Alan Cring Productions in association with the Emergent Light Studio presents
the Illinois State Collegiate Compendium, Academic Lectures in Business and Economics.
This is Business Finance, FIL 240 for spring semester 2024.
Today, bonds and yields. Just a quick look at the numbers for the day so we can see what's going on here and then move on with the fun of the lecture.
Unmute this. There we go.
So as you can see, this is a slightly bare day but it's not really showing much signs of activity. Overall, as far as momentum one way or the other, it's kind of flat.
You can see that the Dow is down a lousy 0.01% which means really nothing and the S&P 500 is down a little more.
But oddly, the NASDAQ has been bouncing up and down on good and bad news as the bears and bulls pull and fight against each other.
There's not really much you can say about this. As you can see right now, the bears are sort of winning, dragging the indexes and the exchange down.
But what you can say from there, you can't really say a whole lot.
Oil had made a run upward and then in the last maybe 30-45 minutes, it's finally beginning to pull back.
It's still in that trading range so no chance of giant spikes in gas prices for the time being.
Interestingly, gold is down and that's good news. That simply means that the markets aren't panicking about anything and running to gold.
Silver is similarly down too. But going over here really quick, the bond market, the prices, the yields were rising which means prices were falling.
That's all good news and we can all celebrate that. Yay.
But at the same time, the yields are up so for what that's worth, that means that prices are down.
There's selling in the bond market. There's also of course selling in the equities market too.
And the money isn't going into gold so that means that the money is just being pulled off the playing field for more indication later about where we are actually headed with the economy.
And it wasn't a good day over. Well, Nikkei was up for the day but as you can see it started running up during the morning over in Tokyo but then it kind of just slowly slid back.
It still finished up but not much. London was just finished closing a while ago and it was down for the day.
I don't know what that was about but there's political issues over in England that probably don't translate much into world issues.
So what was happening over there was just a British thing for the day.
Now I'm going to take you on a little bit of a journey here very quickly.
As far as the Chapter 7 goes, I will not ask math questions about Chapter 7 on the midterm.
We've got one more day of lecture after this. I'll do some of the math with you.
But as far as the actual questions from Chapter 7 that could be on the midterm, they would be more like definitions and words and terms.
Nothing that would have you pulling up calculators or Excel spreadsheets on the specifics of Chapter 7.
So that you should celebrate that as a happy news.
But at the same time there are other issues that we can bring up here from Chapter 7.
Now what I'm going to do here, at least for the first part of this, is to sort of work across Chapters 5, 6, and 7 and bring up a couple of different issues that would be useful for you on the exam.
And I've even improved an Excel sheet that you already have so that you can successfully navigate some of the problems that you would have on the exam.
First things first, let me take this off the board here for a few minutes and put this down, let it quiet down for a little while.
Let me do something here.
As I said earlier, different words mean pretty much the same thing as far as interest rates go.
Yield, return, rate, those all are interest rates, they're all percentage.
And we use just a different term for different types of financial investments.
But very quickly here, a yield, let's do a return.
Let me start it out like this.
You sir, you make an investment of $100 and in one now, and in one year, you have $110.
Now, the holding period return, the HPR, I think the book calls it, I'm not sure, is nothing but the ending value over the beginning value minus 1.
That's all holding period return is, HPR.
So the HPR on this investment is 110 over 100 minus 1, which would be 10%.
Nothing hard about that.
But you sir, now you put in $100 and in six months, you have $110.
So your HPR is also 110 over 100 minus 1, which is 10%.
But those can't be the end of the story because it took you only six months to do what took him a year to do.
That's why we need to make all of the units for calculations of yields, returns, rates, whatever, we need to have them in the same units.
That's where we come to the concept of annualization.
Annualizing returns, so the annualized return would make everything based on a year, APR, annual percentage rate.
That's why you see that A in the APR.
We make everything this way.
The ending value over the beginning value to the 1 over the number of years minus 1.
Don't forget that minus 1 for heaven's sakes.
As you can see, the holding period return is the annual if it's a one-year hold because that would be to the 1 over one year.
But this one, I would have to do something else.
The annualized return would be 110 over 100 to the 1 over a half a year, 1 over.5 year minus 1.
You have to take a 1 over the number of years.
Now, I have modified that spreadsheet that you have for present values and future values,
and I put a new worksheet on there that will do this calculation really fast.
But if I work this out on a calculator, it will come up to be 21%.
So that's where we see that your six-month investment dominated the one year the get got the same HPR.
The HPR doesn't tell us anything, really.
It's that annualized rate that does the leg work.
There are a couple of things you have to watch in this.
I'm going to do this one, that one that you just saw there on the calculator,
just to make sure you see if you want to use the calculator to do an annualized rate of return.
Okay, watch.
Now, on this one, I'm going to do that second one again.
I'm going to do open parenthesis.
You're going to do the ending value divided by the beginning value, 110 divided by 100.
Close the parentheses.
Now, use the exponent.
Now, the exponent you have to put in parentheses.
Watch that.
That's where I always, well, that's one of the places I screw up.
It's one open parenthesis, one divided by the.5.
Close the parenthesis, and then don't forget the minus one.
This is one of those where if you forget the minus one, what comes out will look like a good answer.
Watch it.
That's a classic mistake, and you'll see me even forget the,
I go through all that exponent stuff in the parentheses, and I forget the minus one.
There we go.
There's the 21%.
Now, let me show you what I've done for you in Excel.
This is that spreadsheet that you have, that you've downloaded.
Now, you'll want to download the new version of it, because I put a new worksheet in there,
annualizing, and I've done this.
Beginning amount, 100.
Ending amount, 110, for.5 years.
There you go.
That fast.
Now, this is one thing.
The calculator could have done that fairly quickly.
However, suppose you buy a stock for $17.81,
and you sell it in three years for $19.97.
Let's annualize the return on it, just in the Excel spreadsheet.
All you do is put in the $17.81, and then you go down, and you end $19.97,
and your holding period is three years.
That little trick with the units, I'll show you how to do that later.
It's really a convenience.
There's your annualized rate of return, 3.89.
That fast.
Now, that's a pretty thing right there, because that saves you having to do it on a calculator,
and it looks on the midterm, I will ask you a question just like this.
And you can look like a hero, because it just spits out if you just put the numbers in,
where they belong, out will pop your answer.
Now, as you can see, I've also done a version of this for days instead of years.
Now, I could have done this a little more sophisticated,
but Excel has a way to do days between two dates.
But let's just do one.
You buy a stock on March 18, 2021,
and you sell it on October 8, 2023.
You bought it at $32.32 and 84 cents,
and you sold it at $34.90.
So here you don't have the days.
Now, like I said, you can do this in Excel.
I didn't do it in Excel, but it's not that hard to find the number of days.
Watch.
Even your calculator, your TI can do it, but I'll show you.
Go over here, and the way I do it, if I just need some days between dates,
Google days between dates, date calculator.
You put in the start date.
The month was March.
The day was what? The 18th year was 2021.
Now you ended it on October, so that would be the day,
what day did you do it? 8th of 2023.
Now just calculate it.
That's 934 days.
So now you just go back to Excel.
You began with $32.84.
You ended with $34.90.
And it was what? What did that say?
934 days.
There's your annualized rate, 2.41%.
Like I said, you can do it in Excel, but I didn't write the code for that one.
But what you're actually doing there in that formula is you're doing end over beginning
to the one over the number of days over 365 minus one.
You're turning the days into decimal years.
And as you can see, if you look at the formula, see right here in the formula,
I've got end over beginning, D3 over D2, and then I have the one over,
and then it's taking the number of days that are in cell D4 and dividing it by 365
to turn it into, what would that be, like 2.4 years, something like that.
So the formula needs to be in years or parts of years, years end or parts of years.
And that's how it comes out with that answer.
You can do that on the calculator, but I have found over the years that students have a hard time,
especially on the pressure of an exam, trying to pull off that,
keep everything in the parentheses as you're running it along.
And it can come out to be a fiasco.
But this way, it spits out cleanly for you.
The only thing with this one is you do have to find a resource that will give you the number of days.
Now, on an exam, I would give you years.
I wouldn't make it so that it was days, parts of a year.
So it would just be four years, eight years, something like that.
So it would work out better for you.
I'll show you something real quick here, if I can find it.
Well, let me do this.
And I'll come back to this chart a little later in the course.
Try this.
Historical stock market returns.
I'm looking for one stock one, if I am finding it.
Slick charts now, come on.
If I am finding it, it's useful to know.
Let me try this.
One stock one.
Historical returns.
I'll grab one here.
Let me look at, for example, the S&P 500.
This would be in 1975.
If you had put $68.56 into the S&P 500 in 1975.
Now, this takes us clear down to 2023.
So 1975 to 2023 is 25, and 23 is 48 years.
Watch.
So the beginning amount was what?
$68.56.
The ending value was, what am I looking at here?
$38.3950.
And that would have been, what did I say, 28 years?
75, 20, yeah, that would be 48 years.
Let's see what the annual, if you had just put that money in and left it there.
You would have made an annualized return over that long period of time of 8 3.25%.
In other words, if you had just not touched it, just even in the black swans, you leave it alone, just ride it.
Your annualized return over that period of time would have been 8 3.25%.
Which when you look at it from the perspective of a long-term investment, you couldn't have gotten that in a CD, a 48-year CD.
You couldn't have gotten that in a bank account if you had just left that stupid money alone.
You would have gotten a return of 8.75%.
So that's something that is useful to know, is that you can calculate on an annualized basis,
and you can compare it to shorter investments all along the way.
This is what this can do for you.
So that's there for you now, it's in your files.
You don't want to do that, but it happens.
I was at a stupid graduation ceremony, I forgot to turn it off,
and I didn't realize my dear daughter had put a new ringtone on it.
Boy, was that embarrassing.
I sent her a text message about what kind of depth she was going to have.
Okay, anyway, so there's that.
Okay, so now the next thing that I want to do here in all of this is to show you
something else.
Now remember that this is how we see, whenever you see a yield on a bond or an investment rate
or anything like that, it's going to be one of these annualized.
That way you can compare two investments, one that you've maybe held for a few days,
one you've held for a few years, they're all in the same units,
and you can compare them directly one against the other.
So we go to the next situation, where I bring back that formula for interest rates.
And I emphasize a few things again.
The interest rate, any interest rate, has a substrate of R sub F.
All interest rates will hold this piece.
It is the same for all interest rates.
It is underlying, so we know that it's there, and it isn't disappeared for one and reappeared for another.
For example, let's try it this way.
Sir, do you have a skeleton?
You don't have a skeleton?
Well, yeah, you've got one.
I mean, you're not a jellyfish, you've got a skeleton.
Madam, do you have a skeleton?
Okay, it's smaller than his, but it's there.
We know that you two have skeletons.
That we can say, skeleton, skeleton.
I got a CT scan last week.
I mean, it's gross, the skull looking at it.
Okay, but it's there, and it's always there.
It's the same.
Now, we keep in mind that inside of this is the real interest rate plus the expected inflation premium.
Now, those two are the same for all interest rates, so it sets the rock solid bottom.
Where the action happens is in that risk premium, that default premium plus the maturity premium plus the illiquidity premium.
So if we're looking at the same instrument, same security, the same bond, what have you,
as time goes along, it will have the same default premium.
If I look at the two-year, five-year, it should have the same default premium and same illiquidity premium.
Now, a yield curve.
A yield curve takes the same bond, but looks at different maturities of it.
A one-year, a two-year, a three-year, a five-year, a seven-year, ten-year, twenty-year, thirty-year.
And on this, that's the horizontal axis.
And then on the vertical axis is the yield.
So what we should see, the R sub D and the R sub L should stay the same.
R sub F will be the same.
The only thing that is making a yield curve slope upward or downward is the maturity premium.
Remember, the maturity premium gathers steam, gets bigger the farther out,
because there's more chances of interest rates going up or down.
Now, the one we use to do this analysis, first of all, well, the one we use to do this analysis is a treasury security.
A very short-term, one-year, two-years, three-years, five-years, seven-ten, twenty-thirty.
We look at the yield on treasury securities as time goes on.
Now, one thing that we know is that treasury securities have virtually no default premium.
And they have no illiquidity premium. You can sell a treasury, any kind of treasury bond, with a push of a button.
So we know that those are going to stay the same.
So what the yield curve on a treasury does is show the upward slope that is caused by the building maturity premium.
Maturity premium on a twenty-year is higher than the maturity premium on a ten-year.
The maturity premium on a ten-year is higher than the maturity premium on a seven-year,
which is higher than the maturity premium on a five-year.
So that is what a normal premium, a normal yield curve should look like.
That's what it looks like. It's healthy.
Now, we can have a situation where it swoops up way too much. It's too steep.
Generally, that would be the result of markets saying that inflation is expected to be higher and higher as time goes on.
But that's not very normal.
Now, let me show you two abnormal yield curves.
The first one we would never, ever want to see because it would be pretty much that's closing the shop on the economy.
A yield curve that is exactly backwards. It's going down.
We want to stay light years away from that.
That's a depression, a massive depression yield curve that's going to last for years and years and years.
And we want to stay away from that one as much as we can.
Inflation, well, this one means that we've got deflation happening.
Well, what's wrong with prices going down?
Trust me, you don't want to see that because prices go down if you are nearing the end of an economy.
Prices begin to start falling.
That's a sign of an economy that's getting into the worst possible situation.
So that one, we hope we don't ever see that one, ever, ever.
But there's one that we do see from time to time.
And it's very important because it's a forecaster of a recession that's coming.
This one is called an inverted yield curve.
It begins like a normal yield curve, but then a longer rate is lower than a shorter rate.
That's a sign that we're going to have a recession.
Every recession we've had was preceded about six to nine months before by an inverted yield curve.
It's like a warning shot that here comes a recession.
Now, there have been some yield curves that inverted, and it came out that it wasn't a recession.
It's just like an economic pause.
A recession is technically two quarters, two consecutive quarters of negative GDP growth.
So sometimes, once in a while, an inverted yield curve will precede an economic pause instead of a full recession.
But every full recession has been preceded by an inverted yield curve.
So it's like, it's actually one of the most reliable predictors we have of what's coming in an economy.
And you can do it. Anyone can do it.
Now, let me show you something.
Let me take us back to, now this is U.S. Department of Treasury's yield data on government debt instruments
from three months on out to 30 years, I guess.
And so we can look at, yeah, there were a couple that weren't there back then.
Do you see how the yield curve is rising from the one year, two year?
Usually we look at the one year to start with, but one year, two year, do you see how the yields are rising just nicely?
That is a classic healthy yield curve.
It looks good.
And you can see that upward slope, that's these numbers, upward sloping.
Always going up.
But then, we get to the, let's go to the end of 2022.
Look. Do you see how they were rising and then they start falling?
Whoops, let me highlight those.
Now that is an inversion from hell.
Usually you'll see this, maybe the 10 year, well the 10 year below the 7 year, so you've got an inversion down and then it comes back up.
Maybe a couple of them will be lower than the ones preceding.
But this was the inverted yield curve from hell.
It was unbelievably downward sloping for way out.
That one was more like, a typical inversion would look like that.
The inversion you're seeing was like that.
In my lifetime I've never seen one like that.
You're seeing something that hardly anyone knows, but it's historical.
A curve like that at the end of 2022.
Well of course, every economist and financial analyst worth his or her salt was saying, recession coming, horrible recession, OMG.
Well you know what?
It didn't happen. For the first time an inverted yield curve did not lead to a recession.
It led to a slowdown, a very strong slowdown of the economy, but it didn't lead to a recession.
So let's go to now.
Let me go up here and let's look at 2024.
No, yeah let's look.
Obviously the data won't be a whole year's data, it'll just be the first couple of months.
Okay, apply.
Well look at that.
The son of a dog is still inverted.
Do you see it?
It hasn't corrected the inversion yet.
But we're now going from a recovery to what looks like an expansion.
No recession on the horizon.
And yet the yield curve, despite its historical accuracy or reliability I should say,
is signaling something that didn't happen.
We saw this in 2022, this inversion happened then.
Should have had a serious recession from six to nine months after that, after the inversion started.
Didn't happen, nothing really.
And now we still have it inverted, screaming here comes a recession and there's no recession on the horizon.
So you're living in financial economic times that are just kind of unprecedented.
And we don't, well there is one possible explanation for why it's inverted but it's not a bad thing.
You have to look over here at this.
And you look, it is possible that what the markets are signaling is an expectation of dramatically falling expected inflation premium.
That would be about the only explanation.
It should that EIP should stay about the same.
It might steepen the curve if there's expected inflation that's going to be bad down the road.
But this seems to be saying that the reason it's inverted is that expected inflation premium is going to be draining out of the economy for the foreseeable future.
That's about the only explanation that makes sense is the EIP is what's driving the inversion.
So there you are though.
Historically unique time and you're seeing it right there.
We have an inverted yield curve but no evidence whatsoever of an impending recession in the next year.
The data, the jobs data, manufacturing index, consumer confidence, all of those are pointing to recovery and or expansion of the economy.
So that's that.
Now let me show you, I'm going to keep this up here because I can't even use this stupid.
There's something that they mention in the book, the forward rates.
And forward rates, well I guess I actually could.
Let me see.
Let's see.
I got to keep my eye.
One two is right here.
One two is right there.
Well that's interesting.
We'll talk about that in just a minute or two.
But let me show you one of the uses of that formula right there for interest rates.
Suppose that I have a triple A corporate bond.
Right now the yield on that bond, this is a very safe bond.
Very little chance that it's going to behave badly.
So it's going to be the risk free rate, which is the same for all debt instruments for a given time.
Plus the default premium for the triple A bond.
Plus the maturity premium for the triple A bond.
Plus the illiquidity premium for the triple A bond.
Now suppose that this is a 10 year corporate triple A.
It's got a maturity of 10 years.
10 years out.
So all these numbers are hinging on 10 years.
R sub F will stay constant.
Now let's look at a 10 year government bond.
Technically it's a note.
So that would be R sub F plus the default premium on a government bond.
Plus the maturity premium on a government bond.
Plus the illiquidity premium on a government bond.
Now first things first, the illiquidity premium.
There's going to be virtually none on either a corporate triple A or a government.
You can push a button and sell them anytime you want.
Liquidity is the efficiency with which an asset can be converted to another asset.
Well there you go.
Those corporate triple A bonds you can sell them instantly.
Same with government bonds.
So for these two bonds it's going to be a zero.
Now the maturity premium.
This bond is corporate 10 years.
This is government 10 years.
The 10 years is what matters.
They will have identical maturity premiums because they're both 10 years.
The volatility of interest rates in 10 years is going to be the volatility of interest rates for 10 years,
so these two are going to match each other.
The one that will be different is that the government bond will have no debt, no default premium.
The corporate bond will have a default premium.
Now let me subtract those two.
Going from illiquidity premiums, zero minus zero will be a zero.
If the maturity premiums are the same, then that will be zero when we subtract those.
The R sub D of the triple A bond minus a zero on R sub D for the government bond
means that this one will be R sub D, the default premium, on the corporate bond.
The R sub S will be the same.
So what this tells us is that if I take the yield on a corporate triple A bond
and subtract the yield on the same maturity government bond,
what I would find is the default premium on triple A bonds.
We do this all the time to keep an eye on it.
Like for example, suppose that the yield on the corporate bond is 4.68 percent
and the yield on the government bond is 4.50 percent.
Then if I subtract those two, I will get 0.18.
That means that the default premium on high quality corporate debt is 18 basis points.
Why does that matter?
In and of itself probably doesn't tell us much, but we watch it over time.
That default premium, if it gets bigger, then we know that the markets are assessing
more risk of default by big corporations.
If it gets smaller, then that risk of default is shrinking.
That is a warning or a sign of the expectations of the economy.
I can do the same thing with double A, single A,
to see what different layers of corporate default are doing.
Are they getting bigger? Are they getting smaller?
Right now, they seem to be that R sub D seems to be contracting somewhat,
which means the economy, the expectation is lower chance of default by big corporations.
That's why we look at it, to see which way it's going or is it staying about the same.
Now, I caution one quick thing about this.
You can't really do this below single A bonds, triple A, double A, single A.
The reason you can't do it below that is because you get down into lower grade corporate bonds, junk bonds,
the illiquidity premium starts to show up.
It's not immediate.
I had a junk bond some years back and I put it in order to sell it.
I just wanted to get out from under the day and gone thing.
It took three days before there was an investor who would buy it.
You can't really do this down there too low because the illiquidity premium starts to fuzz up.
You get not just the R sub D, but you get a little bit of R sub I illiquidity in there as well.
So there's that in there.
Now the last thing to do in this, and I will not do this on a test,
but you do see one question or they cover it a little bit in your homework.
Let me get all this off the board here, not to scare you too much.
But this right here.
Well now I don't think I'm going to do that today.
Let me just have you go ahead and, what time is it?
Yeah, why don't you just go ahead and take the quiz and I'll cover the rest of it on Wednesday.
But as far as material today is concerned, that's all I have for you. I thank you.