International Finance

Session 3 — Securities Markets: Money Markets and Bonds

Laura Contreras-Portela

KEDGE Business School

October 2026

A small open economy, in two equations

Every market we open today sits inside one framework. A small open economy with perfect capital mobility, so the domestic rate is pinned to the world rate: i = i^{*}.

IS — the goods market, for a given i^{*}:

Y = C(Y-T) + I(i^{*}) + G + NX(e)

LM — the money market, for a given i^{*}:

M/P = L(i^{*}, Y)

The LM curve comes out vertical in (Y, e) space. Why?

e = foreign currency per unit of domestic currency.

Ten minutes on these three slides. Do not re-derive the model - put it up as the machinery we are going to use, and make them operate it.

Open with the claim, so they know why it is on the board:

Whether a government can do anything at all with monetary policy depends on one choice: fixed or floating. That is what this model tells you, and it is the reason half of today’s instruments exist.

Then put the question up and wait for an answer before you say anything.

[wait]

What you are listening for: the interest rate is fixed at the world rate. Look at the LM equation - if i^{*} is given and M/P is given, then there is only one level of Y that clears the money market. The exchange rate does not appear in it at all. So the curve is vertical.

Then say the consequence out loud, because everything on the next slide follows from it:

If LM is vertical, output is determined by the money market alone. Anything that shifts IS - government spending, taxes, a tariff - moves the exchange rate and leaves output exactly where it was.

What the model predicts

Fill it in. A fiscal expansion, a monetary expansion, an import restriction — what does each do to the exchange rate and to output, under floating and under fixed rates?

Policy	Floating: e	Floating: Y	Fixed: e	Fixed: Y
Fiscal expansion
Monetary expansion
Import restriction

Press C and draw the IS and LM shift for each row before writing the sign.

Which curve moves, and in which direction? Then read the answer off the diagram.

The answers, so you have them:

Floating. Fiscal expansion: IS shifts right, e appreciates, Y unchanged. Monetary expansion: LM shifts right, e depreciates, Y rises. Import restriction: IS shifts right, e appreciates, Y unchanged.

Fixed. Fiscal expansion: Y rises, e fixed by construction. Monetary expansion: powerless - the central bank has to sell reserves to hold the rate, which pulls the money supply straight back in. Import restriction: Y rises.

[pause]

Under floating rates monetary policy works and fiscal policy does not. Under fixed rates it is exactly the other way round. The exchange rate regime decides which instrument your government actually has.

The fixed-rate row, in one country

Thailand, 1997. The baht was fixed at $0.04 while the equilibrium rate had fallen to $0.02.

• To hold the rate the central bank must buy 300 million baht a month, paying in dollars from its reserves.
• That is the fixed-rate row of the table, happening: every intervention contracts the domestic money supply. Monetary policy is not available.
• When the reserves run out the choice is to float or to devalue. In July 1997 Thailand floated, and the baht halved overnight.

Axes: millions of baht per month horizontal, dollars per baht vertical.

Thailand promised to keep the baht at four cents. The market thought it was worth two. The promise costs money to keep.

[press C and draw it: supply and demand for baht, the two horizontal lines at four cents and two cents, and the gap between quantities at the fixed rate]

That distance is what the central bank is buying, every month, out of a finite pile of dollars.

[reveal the bullets one at a time]

This is the row we just filled in. Every time the central bank buys baht it is taking baht out of circulation - the money supply contracts whether it wants that or not. That is what “monetary policy is powerless under a fixed rate” looks like from the inside.

Notice what actually broke. Thai banks had borrowed in dollars, short, and lent in baht, long. Halve the baht and the debts double while the assets do not move. That mismatch - borrow short in one form, lend long in another - is the subject of today’s first market. Same structure, different costume.

Where we are

Sessions 1 and 2 established four prices and the balance-of-payments identity. We now disaggregate the financial system by instrument, and ask how each market transfers funds from surplus units to deficit units.

1. Money markets — short-term debt instruments
2. Bond markets — long-term debt instruments
3. Stock markets — ownership claims in firms

4. Mortgage markets — loans secured by real estate
5. Foreign exchange markets — trading of currencies
6. Derivatives markets — contracts whose value depends on an underlying asset

Each market is analysed through the same two questions: what contractual claim does the instrument represent, and what determines its price. These are the organising questions of the course, and of the examination.

Plus the reading discussion: Sartzetakis (2021) on green bonds.

In the first two sessions we built four prices and one accounting identity. Today we open the box. We stop asking what the exchange rate is, and start asking who issues the paper, who buys it, and what makes the price move.

There are six markets on this list. We do the first two today: money markets and bonds. Stocks, mortgages, currencies and derivatives are next session.

For every one of them I am going to ask you the same two questions. What is the claim? And what determines its price. Those two questions are the course. They are also the exam, so if you find yourself memorising definitions, stop, and go back to those two.

9 August 2007: a funding market stops

BNP Paribas suspended redemptions from three investment funds after liquidity disappeared from parts of the market for mortgage-related securities.

• Financial institutions often borrow short-term to finance longer-term assets. This is known as maturity transformation.
• When short-term debt matures, institutions must repay it or obtain new funding. Much of this short-term funding is obtained in money markets.
• This creates rollover risk: the risk that new funding is unavailable when existing debt matures.
• In 2007, access to short-term funding became increasingly difficult. Similar funding pressures later affected Northern Rock, Bear Stearns, and Lehman Brothers.

Why can a disruption in short-term funding threaten the stability of a financial institution?*

On 9 August 2007, BNP Paribas suspended withdrawals from three investment funds.

The funds held securities linked to US mortgages. Trading in these securities had largely stopped, making their market value difficult to determine.

But why does this matter for the money market?

Many financial institutions held long-term assets like these while relying on short-term borrowing to finance them.

When short-term debt matured, they had to borrow again. This is maturity transformation, and it creates rollover risk.

In 2007, lenders became increasingly worried about the value of mortgage-related assets and stopped providing short-term funding.

So a problem that began with mortgage-related assets became a money-market crisis: institutions could no longer rely on borrowing again when their debt matured.

This same vulnerability later played an important role in the crises of Northern Rock, Bear Stearns, and Lehman Brothers.

1 · Money markets

The corporate cash-timing problem

A firm receives EUR 40 million on the 25th of the month and disburses it on the 5th. For eleven days those funds must earn a return without being committed: the firm requires a liquid, short-dated, low-risk store of value.

• Receipts and disbursements are imperfectly synchronised — for corporations, for banks, and for governments alike.
• The money market exists to price that mismatch. It is a market for liquidity over short horizons, not for long-run investment returns.

Let me make this concrete. You work in treasury. Your company is paid forty million euros on the twenty-fifth of the month, and it pays that money out on the fifth of the next month.

So for eleven days you are sitting on forty million euros. You cannot leave it in a current account earning nothing. You cannot lock it away either, because you need it on the fifth.

[ask] What do you do with it?

You need something short, safe, and sellable. That is the money market. Eleven days at three percent on forty million is about thirty-six thousand euros. That is real money for doing nothing except not being careless.

And this is not only companies. Banks have the same problem. Governments have the same problem. Money comes in and goes out, and the two are never synchronised.

1 · What makes a money market instrument

• Short maturity — under one year, and typically under 120 days. This limits both interest-rate risk and the horizon over which credit quality can deteriorate.
• High liquidity — the instrument can be sold before maturity without a material price concession.
• Low default risk — issuers are sovereigns, large banks and highly rated corporations.
• Large denominations — USD 1 million and above. This is a wholesale market; households participate indirectly, through money market funds.

The four properties are not independent. Short maturity makes low default risk credible; low default risk and standardisation are what sustain a liquid secondary market. Both parties are managing a liquidity-timing problem rather than seeking a risk-adjusted return — which is why these instruments price close to the risk-free curve, and why small deviations from it are informative.

Four properties. They are examinable, and they are connected, so do not learn them as a list.

Short maturity. Under a year, usually under a hundred and twenty days. That matters for two reasons: rates cannot move far against you in three months, and a company’s credit cannot deteriorate far in three months either.

High liquidity. You can sell before maturity without dropping the price to find a buyer.

Low default risk. Look at who is borrowing here: governments, the largest banks, the best-rated companies.

Large denominations. A million dollars and up. None of you will ever buy one of these directly. You reach this market through a money market fund.

[pause]

Now the connection. Short maturity is why the low default risk is believable. And low default risk plus standardisation (unified legal framework) is why there is a liquid secondary market. Pull one property out and the others go with it.

And notice what nobody is doing here. Nobody buys commercial paper because they believe in the company. Both sides are solving a timing problem. That is why these instruments price so close to the risk-free rate — and why when they move away from it, that gap tells you something is wrong.

1 · The instruments

• Treasury bills
• Fed funds
• Repos
• CDs and CP
• BAs and eurodollars

• Zero-coupon obligations of the U.S. Treasury, 28 days to 12 months.
• Issued by auction. Competitive bids specify a price and may be rationed; noncompetitive bids accept the clearing price and are filled in full.
• They constitute the benchmark risk-free asset of the domestic market: every other short rate in this session is quoted relative to them.

• Uncollateralised loans of reserve balances between depository institutions, predominantly overnight.
• Banks use them to satisfy reserve requirements at the close of the maintenance period.
• The federal funds rate is the operating target of U.S. monetary policy, which makes it the anchor of the short end of the yield curve.

• A repurchase agreement is the sale of a security with a simultaneous commitment to repurchase it at a fixed price, typically within 3 to 14 days.
• Economically it is a collateralised loan; the repurchase price less the sale price is the interest. Legally it is a sale, which is why repo receives privileged treatment in bankruptcy.
• The lender applies a haircut — lending less than the collateral’s market value — as protection against a fall in that value.
• Unlike fed funds, non-bank institutions participate, which is what made the repo market both large and, in 2008, a channel for runs.

• Negotiable certificates of deposit: bank-issued time deposits, USD 100,000 to USD 10 million, transferable before maturity.
• Commercial paper: an unsecured promissory note issued by a corporation. Maturity is capped at 270 days because that is the limit of the exemption from SEC registration.
• Being unsecured, commercial paper is a direct claim on the issuer’s creditworthiness — the feature that matters in section 1’s charts.

• A banker’s acceptance is a time draft on which a commercial bank has substituted its own credit for the importer’s.
• This resolves a problem of asymmetric information in cross-border trade: the exporter is paid at once, bears no exchange-rate exposure, and need not evaluate a counterparty it cannot observe. The importer’s bank, which can observe it, performs that assessment.
• Eurodollars are dollar-denominated deposits held at banks outside the United States — a response to the dollar’s role as invoicing and settlement currency, not to any feature of U.S. regulation alone.

I am not going to read all five tabs. You have them in the handout. I want to spend the time on two.

Treasury bills first. Zero coupon, sold at auction, and they are the benchmark. Every other short rate you will see today is quoted relative to them.

[switch to the repo tab]

Now repos, because this is the one that matters.

A repo is a pawn shop for securities. I sell you my bonds today and I promise to buy them back on Thursday at a slightly higher price. That difference is the interest. Legally it is a sale. Economically it is a loan with collateral.

The lender does not lend the full value of the collateral. If the bonds are worth a hundred, they lend you ninety. That ten is called the haircut, and it protects the lender if the collateral falls in value.

[ask] So what happens to me if my lender wakes up one morning and decides the haircut should be thirty instead of ten?

That is the 2008 repo run in one question. Nobody has to refuse to lend. They only have to ask for more collateral.

One more thing before we move on. Commercial paper is unsecured — no collateral at all. Hold on to that word. We come back to it in two slides.

1 · The instruments side by side

Instrument	Issuer	Buyer	Usual maturity	Secondary market
Treasury bills	U.S. government	Consumers and companies	4, 13, 26 weeks	Excellent
Federal funds	Banks	Banks	1 to 7 days	None
Repurchase agreements	Businesses and banks	Businesses and banks	1 to 15 days	Good
Negotiable CDs	Large money-centre banks	Businesses	14 to 120 days	Good
Commercial paper	Finance companies and businesses	Businesses	1 to 270 days	Poor
Banker’s acceptance	Banks	Businesses	30 to 180 days	Good
Eurodollar deposits	Non-US banks	Businesses, governments, banks	1 day to 1 year	Poor

The final column is a ranking of secondary-market liquidity. Adapted from Mishkin, F.S. and Eakins, S.G., Financial Markets and Institutions.

Do not write this down, it is in the handout. Take thirty seconds and read the last column.

[wait]

[ask] Why does that column vary so much? Treasury bills are excellent, commercial paper is poor. Same kind of instrument, same kind of maturity.

The answer is standardisation. One Treasury bill is identical to another, so anyone will buy yours. Commercial paper is a specific claim, on one company, for one maturity — there is no queue of buyers for that. And fed funds are unsecured overnight loans between two named banks. There is nothing to sell.

Liquidity is not a property of the paper. It is a property of how many people want the same thing you are holding.

1 · The rates move together

The series co-move closely because they share a common policy anchor. Under what conditions does the spread between the federal funds rate and the Treasury bill rate widen, and what is that spread measuring?

Three rates here: Treasury bills, federal funds, the prime rate.

[ask] What do you notice?

They move together. All three are anchored to the same policy rate, so most of the time they are on top of each other.

[pause]

Which makes the interesting question the opposite one. What does it mean when they come apart?

The federal funds rate is banks lending to each other, unsecured. The Treasury bill is lending to the government. When the gap between those two widens, it is telling you that banks have stopped trusting each other.

In a normal month that gap is a few basis points. In September 2008 it went past three hundred. Same chart, same two rates — and that spread was the clearest real-time measure we had of the panic.

1 · Commercial paper outstanding

2007 marks a structural break, not a cyclical decline: the series steps down and does not recover its prior level. Which class of issuer exited the market, why could it not return, and what replaced that funding?

Look at this one before I say anything.

[wait]

[ask] What happened in 2007?

I want you to notice that this is not a recession dip. The line does not fall and recover. It steps down and stays down. Twenty years later it has never returned to the old level.

So who left? The issuers who disappeared were the ones funding long-term assets with thirty-day paper — structured investment vehicles, the finance arms of banks. When the paper stopped rolling over, they had two options: sell the assets, or hand them back to the bank that sponsored them. Both happened, and both made things worse.

This is the same chart as the BNP Paribas story we opened with. That is what it looks like in the data.

1 · Price and rate

Money market instruments are zero-coupon: they are purchased below face value and redeemed at face value, so the entire return is the discount. Two conventions are used to express it, and they are not interchangeable.

The discount rate — how far below face value you paid:

i_{discount} = \frac{F-P}{F} \times \frac{360}{n}

The annualised yield — what you actually earned:

i_{yt} = \frac{F-P}{P} \times \frac{365}{n}

One instrument, two measures. The bank discount basis deflates by face value F on a 360-day year — a convention inherited from pre-computational market practice. The annualised yield deflates by the price actually paid, P, on a 365-day year, and is therefore the true holding-period return expressed annually. Since P < F, the yield always exceeds the discount rate. Only the yield is comparable across instruments.

These instruments pay no coupon. You buy at ninety-eight, you get a hundred at maturity, and the whole return is that gap. So there is no interest rate to quote — there is only a discount, and we have to turn it into a rate.

The market does that two ways, and they do not give the same number.

The first one, the discount rate, divides by F — the face value, what you get at the end — and uses a three-hundred-and-sixty-day year.

The second one, the annualised yield, divides by P — what you actually paid — and uses three hundred and sixty-five days.

[pause]

Three hundred and sixty is not a mistake. It is a convention from before calculators, when twelve months of thirty days made the arithmetic possible by hand. We are still using it.

Now: P is always smaller than F. So dividing by P always gives you the bigger number. The yield is always higher than the discount rate on the same instrument.

[ask] If you were selling me this bill, which of the two would you quote?

Only the yield can be compared with a deposit rate or a bond yield. If you take one thing from this slide, take that.

1 · The two rates, drawn

Same two formulas, drawn. Face value a hundred, ninety days.

The only thing to see is that the two lines pull apart as the price falls. When there is almost no discount they agree. The bigger the discount, the more the choice of denominator matters.

Thirty seconds on this slide and we move on.

1 · Problem 2.1

A 28-day T-bill costs $996.73 and is worth $1,000 at maturity.

1. What is the discount rate?
2. What is the annualised yield?

Calculators out. This is the kind of question that appears on the exam.

Twenty-eight day bill, you pay nine hundred and ninety-six seventy-three, you get a thousand.

[give them two minutes, then reveal]

Discount rate, four point two zero percent. Yield, four point two eight.

[pause]

Eight basis points apart. And everybody in the room would describe both of those as “the rate on this bill”. On a hundred million euros, eight basis points is eighty thousand a year. This is why the convention matters.

Worked. Discount rate: (1000 - 996.73) / 1000 x 360/28 = 4.20%. Yield: (1000 - 996.73) / 996.73 x 365/28 = 4.28%.

1 · Problem 2.2

The Treasury auctions $2.5 billion of 91-day bills. Competitive bids:

Bidder	Bid amount	Bid price
1	$500 million	$0.9940
2	$750 million	$0.9901
3	$1.5 billion	$0.9925
4	$1 billion	$0.9936
5	$600 million	$0.9939

It also received $750 million of noncompetitive bids.

Who receives bills, how many, and at what price?

This one is an auction. Two and a half billion of ninety-one day bills, five competitive bidders, and seven hundred and fifty million of noncompetitive bids.

Remember the rule from the Treasury bills tab: noncompetitive bidders take whatever price comes out, and they are always filled.

[ask] So where do we start?

Noncompetitive comes off the top. Two and a half minus zero point seven five leaves one point seven five billion for the competitive bidders.

Now sort them by price, highest first — the highest price is the lowest interest rate, so that is the cheapest money for the Treasury. Bidder one at nine nine four zero. Bidder five. Bidder four. Bidder three.

Work down until the one point seven five billion is gone. Bidder three only gets part of what they asked for, and bidder two gets nothing at all.

[ask] Bidder two bid nine nine zero one. What did they get wrong?

2 · The bond market

Athens, March 2012

In March 2012, Greece restructured around €200 billion of government debt. Private investors accepted losses of roughly 53% of face value. Only a few years earlier, Greek government bonds had been rated investment grade.

• A bond is a contract: the issuer promises specific payments on specific dates.
• But promised payments are not guaranteed. The issuer may be unable or unwilling to pay.
• This possibility is credit risk — and investors require compensation for bearing it.
• Sovereign bonds have an additional complication: enforcing claims against a government can be particularly difficult.

March 2012. Greece restructures around two hundred billion euros of government debt. Private investors accept losses of roughly fifty-three percent of the face value of their bonds.

And only a few years earlier, Greek government bonds had been considered investment grade.

[pause]

This gives us the first important idea about bonds. A bond is a contract. When you buy one, the issuer promises to make certain payments at certain dates. But a promise is not a guarantee. If the issuer gets into financial trouble, you may not receive everything that was originally promised. That possibility is what we call credit risk.

And investors will care about that risk when deciding how much they are willing to pay for a bond.

[ask] So if two bonds promise exactly the same €100 payment one year from now, but one issuer is much more likely to default, would you pay the same price for both?

Probably not.

And that difference is going to be central to how we understand bond prices and yields.

2 · The vocabulary

Term	What it means
Coupon interest rate	The annual interest rate, usually fixed for the whole life
Current yield	Coupon payment divided by the current price
Face amount / par value	The maturity value
Indenture	The contract that specifies the terms of the loan agreement
Market rate	The rate currently in effect on securities of like risk and maturity
Maturity	Number of periods until the security matures
Yield to maturity	The yield if you buy at the current price and hold to maturity

The coupon rate is fixed in the indenture at issue. The market rate on comparable risk and maturity varies continuously. If the contractual payments cannot adjust, the only variable that can reconcile the two is the price. The whole of bond valuation follows from that single observation.

Take a minute to read this. It is all in the handout.

[wait, take questions]

I only want to insist on one line of it.

The coupon rate is written into the indenture on the day the bond is issued, and it never changes. The market rate — what investors currently demand for this much risk and this much time — changes every day.

[ask] So if the payments cannot move, and what people demand has gone up, what is left to adjust?

The price. That is it. That is the whole of bond valuation, and you just said it yourselves.

One warning. Current yield and yield to maturity are not the same thing, and telling me they are is the single most common way to lose marks on this part of the exam. We come back to it in three slides.

2 · The instruments

• Treasuries
• Municipals
• Corporates
• Ratings

• Treasury notes: 1 to 10 years. Treasury bonds: 10 to 30 years.
• Nominal default risk is negligible because the obligation is denominated in a currency the issuer creates. That is a statement about nominal default only.
• Two risks remain and are examinable: inflation risk, which erodes the real value of fixed payments, and interest-rate risk, the capital loss on an existing bond when market rates rise. The latter increases with maturity.

• Issued by local, county and state governments to fund public projects.

• Tax free, which is the whole point. Compare like with like:

  \text{after-tax rate} = \text{taxable rate}\times(1-\text{marginal tax rate})

• General obligation bonds are repaid from taxes; revenue bonds from user fees on the project itself.

• They are not default free. Detroit, 2013.

• Face value usually USD 1,000, interest paid semi-annually.
• Restrictive covenants limit dividends, new debt, ratios — they exist because shareholder and bondholder interests conflict.
• A call provision lets the issuer buy the bond back. A conversion feature lets the holder turn it into equity.
• Secured bondholders have first claim on a specific asset; unsecured ones do not, and charge more for it.

• Agencies map credit risk onto an ordinal scale from Aaa/AAA downwards. Below Baa3/BBB- an issue is speculative grade.
• That threshold has effects beyond information. Many institutional mandates — insurers, pension funds, some trusts — prohibit holdings below it, so a one-notch downgrade can compel sales by investors with no independent view of the credit.
• The result is forced selling into a falling market: a price movement caused by mandate design rather than by fundamentals.
• Note also the issuer-pays model: the entity being rated selects and remunerates the agency. The conflict of interest this creates is central to the post-2008 literature on structured credit.

Four tabs. I want two of them.

[municipals tab]

Municipal bonds are issued by cities and states, and the interest is tax free. That is the whole point of them, and it means you cannot compare them with a corporate bond directly.

To compare, you take the corporate rate and multiply by one minus your marginal tax rate. That gives you what you actually keep. We do this as a problem in a few slides, so make a note of the formula.

And they are not safe. Detroit filed for bankruptcy in 2013 — the pensioners and the bondholders were standing in the same queue.

[ratings tab]

Now ratings, and this is the one I want you to remember.

Below BBB minus, a bond stops being investment grade and becomes speculative. Junk, if you want the market word.

Here is why that line does more than describe risk. A lot of institutions — insurers, pension funds — are simply not allowed to hold anything below it. It is written into their mandate.

[ask] So what happens to the price when a bond is downgraded from BBB minus to BB plus?

It falls — and it falls because people who have no opinion at all about the company are forced to sell it. That is forced selling, and it is a price move caused by regulation, not by anything the company did.

One last thing. Who pays the rating agency? The company being rated chooses the agency and pays the fee. Sit with that for a second. That conflict of interest is at the centre of everything written about structured credit after 2008.

2 · The rating scales

Moody’s	S&P	Fitch	Meaning
Aaa	AAA	AAA	Best quality, least credit risk
Aa1-Aa3	AA+/AA/AA-	AA+/AA/AA-	High quality, very strong capacity
A1-A3	A+/A/A-	A+/A/A-	Upper-medium grade
Baa1-Baa3	BBB+/BBB/BBB-	BBB+/BBB/BBB-	Medium quality, adequate capacity

Moody’s	S&P	Fitch	Meaning
Ba1-Ba3	BB+/BB/BB-	BB+/BB/BB-	Speculative
B1-B3	B+/B/B-	B+/B/B-	Very speculative
Caa-C	CCC/CC/C	CCC/CC/C	Highly speculative, near or in default
—	D	DDD/DD/D	In default

A bond is downgraded just one step, from BBB− to BB+. The change in credit risk may be small. But BB+ is no longer investment grade.

Why might this small downgrade cause a large fall in the bond’s price?

You do not need to memorise this ladder. You need to know where one line is.

It is between Baa3 and Ba1 — investment grade above, speculative below.

[ask] Credit quality is continuous. A company does not become a different company overnight. So why should one notch produce a jump in the price?

[wait]

Some institutional investors can only hold investment-grade bonds → they sell → price falls. The mandates.

A pension fund that is prohibited from holding speculative grade has to sell, whatever it thinks about the credit. Everybody in that position sells at the same time, and there is no natural buyer on the other side.

The market has a name for a bond that crosses that line: a fallen angel. Worth knowing.

2 · Rates by credit quality

Credit ratings summarize differences in credit risk.

If investors think a bond is more likely to default, they will only hold it if it offers a higher yield.

[ ]

So how large is this difference in practice?

Why does the gap between corporate and Treasury yields become much larger during recessions?

We have just seen that ratings summarize credit quality.

Now let’s see what that means for the interest rate a borrower actually pays.

If I lend to the US government, the probability of not being repaid is very low.

If I lend to a company, I take additional credit risk. And I am not going to take that additional risk for free. I want a higher return.

That difference is the credit spread.

[point to lines]

Aaa firms are considered very safe, so their yields are relatively close to Treasuries.

Baa firms are riskier, so investors demand a higher yield.

So far, this is exactly what we would expect from the ratings we just discussed.

But now look at what happens during recessions.

[point at 2008, then 2020]

The gap becomes much larger.

Why?

Two things happen at the same time.

First, firms genuinely become riskier: profits fall and the probability of default increases.

Second, investors become less willing to hold risky assets, so they demand more compensation for taking risk.

Both effects increase credit spreads.

And notice the timing: borrowing becomes most expensive precisely when firms are struggling and may need external finance the most.

This is one sense in which credit conditions are procyclical: they are easier in good times and tighter in bad times.

2 · The price of a bond

A bond is worth today the present value of the payments it promises in the future.

For a bond paying coupon C each year and face value F at maturity:

P = \frac{C}{1+r} + \frac{C}{(1+r)^2} + \dots + \frac{C+F}{(1+r)^n}

where r is the return investors currently require for a bond with similar risk and maturity.

When the required yield rises, the bond price falls:

r \uparrow \quad \Longrightarrow \quad P \downarrow

The bond’s promised payments have not changed. What changes is the price investors are willing to pay for them today.

We know what a bond promises: coupons over time and the face value at maturity.

Now we need to answer a different question:

[ask] How much would you pay today for those future payments?

Suppose a bond will pay me 100 euros one year from now.

I would not normally pay 100 euros for it today. Why?

Because I could invest my money somewhere else and earn a return.

So I need to discount that future payment.

For a bond, we do exactly the same thing with every payment.

Each coupon is discounted back to today, and in the final year we also receive the face value.

Add all those present values together, and we have the price of the bond.

[pause]

Now look at r.

This is the return investors require to hold this bond.

Remember what we just saw with credit risk: if investors perceive more risk, they require a higher return.

So what happens to the price when r increases?

[ask] Look at the formula. If the denominators become larger, what happens to the present value?

It falls.

So:

yield up, price down.

And importantly, nothing about the bond’s promised payments had to change.

The coupons are the same. The face value is the same.

Investors are simply willing to pay less today for those same future payments because they now require a higher return.

2 · Two ways of quoting the return

The yield to maturity is the internal rate of return r that equates the present value of the contractual payments to the observed market price:

0 = -P + \sum_{t=1}^{n}\frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}

The current (coupon) yield ignores any capital gain or loss at redemption:

r_c = \frac{C}{P}

Two assumptions are embedded in the yield to maturity: that the bond is held to maturity, and that every coupon is reinvested at r. Neither holds in general, which is why realised returns differ from quoted yields.

The yield to maturity is the discount rate that makes the price you see and the payments you expect balance exactly. It is an internal rate of return.

Be honest with yourselves about this equation: you cannot solve it for r by rearranging. Beyond two periods there is no formula. In the exam I will give you either a short maturity or a calculator. In a bank, software does it.

[pause]

The current yield underneath is a shortcut. Coupon divided by price. It ignores what happens at redemption entirely.

[ask] Suppose I buy a bond for eighty and it repays a hundred at maturity. Does the current yield capture that extra twenty?

No. That is why it is only an approximation, and the next slide shows you how wrong it gets.

One more thing, and this is the part people skip. The yield to maturity assumes two things. That you hold the bond to the end. And that you reinvest every single coupon at that same rate r.

[ask] What if rates fall after you buy?

Then you are reinvesting those coupons at less than r, and what you actually earn is below the yield you were quoted. That is reinvestment risk. It is the mirror image of the price risk we just talked about — when rates fall your price goes up, but your reinvestment gets worse.

2 · Coupon yield is only an approximation

Blue is the true yield to maturity. Red is the current yield shortcut.

Notice they only touch in one place. At a price of a hundred — at par.

[ask] Look to the left of par, where the bond is cheap. Which line is higher, and why?

The true yield is higher, because if you buy at eighty and get a hundred back, there is a capital gain the current yield is not counting.

[ask] And to the right of par?

The other way round. You paid a hundred and twenty, you get a hundred back, and there is a capital loss the current yield is ignoring.

So the shortcut is not just imprecise. It is wrong in a direction you can predict. Below par it flatters the bond. Above par it flatters it too.

2 · Problem 2.3

1. A corporate bond yields 9%, a municipal bond 6.75%. Which do you buy?
2. A corporate bond yields 5%, a municipal 3.5%, and your marginal tax rate is 28%. Which now?

Two parts. Read the first one.

[wait — let someone attempt an answer]

Nine percent against six seventy-five. Most of you will say the corporate, and I want to push back on that.

[ask] What do you need to know before you can answer at all?

The tax rate. Without it the question has no answer. The municipal is tax free and the corporate is not, so you are comparing two numbers that are not comparable. That is the lesson of part one — notice when a question is missing something.

If you put the tax rate at twenty-five percent, nine times zero point seven five is six seventy-five. Exactly the municipal. Above twenty-five percent, the municipal wins. Worked: 9% x 0.75 = 6.75%.

Part two gives you the rate. Five percent, twenty-eight percent tax. Five times zero point seven two is three point six zero, against three point five tax free. The corporate wins — but only by ten basis points. Worked: 5% x (1 - 0.28) = 3.60%, against 3.5% tax-free.

2 · Problem 2.4

1. What is the coupon yield on a bond with face value $1,000, current price $921.01 and a coupon rate of 10.95%?
2. What is the price of a two-year, 10% coupon bond paying semi-annually, face value $1,000, if the required return is 12%?

Part one is straightforward. The coupon is ten point nine five percent of a thousand, so a hundred and nine fifty a year. Divide by the price of nine twenty-one. Eleven point eight nine percent.

Part two is where people lose marks, so go slowly.

[ask] Semi-annual coupons. What has to change in the formula?

Three things, and you need all three. Halve the coupon — fifty, not a hundred. Halve the rate — six percent per period, not twelve. And double the number of periods — four, not two.

Most people remember one of the three. Some remember two. Three changes.

The answer is nine sixty-five thirty-five. The bond trades below par, and it should — the coupon is ten percent and the market wants twelve.

Worked. Coupon yield: 109.50 / 921.01 = 11.89%. Price: four periods, coupon 50, 6% per period - sum of 50 / 1.06^t for t = 1 to 4, plus 1000 / 1.06^4 = 965.35.

Next session

Session 4 finishes securities markets: stocks, mortgages, foreign exchange and derivatives, then the green bonds discussion.

Bring Sartzetakis (2021) on green bonds, read — and the security your group wants to analyse. Not “a stock”. A specific one, with a ticker.

Press O for the slide overview · C to draw · S for speaker notes · F for fullscreen · E then print for a PDF of the slides.

That is money markets and bonds. Next session we finish securities markets: stocks, mortgages, foreign exchange and derivatives, and then we discuss the green bonds paper.

Two things to bring.

First, read Sartzetakis. Read it before the session, not after — the discussion is part of what I assess, and it does not work if I am the only one who has read it.

Second, your group’s security. Not “a stock”. A specific one, with a ticker, that you can find real data on. Choose it now. Every year somebody chooses in the week before the presentation and it shows.