0:11

Let's talk about the pricing of debt.

That's the first thing we're going to talk about in this module.

And what we're going to learn is the relationship between

the forward probabilities in yields.

Here's some data on US government bond yields that I

collected from the Wall Street Journal in September of 2016.

For example, if you look at a 10 year US treasury

bond had a yield to maturity of 1.674.

What I also did is I collected some data on bond yields for

corporate bonds at the same time.

Here, it actually has the date.

There the exact date when I collected this data was September 20, 2016.

If you look at corporate bonds, for example,

long term corporate bonds on average were yielding 4.22%, right?

So the question that we're going to talk about now is where does this

difference come from, right?

So why is the yield on US government bonds lower than the yield on corporate bonds.

So here are the numbers, you can compare.

The long term corporate bond yield, we don't know exactly what's the maturity.

It's an average across different maturities.

But even if you compare it with a 30 year US treasury bond,

you can see that the corporations are paying higher interest rates, right?

To borrow than the US government, okay?

Recall that in Corporate Finance 1 module 4,

we discuss the concept of yield to maturity and how the yield to

maturity can be used to measure the expected return on that, right?

The expected return on a bond security, right?

2:14

When you think about the US government, we hope that the chance

that the US government is going to default on its bonds is fairly low, right?

It actually has never happened, that's the point of this cartoon here.

The US government has never really defaulted on its bonds and

any type of debt security by the government.

However, what we're going to see later,

there's going to be some interesting data for you.

We're going to learn that the current marketplace default

risk on US government bonds is actually not exactly zero.

But we're going to talk about that later, for

now you can think of a very low risk of default.

On the other hand,

when we think about corporations, the default risk is going to be higher.

And here I'm going to bring our researcher to show us the data, right?

People have done research on default risk for corporate bonds in the real world.

We actually have some pretty good data, and here it is.

If you look on the 10 year horizon, so let me explain to you what these numbers mean.

So here we're taking all bonds of a given rating for example, BBB.

Let's take BBB bonds as an example.

We're taking all bonds that currently have a credit rating of BBB.

And then we are looking in the next 10 years,

what is the cumulative probability that this bond will default?

What is the cumulative probability that the company will default on this

BBB rated bond?

The number is 5%, it's not a huge number, right?

It's a 5% probability on a 10 year periodiwill be 0.5% annually.

But it's definitely higher than the probability that the US government is

going to default on its bond, right?

So this uses historical data, of course.

The only data we have to estimate this probability

is to look at the history of defaults, right?

And try to measure what is chance that different companies default, okay?

4:26

Let me give you an example that uses this default data.

So suppose that in the current marketplace you hold a 10 year BBB

bond that pays a youth to maturity of 3%.

So I pulled out a specific bond from capital IQ.

It's a bond that was issued by Monsanto and this pricing data is fairly recent.

You can see the date there, September 19, 2016.

So it's contemporary to the data that I showed you.

Of course, I don't know when you're going to be watching this lecture.

But this data was collected in September 2016, right?

And if you look at the yield on this Monsanto bond, it's approximately 3%.

So if you hold a bond issued by Monsanto,

you expect a yield to maturity of 3%, okay?

The maturity is 20, 25, so this is approximately a 10 year bond, right?

If we are in 2016, the bond matures in 25.

This is approximately 10 year than your maturity.

The rating is BBB as I said up there, okay?

So what happens?

How do we think about the possibility of default when we invest in this bond,

right?

This is the purpose of this tree.

Remember that we use a dicrease when we were talking about R&D investments.

For example, when we're trying to model real options.

Every time there is uncertainty in finance and you want to depict

the uncertainty in a way that is visually appealing that is easy to see.

These binomial trees are very useful, okay?

In terms of the bond,

this is what's happening if you invest in the Monsanto bond today.

There are two outcomes that are possible next here.

By far the most likely outcome, it has a probability of 99.47%.

The most likely outcome is that you will get a return on the bond, right?

And the expected return if the bond does not default is exactly the yield to

maturity.

This is what we learned in Corporate Finance 1 when we were talking about

mutual maturities.

So you approximately get 3%, if the bond does not default.

But now this is the new thing,

we are explicitly incorporating the probability that the bond defaults.

If you look back at the table, the 10 year probability of default for

a BBB bond on average is 5%.

5.3, so that's why I have 0.53.

I'm basically dividing the number by 10

to estimate the annual probability that the bond will default, right?

So now we have to think about these two scenarios,

and let's ask an important question.

What will happen if Monsanto defaults?

7:28

If a company defaults on its debt, what happens is the debt holders are going to

take over the company and attempt to recover some value from the assets, right?

So that is what we call debt recovery.

Again, we have historical data that tell us on average what have recovery

rates been.

And what we know from the data is that these rates have been

around 40% of the face value for corporate bonds.

So for example, if you hold a bond that had a face value of $100 million,

the company defaults.

What happens is the bond holder would recover foreign yield, okay?

8:11

Putting it back in our graph, so

now what we have is a -60% return, in the case of the fold.

We get 40 back, you lose 60, so your return is -60%.

The question that I want you to think about is what

is the investors expected return when investing in the bond?

How are we going to figure that out now?

8:55

But there is a 0.5% chance that the bond will default.

And you are going to get paid 40 out of 100, so

you're going to get a -60% return, right?

So what you see is that if you put those numbers together,

those two numbers together, the expected return you is going to be 2.62%.

So if you invest in a BBB rated bond like Monsanto,

your expected return is in fact not 3%,

it's 2.6% after you take the risk of default into account, okay?

And this is a general idea,

the bond's expected return is always lower than the yield to maturity.

That's the way to think about it.

The yield to maturity is a promised return is what the corporation promises to

pay you, if the bond defaults the investor will not earn the yield to maturity.

9:52

Another related thought then is that if there is a higher risk of default,

if a company has a very high risk of default, what's going to happen is

the company has to promise a higher yield to maturity as well.

The higher the risk of default,

the greater is going to be the yield to maturity, okay?

And it's very easy to see, using the data.

I showed you the data for some corporate bonds already.

Here, what I added is the bond that is an average yield for

bonds that are rated tripple C.

So these are bonds that are very close to default.

The probability of default is very high.

You can see that the yield to maturity is 13.5%.

So considerably higher than the yields on the highly rated one, okay?

The other issue I want to talk about is that this notion of bond

risk premium that is also worthwhile learning.

Notice that the expected return on the Monsanto bond

is still significantly higher than the US treasury rate.

If you look at the 10 year treasury rate, it was 1.674 in September.

The expected return on Monsanto even after deducting the default premium.

If you hold a Monsanto bond you still expect to make 2.6% on average,

even taking the default risk into account, right?

So what this means is that investors earn a risk premium of close to 1% for

investing in a Monsanto bond.

And the notion here is exactly the notion of a risk premium that we talked about in

Corporate Finance 1.

Monsanto bond is risky, right?

There is default risk, some of this default risk is likely to be systematic.

It's going to be correlated with what's happening in the overall economy.

The way that investors are going to price this is to demand a higher

expected return to investing in the Monsanto bond.

So putting all the data together this is what we learn.

We could decompose the yield to maturity on a corporate bond in three different

numbers.

The first one is the risk free rate, which is what the US government pays.

Then there is the bond risk premium, this is the additional expected return that

investors demand to invest in the bond which is close to 1%.

And then finally, there is the direct compensation for

default which is what we calculated in our numerical example.

For any defaultable bond, you can think about this decomposition of the bond yield

into these three different components.

Which is a useful way to think about a yield to maturity in the real world.