Chapter 24: Credit Risk & Corporate Debt Valuation

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Okay, let's dive in.

We've all spent a lot of time getting our heads around the basics of finance, you know, present value, rates of return, yield to maturity, and that's all essential stuff.

It's a foundation, absolutely.

But when you step out of that, that clean theoretical world of default free government promises, like those tidy treasury bonds, and you jump into the messy reality of corporate finance, well, everything changes.

It really does.

Today, we're talking about the true cost of a company's promise.

And more specifically, how we can measure and put a value on the very real chance that that promise gets broken.

That is the central problem, isn't it?

When we first look at bonds, we lean on these core principles,

spot rates, the term structure, nominal versus real returns.

All of that still applies.

Sure.

But the one thing, the one massive distinction that drives this whole deep dive is credit risk.

You know, government debt, especially from a stable country, that's our baseline.

That's the risk free rate.

Right.

Corporate debt, though, it comes with this huge contingency.

We have to figure out how to account for it.

And you don't have to look very far to see just how big that risk is.

We've got a pretty startling data point right here from the aftermath of the 2008 financial crisis.

It really puts it in perspective.

It does.

Corporate default isn't some abstract idea.

It's a very real, very expensive reality.

In 2009 alone, companies around the world defaulted on.

It was a record breaking $330 billion of debt.

Wow.

$330 billion.

$330 billion in promises that just vanished or at least had to be severely restructured.

And that huge number really frames our mission for today.

Bondholders, they know they might not get all their money back.

So to compensate them for taking on that credit risk, they demand a higher yield.

A risk premium.

A risk premium.

Exactly.

Our job today is to go beyond just saying, oh, the yields are higher.

We need to figure out how much higher they need to be and what really drives that difference.

So we've got a clear plan.

We'll start with how the market prices this risk looking at yield spreads.

And we'll break down that key difference between the return a bond promises versus what you can actually expect to get.

Right.

The promise versus the expected.

Then we're going to get into some heavier theory.

We'll start treating a company's decision to default like a financial option, which is just a fascinating way to connect limited liability directly to valuation.

And then finally, we'll look at the models that analysts and investors use in the real world to try and predict the probability of a company going bankrupt.

Let's get into it.

Okay.

So let's start with that illusion you see in the bond market.

You know, you look at a bond from a company that's maybe struggling a bit and you see this really high advertised yield.

Yield to maturity.

Yeah.

Right.

And for someone who's maybe a little new to this, it can look like an incredible opportunity.

Like, why isn't everyone jumping on this?

It's the classic lure,

but it has this giant invisible asterisk next to it, which is that you only get that high yield if the company actually survives and pays you back in full.

We can use a real example here.

California Resources Corporation CRC back in 2019.

They had these bonds out there with an 8 % coupon.

Okay.

But the company was in some serious financial distress.

So those bonds, they were trading at just 24 cents on the dollar.

24 % of face value.

So if I buy that bond, I'm paying 24 cents for a promise to get a dollar back plus all those coupon payments.

Exactly.

And if you run the numbers on that, the promise yield to maturity was, it was an incredible 54%.

54%.

And what was a safe treasury bond yielding at the time?

Maybe 2%.

So the spread, the difference was 52 percentage points.

That's just a mind boggling number.

So why wasn't the market just flooding in to buy these things up and close that gap?

Because that 54 % return was a long shot.

It was only possible if CRC somehow turned things around and repaid everything in full a few years later.

Which is looking pretty unlikely.

Very unlikely.

And that's the key distinction.

The expected yield, which is the average return you'd get if you factored in the probability of default and how much you'd lose,

was much, much lower than 54%.

We need to really understand the math behind that gap.

Okay, let's do that.

Let's use a simplified example just to nail down how default risk inflates that promised yield.

Perfect.

We'll use the Backwoods Chemical Company scenario.

First, let's set a baseline.

The one -year risk free rate, let's say, is 5%.

Okay.

So that's our opportunity cost for a safe investment.

Right.

And Backwoods issues a simple one -year note with a thousand dollar face value, and it promises to pay 5 % interest.

So the total promise payment at the end of the year is $1 ,050.

So if Backwoods was totally risk free, like the government, the price would be easy.

You'd just discount that 1 ,050 by 1 .05, which is exactly $1 ,000.

Sells at par, yields 5%.

Simple.

But it's not risk free.

It's not.

Now let's introduce credit risk.

Let's assume there's a 20 % chance that Backwoods will default.

And if they do, the bondholders only recover half the face value, so $500.

So we have two states of the world.

An 80 % chance you get the full 1 ,050, and a 20 % chance you only get 500.

Exactly.

So first we calculate the expected payment.

That's 0 .8 times 1 ,050 plus 0 .2 times 500.

Which comes out to 840 plus 100.

$940.

$940.

So right away, you can see the expected payoff is $110 less than the promised payoff.

Okay.

So now we need to figure out what that bond is actually worth today.

And that all depends on the discount rate we use for that $940.

Right.

And this brings us to two really important cases about the nature of that risk.

Case one.

Let's imagine that the risk of Backwoods defaulting is totally unique to them.

Maybe it's about a chemical spill at their plant that has nothing to do with the wider economy.

So it's diversifiable risk, zero beta.

Exactly.

If the risk is diversifiable,

investors don't need a market premium.

So we should discount that expected payoff of $940 at the risk -free rate of 5%.

Okay.

So 940 divided by 1 .05.

That gives us a present value.

A price of about $895.

It sells for less than a thousand because of that default risk.

Now for the big insight.

If you, the investor, pay 895 for this bond, and there's an 80 % chance you get 1 ,050 back, what's your promised yield?

It would be 1 ,050 divided by 895 minus one, which is, wow, it's 17 .3%.

17 .3%.

So wait, the investors only required a 5 % expected return because the risk was diversifiable.

But the bond is advertising this huge 17 .3 % yield.

Where does that difference come from?

That difference isn't a premium for market risk.

It's the compensation the bond has to offer to cover the potential loss of principal from default.

The smart investor knows their expected yield is only 5%.

The promised yield is just inflated to make up for that 20 % chance of a big loss.

That's the crucial distinction.

But of course, this assumes the risk is completely diversifiable, which it usually isn't.

Right.

Let's get to case two.

Defaults happen more often in recessions.

Corporate bonds have market risk.

They absolutely do.

They have positive betas.

So investors will demand a market risk premium.

Let's say for this risk, they now demand an 8 % expected rate of return.

That's the 5 % risk free plus a 3 % risk premium.

The expected payoff is still $940, but now we're discounting it at 8 % instead of five.

Which means the price has to be lower.

940 divided by 1 .08.

That brings the price down to about $870.

So now what's the new promised yield?

It's 1 ,050 divided by that new lower price of 870.

That works out to 20 .7%.

20 .7.

So you see, because we introduced market risk, the required expected return went from 5 to 8%.

That pushed the bond's price down, which in turn forced the promised yield even higher.

And it must be super sensitive to how bad the default is.

You assumed a 50 % recovery.

What if bondholders get nothing?

Oh, it balloons.

If recovery is zero, the expected payoff drops to just 840.

To still get an 8 % expected return, the price would have to crash, and the promised yield would skyrocket to an incredible 35%.

The worse the potential loss, the more absurd the promised yield has to get.

Exactly.

So that difference between the promised corporate yield and the safe treasury yield, that's what we call the yield spread.

It's the market's price tag on credit risk.

It is.

And the most common tool investors use to quickly gauge this risk is the bond rating from agencies like Moody's or S &P.

And if you look at the data, the spreads vary massively depending on the company's rating.

Right.

Looking at the historical data, overrated bonds, that's the top tier, the safest companies, they've historically had a spread of only about 1 % over treasuries.

They're barely riskier than government debt.

But if you go down just a few notches to ball, which is still investment grade.

The spread basically doubles to a little over 2%.

You can see the market demanding more compensation for just a bit more risk.

And then you fall off the investment grade cliff into the junk bond market.

The high yield market, yeah.

For those bonds, the average spread is around 6%.

But, and this is a huge but, that's just the average.

That part of the market is incredibly volatile.

In a crisis, those spreads can just rocket skyward.

You can see that volatility perfectly in the charts.

The spreads weren't stable.

There were these huge spikes around 2000 and then again in 2008 and 9.

And those periods line up perfectly with the spikes in corporate default rates.

The connection is obvious.

More defaults, wider spreads.

But there's a nuance here, right?

The swings seem almost too big.

They do.

The fluctuations, especially for the low grade stuff, seem too large to be explained only by the changing probability of default.

There's something else going on.

What is it?

Investor psychology.

It has to be.

It's a flight to quality.

When a crisis hits, investors get really risk averse.

They just, they scurry to the safety of government debt, which pushes treasury yields down and corporate spreads way, way wider than the historical default data alone would suggest.

So this brings us back to a really core idea in finance, the law of one price.

We can actually think of that yield spread as the cost of insurance.

That's the perfect way to frame it.

Imagine two different strategies to get a risk -free payoff.

Okay.

Strategy one, you put a thousand dollars in a default free bond that yields 9%.

Simple, safe.

You put that same thousand dollars in a corporate bond that promises a higher yield, say 10%.

But at the same time, you buy an insurance policy on that bond that costs you 1 % a year.

So if the company defaults, the insurance pays you back, you're made whole.

Exactly.

Now you have two strategies with the exact same risk -free payoff.

The law of one price says they have to have the same return.

In strategy two, I get an extra 1 % from the bond's yield, but I pay 1 % for the insurance.

They cancel out.

They perfectly offset.

Therefore, the law of one price demands that the yield spread,

the 1 % difference between the corporate and treasury yields must be equal to the cost of insuring the bond.

That's a huge takeaway.

The yield spread isn't just a penalty.

It's the market price for transferring risk.

It's an insurance premium.

That's it.

So if the spread is an insurance premium, let's talk about the actual insurance policy, the credit default swap or CDS.

Right.

A CDS is at its heart, just a contract.

The buyer of the CDS pays a regular premium called the CDS spread.

And in return.

The seller of the CDS promises to pay the buyer for any losses if the company defaults on its debt.

So for example, if we look at Boeing back in early 2020, its CDS spread was 45 basis points.

Or 0 .45%.

So if you own $10 million of Boeing bonds and you wanted to ensure them, you'd pay the CDS seller $45 ,000 a year.

And if Boeing defaults, the seller pays me.

What?

They pay you the difference between the bond's face value and whatever it's worth after the default, its recovery value.

It's an incredibly efficient way to move credit risk around the financial system.

And we mentioned that the CDS spread isn't always exactly the same as the bond's yield spread.

That little difference is called the basis.

Right.

Now, one of the tricky parts is figuring out what a defaulted bond is actually worth.

The price can be all over the place right after a bankruptcy filing.

We saw this with the D &E case back in 2011.

Right.

They filed for bankruptcy and they had to figure out how to settle all these CDS contracts that were tied to their debt.

So they set up a formal two stage auction to find a true market price for the defaulted bonds.

It was a really clever way to establish a single official recovery value for everyone.

And the final price they settled on was 71 .25 % of face value, which means the loss was 28 .75%.

So if you had bought CDS protection on $10 million of Diridji debt,

the seller would have paid you $2 .875 million.

It's a very clean mechanism, but the popularity of these things, it just exploded.

And that led to some massive systemic problems, right?

The AIG collapse.

Oh, the growth was astronomical.

Yeah.

From basically zero in 2000, the notional value of these swaps hit $62 trillion by 2008.

It's 62 trillion.

A huge chunk of that risk was being sold by these specialist firms called monoline insurers.

And they started out insuring safe things like municipal bonds.

But then they got greedy.

They did.

They dove head first into guaranteeing riskier products, especially those securities that were backed by subprime mortgages.

And AIG was the biggest player of all.

They were guaranteeing hundreds of billions of this stuff.

They were.

And their big mistake, their fatal flaw was that they wrote these collateral clauses into their contracts.

Right.

The clauses said that if AIG's own credit rating fell, they would have to post billions of dollars in cash as collateral.

Exactly.

So when the housing market collapsed, the rating agencies finally downgraded AIG.

And that triggered the collateral calls.

Instantly.

They were on the hook for $32 billion that they just did not have.

And if AIG failed,

all that insurance it had sold would have just disappeared.

It could have brought down the entire global financial system.

Which is why the Federal Reserve had to step in with that $85 billion bailout.

The largest in history at that time.

It was a terrifying lesson in how a market designed to manage risk could itself become the biggest risk of all.

So we've seen how the market prices this risk.

Now we need to go deeper and look at the theory that explains why this risk exists in the first place.

It's time to connect it all back to corporate finance theory.

This brings us to a really elegant part of the theory where we connect the idea of limited liability directly to option pricing.

It's a powerful insight.

The fundamental difference between a risky corporate bond and a safe treasury bond is that the corporation holds a valuable financial option.

The option to default.

The option to default.

And that option belongs to the shareholders.

Limited liability means that if the company's assets are worth less than its debts, the shareholders can just walk away.

They hand the assets over to the bondholders and their liability is gone.

So how do we frame that legal right as a financial option?

Well, think about what happens when a company issues debt.

It's like two things are happening at once.

First, the company issues a safe default free bond.

But second, the shareholders get a put option from the bondholders.

A put option.

So it's the right to sell something.

It's the right to sell the firm's assets to the bondholders for a specific price.

And that price, the exercise price must be the face value of the debt.

Exactly.

The promised debt payment.

The decision for the shareholders is simple.

If at maturity the company's assets are worth less than the debt, they exercise their option.

They sell the assets to the bondholders by defaulting and walk away clean.

And if the assets are worth more than the debt, they don't exercise.

They pay off the debt and keep the extra value for themselves.

That's it.

Default is just the shareholders exercising their default put.

Let's bring back the old circular file company example.

It's perfect for this.

Their assets were worth $30, but they owed $50 in debt due in one year.

Right.

And even though the company was clearly underwater, its stock still had value.

The balance sheet showed $30 in assets financed by $27 in bond value and $3 in stock value.

Why was the stock worth anything at all?

Why wasn't it zero?

That $3 was the value of the option the default put.

The shareholders had a year.

And in that year, there was some small chance that the asset value could recover, that it could shoot up past $50.

So they had all the upside if things went well.

And limited downside.

If the assets fell even further, they'd just exercise the put and lose nothing more.

That $3 was the price of that valuable option.

So because a corporate bond is like a safe bond minus this default option that the shareholders own, we get a really clean valuation formula.

We do.

The value of the bond is equal to the value of a default free bond minus the value of the put option on the company's assets.

Which breaks the problem into two steps.

Step one is easy.

Step one is just calculating the default free value.

For a circular file that was $50 discounted at the risk -free rate, which we'll say is 10%.

So $45 .45.

Step two is the hard part.

Valuing that put option, that's where you need something like the Black Schools model.

You do.

You need all the inputs.

Asset value, exercise price, time, risk -free rate.

And crucially, you need the volatility of the assets.

Let's assume it's 60%.

60 % is really high volatility.

It is.

But that's what makes the option valuable.

The more volatile the assets, the higher the chance of a huge swing up or down.

And remember, the shareholders love that.

Right.

So we plug all those numbers into Black Schools and the value of that default put comes out to $18 .60.

So now we just complete the formula.

Right.

$45 .45 for the safe bond minus $18 .60 for the value of the put option.

And that gives us $26 .85, which is almost exactly the $27 bond value we started with.

The theory perfectly explains the price.

It does.

So if this theory is so perfect, why aren't bond traders just using Black Schools all day long?

Because the real world is much messier.

Circular file was a simple case.

One payment at the end of the year.

Most bonds have coupon payments every six months for 10 or 20 years.

Ah.

So at every coupon date, the company has a new decision.

Pay the coupon or default?

Exactly.

If they pay the first coupon, they've essentially bought themselves another option to default six months later.

And then another one and another one.

It's called a compound put option.

And valuing that must be incredibly complicated.

It's extremely difficult.

So in practice, while the theory is perfect for understanding what drives the risk,

traders usually just rely on comparing yield spreads on similar bonds.

But that theory is still invaluable because it tells us exactly what variables drive the value of that default put and therefore the riskiness of the debt.

It gives us the five key drivers.

We can just run through them.

Okay, let's do it.

First, an increase in the value of the company's assets.

The put value declines.

The company is safer.

So the option to default is less valuable.

Makes sense.

Second, an increase in the volatility of the assets.

The put value rises.

This is the key one.

More volatility means more upside for shareholders and more downside for bondholders.

The option is more valuable.

Which highlights that conflict of interest between them.

It does.

Okay.

Third, an increase in the amount of debt.

That rises the put value.

The debt is the exercise price.

A higher exercise price always makes a put option more valuable.

Fourth, an increase in debt maturity.

Also rises the put value.

More time means more time for that volatility to work in the shareholders favor.

Okay, and the last one is a bit tricky.

An increase in the default free interest rate.

Right.

When interest rates go up, the present value of that fixed debt payment goes down.

That makes the liability seem cheaper today, which actually makes the option to walk away from it more attractive.

So the put value rises.

And we should quickly mention that paying out big dividends also makes the put more valuable, since it's cash leaving the firm that could have paid bondholders.

Yes, that's another important one.

And this whole option framework, it's not just for corporate bonds.

It's essential for valuing things like government guarantees.

Absolutely.

Think about the Pension Benefit Guarantee Corporation, the PBGC.

They insure private pensions.

Like they did with American Airlines when they went bankrupt.

The pension fund was billions short.

Exactly.

The PBGC stepped in.

And what they did financially was transform a risky corporate promise into a safe government -backed promise.

And to figure out the true cost of that guarantee,

you have to use option pricing.

You do.

The cost of the guarantee is the value of the safe guaranteed pension minus the value of the risky pension promise without the guarantee.

And that difference between a safe promise and a risky one.

It is, by definition, the value of the firm's option to default, the put option.

It's the only way to get a true economic cost of these massive government backstops.

Before we move on, let's just quickly tie this all together with equity.

We can use put call parity to look at this from the shareholders perspective.

Right.

We can flip the whole thing on its head.

The value of a company's equity is equivalent to the value of a call option on the company's assets, where the exercise price is the face value of the debt.

That's a great way to think about it.

The bondholders kind of own the company, but the shareholders have the right, the call option, to buy it back from them by paying off the debt.

It's a beautiful, coherent framework that links assets, debt, and equity all through the lens of option theory.

All right.

Let's bring this back to the real world.

How do investors and managers actually go about predicting default risk day to day?

The oldest and most common method is just looking at bond ratings.

From Moody's, S &P, Fitch.

These are qualitative judgments, but they're the bedrock of the market.

The system is pretty well known.

You have triple A at the top.

Anything rated B or higher is considered investment grade.

And that's a really important line.

A lot of big institutions like pension funds are only allowed to hold investment grade bonds.

And then below that line, you have high yield or junk bonds.

Junk funds.

They used to just be fallen angels.

Companies that were once strong, but fell on hard times.

But then in the 1980s, the market just exploded.

Right.

That's when companies started issuing jump bonds directly to finance these huge hostile takeovers.

A small company could suddenly raise billions of dollars to buy a massive one, leaving the new company with a staggering amount of debt.

And even though these ratings are qualitative, they line up really well with the actual financial number.

Oh, absolutely.

If you look at the data, A firms have huge operating margins.

They can cover their interest payments 14 times over and their debt ratios are low.

Compare that to the riskiest firms, the KAC rated ones.

Their margins are tiny.

They can barely cover their interest payments and their debt ratios are up in the 90s.

The ratings clearly reflect financial reality.

And most importantly, they predict defaults.

The data shows that for A bonds, defaults are basically zero.

But for those KSE bonds, about half of them default within 10 years.

So the rating is a powerful predictor.

But we have to add the big caveat.

The rating agencies can get it spectacularly wrong.

Enron is the classic case.

It was rated investment grade just a couple of months before it completely imploded.

And then, of course, there was the 2008 crisis where they gave AAA ratings to all those mortgage -backed securities that turned out to be toxic.

So because of those occasional failures, a lot of people turn to more quantitative tools, the first type being statistical models.

These are basically like the credit scores that banks use for consumers, right?

They crunch a board of numbers to spit out a single score.

That's the idea.

You look at companies that went bankrupt in the past and you find the financial ratios that were flashing red flags beforehand.

And the data shows clear patterns.

In the years leading up to bankruptcy, you see margins falling, debt levels rising, and liquidity just drying up.

The models are designed to capture all of those trends at once and combine them into one score to, as the textbook says, separate the credit -worthy sheep from the impecunious goats.

And the most famous model for this is the z -score model from Edward Altman.

He came up with a formula that weights five different financial ratios.

Right.

The formula is z equals 1 .2 times the first variable, plus 1 .4 times the second, and so on.

The weights show which factors Altman found to be most important.

Let's quickly break down the variables.

The first is working capital to total assets.

That's a liquidity measure.

The second is retained earnings to total assets.

That's a measure of cumulative profitability and maybe age.

The third one, EBIT to total assets, has the biggest weight by far.

3 .3.

That's a measure of core earning power.

And that makes perfect sense.

If the business isn't generating profits from its assets, nothing else really matters in the long run.

It's the engine of the whole thing.

Then you have the market value of equity to total liabilities, a market -based leverage measure, and finally sales to total assets, which is an efficiency ratio.

Altman's rule is simple.

A z -score below 1 .8 was a strong signal of impending bankruptcy.

It's a handy tool, but there's a big risk with these kinds of models, right?

A huge risk.

It's called data mining.

If you test enough variables, you'll eventually find a formula that perfectly explains all the bankruptcies in your historical data set just by pure chance.

And that formula might be useless for predicting future bankruptcies.

Exactly.

You've overfitted the model to the past.

It looks brilliant in backtesting, but it can fail spectacularly in the real world.

So you have to be really careful how much faith you put in these scores.

So that brings us to the third and final approach, which is the most grounded in theory,

structural models.

Right.

These models don't really rely on historical accounting ratios.

They go straight back to the option theory we just talked about.

The core idea being that shareholders will only default if the value of the company's assets falls below the value of its debt.

That's it.

And the most famous of these is the Merton model.

It's all about calculating the probability of that event happening.

Let's use the Epsilon Company example.

They have assets worth $100 and a simple zero -coupon bond with a face value of 60 due in a year.

So using the option pricing model, we can calculate everything.

The value of the risky debt comes out to $56 .87.

The equity is worth $43 .13.

It gives us a complete coherent balance sheet.

But the real goal is to get a probability of default out of this.

Right.

And the model can do that.

It uses the same math that's inside the Black Scholes formula to calculate the risk -neutral probability that the asset value will end up below that $60 debt threshold.

And for Epsilon, that probability comes out to 4 .3%.

It's a theoretically pure market -driven probability.

And the model is incredibly responsive.

If you increase Epsilon's debt from 60 to 70, the probability of default jumps all the way up to 11 .5%.

It directly links changes in the capital structure to changes in credit risk.

It does.

So these models are theoretically beautiful.

But what's the big practical challenge in using them?

The challenge is that you need to know the market value and the volatility of the company's total assets.

And you can't just look those numbers up on a screen.

You can see the stock price and its volatility, but not the whole asset base.

Exactly.

So you have to use the model to work backwards.

You use the equity value that you can see to try and infer what the unobservable asset value and volatility must be.

And that's a really complex estimation process.

So it's powerful, but not as straightforward as just calculating a Z score.

Not at all.

So to wrap this all up, let's just quickly recap the most important principles from this whole deep dive.

These are the key ideas that really change how you should think about corporate liabilities.

Okay.

Principle number one,

don't be fooled by high yields.

Because of limited liability, the expected yield you'll actually earn on a bond is always going to be lower than the advertised promised yield.

That big promise number is just there to compensate you for the risk of losing your principal.

Principle two, the yield spread is a price.

The spread over a government bond is effectively the annual premium you'd have to pay to ensure that bond against default.

And you can often see that price directly in the market through a credit default swap.

Principle three, limited liability is an option.

The risk in a corporate bond is fundamentally driven by the value of the shareholders default put.

Put their option to walk away.

And that option framework tells us exactly what drives risk.

Asset value,

volatility, leverage, and time.

And finally, principle four, there are three ways to predict.

You can estimate default risk qualitatively using bond ratings, or you can do it quantitatively using historical models like the Z score, or the more theoretically robust structural models that are built on option pricing.

Understanding all this really changes how you look at a company's balance sheet.

It's not just a set of promises.

It's a complex web of contingent risks and options that shifts value between bondholders and shareholders.

And that conflict, that tension between the two leads us to a final provocative thought for you to chew on.

We established that shareholders benefit when asset volatility goes up their equities like a call option.

We also know that higher volatility increases the risk to bondholders and makes the company's debt more expensive.

So what does this imply about the incentives of a manager whose job is to maximize shareholder value?

Why might the very actions that are best for shareholders taking on risky projects that increase volatility be the exact same actions that are worse for the company's bondholders?

It's a central conflict in corporate finance.

Food for thought indeed.

Thank you for taking this deep dive with us today.