0:11

Let's talk about the pricing of debt.

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

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

Â the forward probabilities in yields.

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

Â collected from the Wall Street Journal in September of 2016.

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

Â bond had a yield to maturity of 1.674.

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

Â corporate bonds at the same time.

Â Here, it actually has the date.

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

Â If you look at corporate bonds, for example,

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

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

Â difference come from, right?

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

Â So here are the numbers, you can compare.

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

Â It's an average across different maturities.

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

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

Â To borrow than the US government, okay?

Â Recall that in Corporate Finance 1 module 4,

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

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

Â The expected return on a bond security, right?

Â 2:14

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

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

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

Â The US government has never really defaulted on its bonds and

Â any type of debt security by the government.

Â However, what we're going to see later,

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

Â We're going to learn that the current marketplace default

Â risk on US government bonds is actually not exactly zero.

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

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

Â On the other hand,

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

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

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

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

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

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

Â Let's take BBB bonds as an example.

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

Â And then we are looking in the next 10 years,

Â what is the cumulative probability that this bond will default?

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

Â BBB rated bond?

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

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

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

Â going to default on its bond, right?

Â So this uses historical data, of course.

Â The only data we have to estimate this probability

Â is to look at the history of defaults, right?

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

Â 4:26

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

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

Â bond that pays a youth to maturity of 3%.

Â So I pulled out a specific bond from capital IQ.

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

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

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

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

Â But this data was collected in September 2016, right?

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

Â So if you hold a bond issued by Monsanto,

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

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

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

Â This is approximately 10 year than your maturity.

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

Â So what happens?

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

Â right?

Â This is the purpose of this tree.

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

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

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

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

Â These binomial trees are very useful, okay?

Â In terms of the bond,

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

Â There are two outcomes that are possible next here.

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

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

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

Â maturity.

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

Â mutual maturities.

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

Â But now this is the new thing,

Â we are explicitly incorporating the probability that the bond defaults.

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

Â a BBB bond on average is 5%.

Â 5.3, so that's why I have 0.53.

Â I'm basically dividing the number by 10

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

Â So now we have to think about these two scenarios,

Â and let's ask an important question.

Â What will happen if Monsanto defaults?

Â 7:28

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

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

Â So that is what we call debt recovery.

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

Â rates been.

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

Â around 40% of the face value for corporate bonds.

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

Â the company defaults.

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

Â 8:11

Putting it back in our graph, so

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

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

Â The question that I want you to think about is what

Â is the investors expected return when investing in the bond?

Â How are we going to figure that out now?

Â 8:55

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

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

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

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

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

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

Â your expected return is in fact not 3%,

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

Â And this is a general idea,

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

Â That's the way to think about it.

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

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

Â 9:52

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

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

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

Â The higher the risk of default,

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

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

Â I showed you the data for some corporate bonds already.

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

Â bonds that are rated tripple C.

Â So these are bonds that are very close to default.

Â The probability of default is very high.

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

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

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

Â risk premium that is also worthwhile learning.

Â Notice that the expected return on the Monsanto bond

Â is still significantly higher than the US treasury rate.

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

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

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

Â even taking the default risk into account, right?

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

Â investing in a Monsanto bond.

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

Â Corporate Finance 1.

Â Monsanto bond is risky, right?

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

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

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

Â expected return to investing in the Monsanto bond.

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

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

Â numbers.

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

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

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

Â And then finally, there is the direct compensation for

Â default which is what we calculated in our numerical example.

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

Â into these three different components.

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

Â