contracted, there are a couple of tricks that
can be done, the Fed can do, to actually pump money into an economy, but at the same time
it looks like they're contracting the money supply.
Maybe.
My good teaching assistant remembers, probably not too happily, the whole thing with repos
and reverse repos, how the government can sell treasuries to banks, which makes them
less liquid, but they are also at the same time promising that they will buy those treasuries
back in one, two, five days, something like that, so that it looks like money is disappearing
from the banks, but it's flipping right back around, and then the next day they do it so
that there's this constant bladder of money in the system flowing both ways, and if you
use the right balance between the buys and the sells, you can actually expand the money
supply, but it looks like through your plain old open market operations, you're contracting
the money supply.
But that should not have been good for inflation, and yet we have won, at least for now, the
battle against inflation.
So you might want to stick to some other world other than the theoretical side of it, because
right now we are in a period we've never seen before, and that's where you guys come in.
Now let me talk to you a little bit about all of this, but first I need to show you
something, that last Excel sheet that I did, I have now upgraded it again for you, my good
students.
It does a calculation for you now that I should have shown you, usually I do this at this
point, but I realized that there were some questions in the book that kind of, you should
have known this, you should know this, and they covered it in the book, but I'm going
to give you, I have in the Excel sheet now, something that will do this for you.
It has to do with yields and returns.
Now as I said maybe a week or two ago, yield and return and rate, interest rate, they're
all different ways of saying the same thing.
The yield on a bond, the return on a stock, the interest rate on a loan, those are all
the same thing, they're interest rates, but we use different words for different kinds.
Now let me show you a stupid pet trick.
This is a simple one, but to do this I have to make sure you understand that we need a
common unit of measure for rates, yields, returns.
The common denominator is the annualized.
We make everything annualized.
So that you pay $100 and in one year you've got $110, well that would be 10%.
The holding period was one year, so that would be an annualized rate right there.
But this young gentleman, he put in $100 and he pulled it out after six months and he had
$110.
So his return on an annualized basis isn't the same as yours, but it's not quite just
10% times two because of the compounding phenomenon.
Remember finding present values is discounting, finding future values is compounding.
So we need to put everything into annualized terms.
And the formula to do that is you take the ending value over the beginning value and
you raise it to one over the number of years and then you subtract one.
Now that's fine if you have whole numbers of years.
So you invest $200 and in three years you have $225.
Now just your plain old holding period return.
The holding period return doesn't care about annualization.
Holding period return, all you do is take $225 divided by $200 minus one.
That's the HPR, the holding period return.
Doesn't matter what the period is, that's just a raw measure.
And that's not hard to do, you can whip that out on a calculator any old day of the week.
If I could find a stupid calculator, well let me use the TI just to have it up there.
So I would take 225 divided by 200 minus one.
So my HPR is 12.5%.
But that doesn't do us much good if we want to compare that to an investment that was
not that number of years.
So the way we annualize it is with that formula up there.
The annualized return, the APR as it were, is 225 over 200 to the one over two or one
over three.
That turns it into an annualized rate using the geometric mean.
Now some people would say, well why just take 12.5 divided by three?
That would be what's called an arithmetic mean, not a geometric mean.
We use the geometric almost always.
So in this case, open parenthesis, 225 divided by 200, close the parentheses and raise that,
open parenthesis, one divided by three.
Close the parenthesis.
Minus one.
Don't forget the minus one.
I'm always forgetting minus one and then I'm getting a wrong number.
So it's actually 4%.
Okay.
You notice that it's less than if you had taken 12.5% divided by three.
A little less.
Here's where it gets to be a pain in the ass.
It's when you have fractions of years.
Or days.
You have to turn days into years.
And so in your Excel sheet, I have added another worksheet.
The one present values and future values.
I've added another worksheet.
Annualizing.
Because technically in order, if you have days, if you have days, what you would have
to do is take end, ending value over the beginning value and raise that to the one over the number
of days over 365.
That thing down there in parenthesis minus one.
You have to turn the number of days into years.
So I've created an Excel spreadsheet that does years if all you need is years.
But it also does days if you're given the number of days.
So in this one, I could take that 200 initial investment, take it to 225 for three years.
And I'll show you how this trick if you don't know that trick.
You get your 4% that I got with the calculator.
But what happens if you put in $500 and in, you come out with $538 after let's say $500
for 525 days.
So this will turn it into days.
This one you can use for days.
Now how do you get the days?
I may put one other in there.
There are a couple of ways.
Excel has a days between dates so that you could actually take the dates and figure out
the number of days from the dates.
You could do it that way.
Others can do it.
I mean even on Google, there's a calculator you can pull up there that will find the number
of days between two dates.
But one way or the other, this simplifies that calculation just a lot and makes you
a much happier person.
But this will help you with calculating annualized yields.
Now remember that those yield curves that I showed you, those are all annualized yields.
You saw those 4.86 for a five year or something like that, 8.6%.
That is annualized one over five.
The 10 year is the annualized one over 10.
So they're doing in all of those and in almost anything you will see, they won't be talking
about HPRs.
They'll be talking about annualized yields, annualized returns, annualized everything
so that we can compare everything like we do in those yield curves.
But this is up there now and it's nice to have it because then you can look at, well
I made a trade, for example, I did a trade where I put in $230, I think it was.
Twelve days later I came out with $246.
So in that one I had, I'm thinking I put in $230 and then 12 days later I got out of the
position and I had $245 for 12 days.
That's a darn nice return.
You could do that.
Of course you'd also get the ones that are negative in there.
I put in $230 and I came out with $205 eight days later.
But this way you can track all of your returns regardless of the holding period against each
other in terms of their annualized performance.
Just something for you to use.
Now you have a quiz to do right now.