FINANCIAL MARKETS AND INSTITUTIONS:
Why do we need a financial sector? Is finance good for the economy?
One aspect of finance is that it has the role to increase efficiency in an economy, while a negative
aspect is that we narrow it down so much to numbers, that we don’t consider anymore society and
its surroundings (too narrow focus while you have several externalities such as social, planet,
animal, plants…).
We can therefore say that in general finance is good for the economy, so that the main idea around
finance is to move dollars from those who lack productive investment opportunities to those who
have them. In the economy funds are not distributed equally:
- Some have surpluses (lender – savers)
- Others have shortages (borrower – spenders)
The function of the financial sector is therefore to channel funds from the first group to the second
one→ efficient use of capital.
Corporation tax:
Also due to the many crises and problems of these times, such as covid, governments worldwide
have been giving trillions of dollars in financial aid to firms and workers, but where do
governments get all this money? By raising taxes, but when this is not enough others would borrow
to them. But how can a government borrow money? And who can lend so much money?
What is an asset?
We can define a real asset as an entity producing flow of goods or services, such as land,
machinery, people, goodwill, reputation, brand… (distinction between tangible and intangible).
Financial asset instead is a contract giving its owner a claim to payments such as currency, bonds,
stocks, deposits, loans and insurance contracts.
Typically, borrowers sell or issue financial assets to lenders and use the proceeds to buy real assets
(an investment).
Who are involved? We have two main relations:
- Lenders-savers: households, business firms, government and foreigners
- Borrower-spenders: business firms, government, households and foreigners
We can divide financial markets in two main
categories:
1. Direct finance→ borrowers borrow directly
from lenders in financial markets by selling
financial assets (claims on borrower’s future
income or real assets).
2. Indirect finance→ borrowers borrow
indirectly from lenders via financial
intermediaries (established to source both
loanable funds and loan opportunities) by
issuing financial assets.
(The arrows show that funds flow from lendersavers to borrower-spenders via two routes: direct finance, in which borrowers borrow funds
directly from financial markets by selling securities, and indirect finance, in which a financial
intermediary borrows funds from lender-savers and then uses these funds to make loans to
borrowers-spenders.
Structure of direct financial markets:
It helps to define financial markets along a variety of dimensions, as there are many dimensions
depending on: type of securities, type of issuance market/transacting party or by maturity.
We have financial markets securities:
- Debt (bond markets): issued by companies and governments and provide key macro
variable, interest rates.
- Equity (stock) markets: represents an ownership claim in the firm, it can pay dividends.
- Derivatives (options, swaps, futures…): financial instruments that depend on other assets.
We also have two types of issuance markets:
1. Primary market→ new securities are sold to initial buyers, such as investment bank which
arranges sales of securities, or treasury which issues government bonds (almost never hear
about them, apart from when very big private companies turn public, or when government
have problems placing security).
2. Secondary market→ security previously issued are bought and sold.
Function of financial intermediaries, indirect finance:
Instead of savers lending/investing directly with borrowers, a financial intermediary (FI), such as
a bank, acts as the middleman, where the intermediary obtain funds from savers and the
intermediary then makes loans/investments.
Interest rates and valuation:
Debt instruments differ by: streams of cash payments (cash flows) and timing, the evaluation of
amounts at different points in time is called present value analysis and all calculations are of this
𝑠𝑡𝑟𝑒𝑎𝑚 𝑜𝑓 𝑓𝑢𝑡𝑢𝑟𝑒 𝑐𝑎𝑠ℎ𝑓𝑙𝑜𝑤𝑠
kind: 𝑃𝑉 = 𝑓(
).
1+𝑖
In previous formula we call the yield to maturity, if the price of the security is equal to the present
value of its future cash flows, if the YTM is the interest rate that makes the PV of a debt instrument
equal to its value price today. 𝑖 ≠ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛
In most finance applications 𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑦 ′ 𝑠𝑝𝑟𝑖𝑐𝑒 = 𝑃𝑉(𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑠), and the fact that 𝑃 = 𝑃𝑉 is
true under certain assumption on investors’ rationality and efficiency of financial markets.
There are two basic types of debt instruments which incorporate present value concepts:
1. Loans
2. Bonds (which can be divided in coupon bonds and discount bonds)
→ a coupon bond is a bond that makes a fixed payment (coupon) at specific dates plus a final
amount (face or par value) at maturity. The amount it pays every year is expressed as a percentage
of face value. For example, a 10% coupon bond with a face value of $1,000 and 10 years to
maturity will have a cash flow of $100 each year plus a payment of 1,000 at the end.
The price today of a coupon bond is the present value of its future cash flows, where is the coupon
payment, is the face value and the years to maturity and we can say that:
- If 𝑃 = 𝐹𝑉 → par bond
- If 𝑃 < 𝐹𝑉 → at discount
- If 𝑃 > 𝐹𝑉 → at premium
A special case is perpetuity, which is a coupon bond providing a coupon forever with no maturity
date. It is convenient because it is easy to calculate its price. The perpetuity allows us to introduce
the concept of current yield, which is a useful approximation to the YTM for long term bonds,
with price near par.
𝑐𝑜𝑢𝑝𝑜𝑛
𝑐𝑜𝑢𝑝𝑜𝑛
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑖𝑒𝑙𝑑 =
𝑐𝑜𝑢𝑝𝑜𝑛 𝑟𝑎𝑡𝑒 =
𝑝𝑟𝑖𝑐𝑒
𝑓𝑎𝑐𝑒 𝑣𝑎𝑙𝑢𝑒
(For a par bond the two coincide).
→ a discount bond does not give any coupon (zero- coupon) but only the face value at the end. It
normally sells at a price below the face value (at discount), such as the US T-bills, and the YTM.
For a zero-coupon bond with 1 year maturity is easy to calculate.
So, is it more important the YTM or the price?
Mathematically, it doesn’t matter, given one, the other one is determined via the PV formula, but
economically we think of the YTM determining the price, not vice versa. In fact, you should think
of the YTM as the fair return an investor requires considering the risk. Then the investors will
price the bonds so that in equilibrium they get this fair return.
(If 𝑖 increases, the PV of any cash flow is lower, hence, the price of the bond must be lower).
The YTM is greater than the coupon rate when bond price is below par value, and this means that
if the required yield on the bond is more than what the bond actually pays, then it needs to sell at
discount to attract investors, because investors can make a larger return in the market, they need
an extra incentive to invest in the bond.
The real interest rate (𝑖𝑟), is the nominal interest rate (𝑖) adjusted for expected inflation.
𝑖𝑟 = 𝑖 − 𝜋 𝑒
When the real rate is low, there are greater incentives to borrow and less to lend, this phenomenon
is known as deflation, which is a big problem because the real rate will always be positive.
𝐶 + 𝑃𝑡 + 1 − 𝑃𝑡
𝐶
𝑃𝑡 + 1 − 𝑃𝑡
𝑟𝑒𝑡𝑢𝑟𝑛 =
= 𝑖𝑐 + 𝑔 → 𝑖𝑐 =
→𝑔=
− 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛𝑠
𝑃𝑡
𝑃𝑡
𝑃𝑡
For bonds with maturity greater than holding
period, we have an increase in 𝑖 and a decrease in
𝑃, implying therefore capital loss. The longer the
maturity, the greater the price change for any.
Only bond whose return is equal to yield has
maturity equal to holding period. Bond with high
initial interest rate can have negative return if we
have an increase in 𝑖.
Prices are more volatile for long term bonds, and the risk of losing money, if interest rate change
is called interest rate risk (IRR), it come from the fact that the bonds may be sold before maturity,
in that case you don’t know what the interest rate will be in the future. (Close related risk =
reinvestment risk).
Summary:
- For bonds with maturity > holding period, i  P  implying capital loss
- The longer the maturity, the greater the price change for any ∆𝑖
-
Only bond whose return = yield has maturity = holding period
Bond with high initial interest rate can have negative return if i 
Interest rate risk:
Prices are more volatile for long term bonds, in fact for the same ∆𝑖 ↑, ∆𝑃 is more negative for
long term bonds. The risk of losing money (∆𝑃 < 0) if interest rates change is called interest rate
risk (IRR). It comes from the fact that you may want to sell your bonds before maturity. In that
case, you don’t know what the interest rate will be in the future.
Duration→ it is the weighted average of the maturities of the cash payments, it’s like an effective
maturity, and it is useful because it allows to quantify the IRR, and the longer the duration, the
bigger the IRR.
(Consider that it makes sense to define the duration of a zero-coupon bond equal to its maturity
then).
𝑛
𝐶𝑃𝑡
𝐷𝑈𝑅 = ∑ 𝑡
(1 + 𝑖)𝑡
𝑡=1
Where t is the discount bond duration and where 𝐶𝑃𝑡 = 𝐶 𝑓𝑜𝑟 𝑡 < 𝑛; 𝐶𝑃𝑡 = 𝐶 + 𝐹𝑉 𝑓𝑜𝑟 𝑡 = 𝑛
Based on the intuition that the effective maturity of coupon bonds is a weighted average of
effective maturities on discount bonds. Each coupon payment is like a discount bond, and the
weights are equal to the proportion of the total value represented by each discount bond.
Key facts about duration, it increases if:
1. Maturity increases
𝐶
2. 𝐶𝑃 = 𝐹𝑉 (coupon rate) decreases, zero coupon bonds have max duration equal to maturity
3. Interest rate decreases, so sensitivity to changes in rates diminishes as rates rises.
→ the IRR is given by the price change of a coupon bond if 𝑖 changes. With the duration we can
approximate the % price change (for small changes in interest rate) with:
∆𝑖
%∆𝑃 ≈ −𝐷𝑈𝑅 ∙
1+𝑖
The greater the duration of a security, the greater the percentage change in the market value of the
security for a given change in interest rates. Therefore, the greater the duration of a security, the
greater its interest rate risk. The duration is not quite the same as the IRR, but it measures its
intensity.
Duration is additive, hence the duration of a portfolio of securities is the weighted average of the
durations of the individual securities, with the weights equaling the proportion of the portfolio
invested in each security.
Determinants of financial asset demand:
1. Wealth: the total resources owned by the individual (house, car…), and it differs from the
income as it’s a stock variable, not a flow.
2. Expected return: on one asset relative to alternative assets.
3. Risk: uncertainty on asset return, on one asset relative to alternative assets.
4. Liquidity: the ease and speed with which an asset can be turned into cash, relative to
alternative assets.
→ wealth has a positive effect on the demand of financial assets, and it is quite obvious as financial
assets are normal goods, so by holding everything else constant, an increase in wealth increases
the demand of an asset.
→ expected return is the average return across all states of nature. 𝐸(𝑅) = ∑𝑁
𝑖=1 𝑝𝑖 ∙ 𝑅𝑖 , where Ri,
is the return in state 𝑅𝑖 and 𝑝𝑖 is the probability of state 𝑖 occurring.
Nice thing about expected returns is that their additive, the expected return of a portfolio p of two
stocks A and B is the sum of the expected returns of the two stocks:
𝐸(𝑅𝑝𝑜𝑟𝑡) = 𝐸(𝑅𝑎 + 𝑅𝑏) = 𝐸(𝑅𝑎) + 𝐸(𝑅𝑏)
Holding everything else constant, an increase in the expected return increases the demand of an
asset. Note that the ceteris paribus condition is key: you may very well prefer an asset with lower
expected return, but lower risk. Often, high expected returns assets also have high risk.
→ risk is measured as the standard deviation of an asset return:
𝑁
𝜎(𝑅) = √∑ 𝑝𝑖 ∙ (𝑅𝑖 − 𝐸(𝑅))
2
𝑖=1
A risk averse person prefers a sure thing stock rather than a riskier asset, even though the stocks
have the same expected return, 8%. We assume that people are risk averse, especially in their
financial decisions. A risk averse individual prefers the asset with the lower standard deviation.
Therefore, holding everything else constant, an increase in risk decreases the demand of an asset.
→ liquidity: ease and speed with which an asset is turn
into cash. Needs many buyers and sellers and active
trades. A house in general is an illiquid asset
compared to securities, therefore holding everything
else constant, an increase in liquidity increases the
demand on an asset.
Supply and demand in the bond market:
Determination of interest rates happen through demand and supply. Corporate bonds are different
from government bonds or mortgages, as they all have different interest rates. However, because
rates tend to move together, we will proceed as if there is one interest rate for the entire economy.
𝐹𝑉 − 𝑃
𝑖 = 𝑅𝑒 =
𝑃
The derivation follows the same ideas as the demand curve, more bonds will be offered if the
expected return (cost for the issuer) is lower.
Market equilibrium instead occurs when the amount that people are willing to buy equals the
amount that people are willing to sell at a given price. Excess supply and excess demand are only
temporary conditions in a competitive market. Market forces will tend to equate quantities
demanded and supplied at the equilibrium price/interest rate.
We now turn our attention to shifts in demand and supply. Then, we are going to put them together
to derive equilibrium interest rates (movements along the curves will be due to price changes alone,
if anything else not on the axes changes, it’s a shift of either or both curves).
Shift in demand can be caused by:
- Wealth
- Expected future interest rate
- Riskiness
- Expected future inflation
- Liquidity
Shift in supply can be caused by:
- Profitability of investments (productivity)
- Expected future inflation
- Government deficit
Negative interest rates: why would anyone ever buy a government bond with negative yield? Due
to safety and makes sense if inflation is low and other investment opportunities are scarce.
The money market:
We call it money market, but money is not actually traded, and the securities in money markets
are short term with high liquidity so are close to being money. (During the financial crisis of 2008
many money markets instruments lost their liquidity, and this created the panic).
The most important characteristics of the money market are that are usually sold in large
denominations, low default risk and original maturity of one year or less (although vast majority
matures in less than 120 days).
→ original maturity differs from residual maturity, a 3year bond with 2 months left to maturity (residual
maturity), is not a money market instrument.
The main purpose of money markets is:
- For the lenders/buyers: warehouse surplus funds for
short periods of time, they do not care about the return,
but about the liquidity (act quickly if other investments
become available).
- For borrowers/sellers: low-cost source of temporary
funds, not for large capital projects with high return.
Cash management, the timing of cash inflows and
outflows are not well synchronized.
There are many moneys market instruments such as treasury bills, federal funds, repurchase
agreements, negotiable certificates of deposit, commercial paper and Eurodollars.
T bills have 4-, 13-, 26- and 52-week maturities, T bills are discount bonds and one of the most
liquid financial markets, therefore discounting is common to S-T securities because there is little
time to collect coupons.
T bills are auctioned to the primary dealers (23 banks), example of primary markets, treasury
announces how many and what kind of T bills are.
In a competitive bid, dealers put in quantity and price. The bids are accepted in ascending order of
yield until offering amount is reached (treasury will then sell T bills at the highest yield among the
accepted bids).
In noncompetitive bids, bidders only provide amount not price. The treasury automatically accepts
all these. The noncompetitive bidders will pay the price determined by the competitive bidders but
are guaranteed the amount.
Note that to ensure competitiveness, no competitive bidder can get more than 35% of each issue.
The dealers will then sell the T bills to the public (secondary markets) and they act as the market
maker for the security.
𝐹 − 𝑃 360
𝐹 − 𝑃 365
𝑖𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 =
∙
,
𝑖𝑦𝑡 =
∙
𝐹
𝑁
𝑃
𝑛
Fed funds are short term funds loaned or borrowed between financial institutions, usually
overnight. The monetary policy implemented on this market; it is called target/intended fed funds
rate because that’s what the fed wants to see. The effective rate is determined by demand and
supply between banks, but it moves around target.
Repurchase agreements: it is an agreement where a financial instrument is sold and bought back
(repurchased) at a later date. If the borrower does not buy back, the lender can sell T bills
(collateral).
(𝑃−𝑋)
𝑌−𝑋
is the repo rate and it is like a discount rate. If P is the market price of T bills 𝑃 is the
𝑋
haircut, typically 2% for high quality collateral.
Often the collateral consists of government bonds: highly liquid, stable securities and the set up
makes a repo agreement essentially a short-term collateralized loan. This means that the lender is
secured, and it is different from fed funds, that are unsecured loans. The repos are normally low
risk because S-T and liquid collateral, but losses can happen.
Negotiable certificates of deposit: a bank issued deposit that specifies the interest rate and the
maturity date. It is a term deposit you cannot withdraw before maturity (opposed to demand
deposit), traded in large volumes (from 100k to 10m), second to T bill only.
Commercial paper: unsecured promissory notes (a promise to pay), issued by corporations with
maturity < 270 days. It is sold on a discount
basis, like T bills, and since it is unsecured,
only the largest corporations’ issues
commercial paper. They are sold directly
to buyers and there is no secondary market.
Asset backed commercial paper: a specific
type of commercial paper, known as asset,
backed commercial paper. Asset backed
means that it is secured by some asset, and
it is mostly issued by banks (low quality
US mortgages).
Eurodollars: $ denominated deposits held
in foreign banks, they are short term
interbank deposits, often o/n. London
interbank offer rate (LIBOR) rate on Euros and is a trimmed average of all responses is taken (top
and bottom submissions are excluded).
Capital markets participants: primary issuers of securities in capital markets:
- Governments: debt only
- Corporations: equity and debt
The choice between debt and equity is called capital structure, we have many strategic reasons
other than raising capital to get listed on stock market but issuing bonds certainly to satisfy
financing needs. In general, the largest buyers of securities are households.
Bonds:
They can be divided in:
- Government bonds, especially US treasuries
- Municipal bonds, issued by US states/cities
- Agency bonds, issued by quasi-public entities
- Corporate bonds
Treasury notes and bonds: US government
bonds are considered risk free asset, and the T
bill is even more risk free because it has short
maturity. This does not apply to all
government bonds (Argentina, Greece), but
still there is inflation risk.
In the US there are also municipal bonds,
which are issued by local, counties and state governments (they are not default free), and there are
two main types:
1. Revenue bonds→ backed by the cash flow of a particular project
2. General obligation bonds→ do not have a specific project, backed by full faith and credit
of the government
Because they are tax free, 𝑚𝑢𝑛𝑖 𝑟𝑎𝑡𝑒 = 𝑜𝑡ℎ𝑒𝑟 𝑏𝑜𝑛𝑑 𝑟𝑎𝑡𝑒 ∙ (1 − 𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒).
Agency bonds instead, are issued by US government sponsored enterprises, they are private
companies that can issue government securities agency bonds and they buy mortgages from banks
and sell insurance.
Corporate bonds instead are issued by larger corporations and the default risk is significantly
higher than for treasury bonds, but there is a lot of firm heterogeneity. Risk is assessed by credit
rating agencies and somewhat different scales but in general:
- Investment grade
- Speculative/high yield
In general, bonds have bond indenture, which is a contract stating lender’s rights and borrower’s
obligations, such as restrictive covenants (the bondholders place some limits on what the
company can do, it may limit dividends, new debt, mergers… if covenants are more restrictive,
does interest increase or decrease? It decreases because firms are already accepting lots of
conditions from bondholders so they can lower the interest, so that it is safer for bonds holders),
call provision (a bond may be callable, and issuer can force bondholder to sell back bonds. All
else equal interest for a callable bond is higher than for non-callable bonds. If interest decreases
are the firm more or less likely to buy back?), conversion option (debt that may be converted to
equity by a holder, and it is likely buying a bond and a stock option. Hence interest will be lower
for a convertible bond than for a non-convertible bond) and so on but in general not all corporate
bonds have these three characteristics, may be none, may be all.
The final feature of corporate bonds is seniority, which means that if a company defaults
bondholders are senior to stockholders. Among bondholders, there is seniority too, as they get paid
before junior/subordinated bondholders. If a bond is secured, it means that there is a specific
collateral, and this get paid for sure.
So far, we have always assumed annual coupon payments. But actually, coupon pay semi-annually,
so:
2𝑛
𝑃=∑
𝑡=1
𝐶/2
𝐹𝑉
+
(1 + 𝑖/2)𝑡 (1 + 𝑖/2)2𝑛
where 𝐶, 𝑖 are annual and 𝑛 are the years to maturity.
Semiannual payments make a difference because of compounding, due to the fact that if you
reinvest at shorter intervals, you make more money, as you earn interest on interest.
Junk bonds: very illiquid secondary market. Often trusts and insurance companies are not
permitted to invest in junk debt. In fact, before 1980, only investment grade bonds existed, and
Michael Milken was the investment banker that created the junk, market maker and extended credit
to junk firms. They earned substantial fees (2-3%). In 1980s take overs were popular, buying firms
would issue junk bonds to finance buy out, and was subsequently convicted of insider trading.
→ a share of stock or equity represents ownership in a firm. A stock- share- equity holder owns a
% of the firm. Ownership entitles the stockholder to say something on firms’ actions (vote) and a
share of profits (dividends). They also earn if stock prices increases and much riskier than bonds
because neither dividends nor price rises are guaranteed. There is no maturity date.
Stock residual claimant in a default they get what’s left after all other creditors have been paid off.
The order of payment is called seniority: debt is senior to equity because it gets paid first.
The stock market:
→ stocks and bonds have a balanced trade off of control rights and cash flows.
1. Stocks: high control right, uncertain cash flow (volatile price, uncertain dividend)
2. Bonds: low control rights (other than bankruptcy), certain cash flow.
The stock market is the other capital market together with the bond market, and it receives a lot of
attention because the gains are potentially infinite, and also it is easy to see the stock market.
A share of stock or equity represents ownership in a firm. A stockholder owns a percentage of the
firm. Ownership entitles the stockholder to say something on firms’ actions and a share profits
(dividends), and they also earn if stock price increases. In general, it is much riskier than bonds
because neither dividend nor price rises are guaranteed, and there is no maturity date.
Stocks residual claimant, in a default they get what’s left after all other creditors have been paid
off, and the order of payment is called seniority: debt is senior to equity because it gets paid first.
There are mainly two types of stocks:
- Common stock: gives rights to vote.
-
Preferred stock: pays a fixed dividend (like a bond), thus price is stable (easy to forecast
cashflows), there are no voting rights (unless dividends have not been paid) and have higher
seniority than common stockholders (but still lower than bondholders).
→ stocks and bonds have a balanced trade-off of control rights and cash flows. In general stocks
have high control rights (such as vote), but with uncertain cash flow (due to volatile price and
uncertain dividend). Bonds instead, have low control rights (other than bankruptcy), but have
certain cash flow.
In general equity funding is more costly than debt funding, because the interest rate from bonds is
tax deductible, while dividends are not.
Shares:
On the one hand we can have authorized shares, which has a maximum number of shares the
company can issue during its lifetime and decided at the time the firm files the registration
statement and it can be changed but it needs shareholders’ vote. There are also outstanding shares,
which are a number of shares a company has issued (they include restricted share, which cannot
be bought or sold by the public, it is usually given to employees and insiders as part of salaries or
bonus→ private companies. The other type included is float, which are freely bought and sold
without restrictions by the public). In general, outstanding shares are typically used to calculate a
company’s market capitalization = 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 ∙ 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒𝑠.
Thinking again of the primary market we can say that new security issues are sold to initial buyers
and for investment bank arranges the sale of securities (for stocks), although we almost never see
primary market. Instead in the secondary market securities are previously bought and sold, and it
involves matching of buyers and sellers→ can be organized as an exchange.
To be listed a firm must satisfy many requirements:
- Market capitalizations > 100 million
- Number of shares outstanding > 1 million
- Stock price > 4$
- Plus, a number of further criteria
Being listed has some advantages such a stocks trade on a more liquid market, and it confers more
prestige.
Over the counter markets:
In this case, there is no trade floor, but it is all electronic and there are low listing requirements.
Dealers and market makers stand ready to make a market and they have inventory of stocks and
are ready to buy at the bid price and sell at the ask price. There are many dealers for each stock
(competition)→ they earn bid ask spread and commission fees.
Stock market indexes are used to monitor the behavior of a group of stocks. These indexes are just
averages of the stocks composing the index. An example could be the price weighted index, which
1
is a simple arithmetic mean and every stock has the same weight 𝑁 ∑𝑁
𝑖=1 𝑝𝑖
Every stock has the same weight, and the DIJA is an example of a price weighted index, but it has
adjustments, and its formula is∑30
𝑖=1 𝑝𝑖/𝐷𝑜𝑤𝑑𝑖𝑣𝑖𝑠𝑜𝑟 , where the divisor keeps track of stock splits
dividends to maintain historical continuity.
Price of a stock: the principle of valuing common stock is no different from valuing debt
securities, in fact you should:
1. Determine the cash flows
2. Discount them to the present
3. Price them at their PV
The two main items that compose a stock cash flow are dividends, which are shares of a
company’s profits distributed to stockholders, and future sales price. In order to calculate it we
can use different models and an example could be:
→ one period valuation model: simplest model where you only use the expected dividend and price
𝐷𝑖𝑣
𝑃
over the next year, 𝑃0 = 1+𝑘1 + 1+𝑘1 where:
𝑒
-
𝑒
P0 is the price today
P1 is the price next year
Div1 is the expected dividend next year
Ke is the required return on equity, it works like the YTM, but usually it’s higher, because
stocks are riskier.
Suppose you see a stock trading at 50$, paying 0.16 in dividend per yar. You read an analyst
forecast that price is expected to rise to 60$ next year, and you decide you want to have 12% to be
compensated for risk, should you buy it?
0.16
60
𝑝𝑟𝑖𝑐𝑒 =
+
= 53.71, 𝑤ℎ𝑒𝑟𝑒 53.71 > 50 𝐵𝑈𝑌
(1 + 0.12) (1 + 0.12)
𝐷𝑖𝑣
𝐷𝑖𝑣
𝐷𝑖𝑣
𝑃
→ generalized dividend valuation model: 𝑃0 = 1+𝑘1 + (1+𝑘 2)2 + ⋯ + (1+𝑘 𝑛)𝑛 + (1+𝑘𝑛 )𝑛 you should
𝑒
𝑒
𝑒
𝑒
use the same logic, extended to n periods, but as n grows, the last item in the summation gets
𝐷𝑖𝑣𝑡
smaller, as the discounting is higher. 𝑃0 = ∑∞
𝑡=1 (1+𝑘 )𝑡 , there is no final P in this expression, just
𝑒
PV of all future dividends matter.
→ Gordon growth model: same as the previous model but assume that dividends grow at a constant
rate g, where you should estimate g and a required return. 𝐷𝑖𝑣𝑡+1 = (1 + 𝑔)𝐷𝑖𝑣𝑡
𝐷𝑖𝑣𝑡
𝐷𝑖𝑣1
With some algebra we can show that 𝑃0 = ∑∞
𝑡=1 (1+𝑘 )𝑡 = 𝑘 −𝑔.
𝑒
𝑒
Dividends don’t grow at a constant rate forever, but as long as they grow constantly for some time
𝐷1
the model is reasonable. Also note that 𝑘𝑒 > 𝑔 otherwise we can’t simplify to 𝑃0 = 𝐾𝑒−𝑔, but this
is also reasonable, firm value would be infinite if 𝑔 > 𝑘𝑒, and so the Gordon formula is no longer
valid.
Price earnings valuation: easy to calculate and avoid dividends by looking at earnings (price
𝑃
earnings ratio). 𝑃𝑟𝑖𝑐𝑒 = 𝐸 ∙ 𝐸, where E is expected earnings per share (in practice you will see PE
based on actual earnings per share EPS over the last 12 months, and it can also be taken from
industry average) and the PE can also be taken from industry average and compared to company’s
individual PE. In general, a high PE has two interpretations:
1. Earnings are expected to rise in the future compared to woe PE companies.
2. The company is low risk, the market pays a premium for its earnings.
All models require to compute expected earning, dividends and growth rates. Growth/glamour
stocks are those with high PE and value stocks are those with low PE.
Note that all the models require to compute expected earnings/dividends/growth rates, sometimes
far ahead in the future and small errors in evaluating each can lead to bad mistakes, and for the
Gordon model we need to item: 𝑔 𝑎𝑛𝑑 𝑘𝑒.
→ derivatives are a financial instrument designed to manage risk (hedging), and Warren Buffett
stated that: “essentially these instruments call for money to change hands at some future date, with
the amount to be determined by one or more reference items, such as interest rates, stock prices or
currency value”.
So financial contracts whose price and cash flows are determined by other, underlying items.
Do derivatives contain or amplify risk? Both views are true, derivatives allow to hedge risk, but
can also concentrate risk in the hands of a few (counterparty risk). If these few are interconnected
to everyone a small problem, can lead to a collapse of the system.
There are many derivatives such as:
- Forward
- Futures
- Options
Hedging involved engaging in a financial transaction that reduces or eliminates risk. The idea is
to enter in a financial contract with a risk that is opposite (negatively correlated) with the original
risk and it is useful to define two notions for the sides of risk: which are long position (you profit
if the price goes up) and short position (you profit if the price goes down, or if you are selling now
an asset which is borrowed, but must be returned in the future to original owner).
→ if you are long, it means that you run the risk that the price goes down, while if you are short, it
means you take the risk that the price increases.
Returning to the derivatives we can say that it is a zero-sum game (for every winner there is a
loser), but ex ante it reduces risk for both. Each party sacrifices some profits in one state of the
world so each can benefit from insurance.
Forward contract: an agreement to enter a transaction at some future date. It is not standardized
in any way but at least it should specify what item should be delivered, how much, at what price
and the date. In substance it eliminates uncertainty about the future price.
Profits of the party selling a forward contract = difference between F (agreed forward price) and
the spot market price St on the day of maturity T (which would have been attained otherwise):
𝜋𝑠ℎ𝑜𝑟𝑡 = 𝐹 − 𝑆𝑡
Selling a forward contract opens a
short position, which is the most
valuable the lower the spot price of
the asset will be in the future.
Profits of the party buying a
forward contract, and it is equal to
the difference between the value of
the item at the delivery time, the
party would have attained without
the contract and:
𝜋𝑙𝑜𝑛𝑔 = 𝑆𝑡 − 𝐹
Buying a forward contract opens a long position, which is the more valuable the higher the spot
price of the asset will be in the future.
The pro of forward contracts is that they are not standardized, so flexible, while the cons are that
it is hard to find a counter party as there is a lack of liquidity in the secondary market, and that the
subject is to default risk of the counterparty.
Future contracts: exchange traded contracts that specify an agreement to exchange an asset at a
future date at a price specified today. It is similar to forwards, but traded on exchanges and
standardized
in
amounts, quality and
date of delivery.
Trading
on
an
exchange, means that
you can get a price for
the future contract even
before delivery:
Standardization overcomes the problem of market liquidity (i.e. find a counterparty) that
forwards have. Futures standardize the:
1. Contract size: 4ex. $100,000 face value of T-bonds
2. Delivery dates: last business days of each quarter: March, June, September, December
3. Quality: very specific. 4ex.: orange juice futures need to use this definition for orange juice
The delivery of items in futures market almost never actually happens. This is because you can
“close” your position with another offsetting position with the exchange directly.
If you’re long (bought a future), you can enter a short position (sell the same future) with the
exchange. The exchange cancels both contracts. Avoids the cost of delivery (transaction costs)
Future: prices
An important fact is that the future price will converge to the spot price at the delivery date
(𝐹𝑡 = 𝑆𝑡), why? Because there is an arbitrage opportunity:
- If the future price for today is lower than spot price, we can buy a future today, get the
good and sell it immediately for profit at the spot price.
- If the future is above, buy at spot and sell futures.
Future: payoffs
Payoff to the long side of a future contract closed at date t: 𝐹𝑡 − 𝐹0, where 𝐹0 is the price initially
paid on the future and 𝐹𝑡 is the price of the future when closing. Payoff to the short side of a future
contract closed at date t: 𝐹0 − 𝐹𝑡, where 𝐹0 is the price initially received on the future and 𝐹𝑡 is
the price of the future when closing.
If the contract is kept until delivery, then 𝑡 = 𝑇 and 𝐹𝑡 = 𝐹𝑇 = 𝑆𝑡
Exchanges and default risk:
The exchange deals with the other big issue of a forward contract, default risk of the counterparty.
How? Where does it get the money?
- The exchange acts as a clearinghouse for both traders. The clearing house guarantees all
futures will be executed even if one counterparty defaults.
-
From the buyers and sellers margin accounts, whose amount is tied to the value of the
future contract.
→ the first clearing house was created in Le Havre, France, in 1882. The first cleared contracts
were coffee futures, and in response to its creation trade flows from overseas colonies to Europe
were significantly altered to the benefit of Le Havre and this contracting innovation then spread
quickly to other exchanges.
Future: margin accounts
The margin account is called so because the exchange will make a margin call in case the value of
the future contract changes. The key point is that it is adjusted daily: daily settlement. At each
closing date, market prices determine the value in each margin account, marking to market and
this eliminates default risk.
→ marking to market: at the end of every day, the exchange looks at how futures prices have
moved. It credits the margin account of the party whose contract has become more valuable and
debits the counterparty’s account by exactly the same amount. The amount debited/credited
corresponds exactly to the change in future prices between today and yesterday. If the margin
account has insufficient funds and the party does not top up funds after receiving a margin call,
the position will be automatically closed.
A stock index future has a stock market index as the underlying asset. Useful to hedge stock market
risk, but what item is delivered? Cash. How much? The cash amount is equal to the stock market
index at the delivery date times the multiplier.
𝜋𝑙𝑜𝑛𝑔 = 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 × (𝑆𝑇 − 𝐹0 )
𝜋𝑠ℎ𝑜𝑟𝑡 = 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 × (𝐹0 − 𝑆𝑇 )
Why would you use a stock index
future?
Suppose you are long in a portfolio of
stocks of $100M that moves one-toone with the S&P500. The S&P500
today is 1,000. You want to hedge a
downturn. Go short on S&P500
Hedge for one year. The S&P500
futures currently selling at 1,000
(multiplier of $250). How many
contracts do you need?
100,000,000/(1,000 × 250) = 400 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠
Options: an option gives you the right to buy or sell an underlying asset in the future at a predetermined price at a predetermined date.
Unlike a forward contract, the holder of an option is not obliged to make the purchase/sale of the
underlying asset if this is unfavorable to him. The writer of the option however has the obligation
of complying with these terms and cannot refuse buy/sell the asset under unfavorable conditions.
In other words, there is a fundamental asymmetry between the rights of holder of an option vs
those of a writer. To compensate for his weaker rights, the seller of an option will demand a
compensation, called the option premium. The buyer of the option will always have to pay the
premium, no matter if he exercises the option or not. There are two options:
-
Call option: gives you the right to buy at the strike price within a specified period of time.
Put option: gives you the right to sell at the strike price within a specified period of time.
The option payoff is the amount the option pays at expiration. The option profit is the gross payoff
minus premium paid (long side) or plus the premium received (short side), and we call the option
payoff the option value.
Profit for holder (long):
- Call option: exercise a call option only if
buying at the strike price X is more favorable
than spot price S. Payoff is the difference
between the value S and X, and in any case
never below zero (because if 𝑆 < 𝑋 , you
don’t exercise the option). To get the profit
subtract 𝑝.
𝐶𝑎𝑙𝑙
𝜋𝑙𝑜𝑛𝑔
= max(𝑆 − 𝑋, 0) − 𝑝
- Put option: exercise a put option only if
selling at the strike price X is more favorable
than the spot price S
𝑃𝑢𝑡
𝜋𝑙𝑜𝑛𝑔
= max(𝑋 − 𝑆, 0) − 𝑝
Profit for writer (short):
- Call Option: you are obligated to sell if the
buyer of the call exercises the option. He will
exercise only if 𝑆 > 𝑋 , but he always pays the
premium. Hence your profit is:
𝐶𝑎𝑙𝑙
𝜋𝑠ℎ𝑜𝑟𝑡
= 𝑝 − 𝑚𝑎𝑥(𝑆 − 𝑋, 0)
- Put Option: you are obligated to buy if the
buyer of the put exercises the option. He will
exercise only i𝑓 𝑋 > 𝑆, but he always pays the
premium. Hence your profit is:
𝑃𝑢𝑡
𝜋𝑠ℎ𝑜𝑟𝑡
= 𝑝 − 𝑚𝑎𝑥(𝑋 − 𝑆, 0)
Some examples of options:
→ callable bonds: bonds that can be called back by the issuing corporation, is a call option. Notice
that the firm decides not to exercise the option if the price of the bond (spot). Is below the face
value (strike price) and the firm pays a premium in terms of higher interest.
→ stock options: a popular compensation scheme for managers. Call options at a strike price at
specified dates and in theory it aligns the incentives of manager and company, pay linked to
performance.
We can have several types of options:
1. European options
2. American options
3. Exotic options
Terminology:
-
In the money: exercise today would be profitable
At the money: the strike equals the current price of the asset (the option’s intrinsic value is
zero)
- Out of the money: exercise today would be unprofitable
(A call is in the money if the 𝑆 > 𝑋, a call is out of the money if the 𝑆 < 𝑋, a put is in the money
if 𝑋 > 𝑆, a put is out of the money if 𝑋 < 𝑆).
Options pricing (premium)→ pricing of options is
a difficult business, need mathematical models, but
we will examine strike price, spot price at
expiration, volatility of underlying asset and term
to expiration.
The main determinants are the effects of increases
in strike and spot prices for call and put option has
been examined. Why both volatility and term to
expiration increase the value of both call and put options? There are potentially large gains, but
only limited losses. Volatility can only have a positive effect (you can always decide not to exercise
the option). The same logic for term to expiration, it only increases the chance of a positive gain,
with no impact on losses (capped at p). given by the non-linearity of the profit function. In general,
the additional value of buying the put option compared to not buying it.
Options vs futures:
Futures are one sided bet: you gain if the bet is correct and lose otherwise. Same is true for the
counterparty. Options instead are asymmetric bets. The buyer of the option will experience large
gains if his/her bet is correct and will face limited losses if his/her bet is incorrect. The seller of
the option will experience limited gains and potentially large losses.
Once again, futures are obligations for both parties, and options give a right to the option holder,
which is an obligation for the option writer. Futures are costless to initiate, while options are not
costless to initiate, the buyer has to pay the seller an option premium.
Lecture 11: exercises
Are financial markets efficient?
In order to understand it, we should talk of expectations and how expectations are formed. We can
say that investors are rational, and this means that they form their best guess of the future using all
available information, and market prices reflect all available information. In essence, it is the
efficient market hypothesis (EMH), the rationale behind it is arbitrage. We have encountered
arbitrage when we talked about futures converging to spot prices at delivery, if the future price at
delivery date is higher than the spot price, you can but at spot and sell a future by earning risk free
profit (reverse if 𝐹 < 𝑆) and arbitrage opportunities are risk free profit opportunities that exploit
mispricing’s. Other arbitrage examples are:
1. Same asset trades with different prices on two different exchanges
2. Two assets with identical cash flows and risk but different prices
What happens when arbitrage opportunities are being exploited? They disappear.
3. Buy the cheaper asset (demand increases)
4. Ceteris paribus, the price of the cheaper asset will go up (law of demand)
5. When the price of the cheaper asset converges to the higher price, no more arbitrage
opportunities
Arbitrage opportunities cannot survive for long in a competitive market, as there are other investors
who will see a profit and take advantage of it. The fact that there are few arbitrage opportunities,
tells you that there are few securities whose price doesn’t reflect publicly available information,
otherwise there would be an easy arbitrage opportunity→ Efficient market hypothesis.
We now define EMH as the security price that reflects all available public information at all times,
this means for example that you cannot predict the future price of stock from any information that
is public knowledge. It doesn’t say that you cannot profit from private information: that is not
incorporated in the stock price. There are two other definitions of EMH:
- Weak efficiency: all past stock prices are reflected in today’s stock price
- Strong efficiency: all information, whether public or private is priced in. prices reflect the
true fundamental intrinsic value of securities.
It doesn’t imply that prices do not change, as new information comes in and securities are
evaluated. EMH doesn’t imply that a rational investor always gets the price right, only that his
expectations are correct. Also, EMH doesn’t imply a zero average market return: earn a fair return
in equilibrium based on the riskiness of the security.
Evidence on efficient market hypothesis:
- Random walk behavior of stock prices→ future changes in stock prices should be
unpredictable. If EHM is right, prices should be a random walk, which technically means
that the best predictor for tomorrow’s price is today’s price (random because if today is
your best guess for tomorrow then you really have no idea about tomorrow).
- Anticipated announcements don’t affect stock price→ a positive but negative but
anticipated announcement about a company that will not raise (decrease) the price of its
stock. Why? Because this information was already reflected in the stock price.
- You can’t beat the market→ if EMH is right, investment analysts and mutual funds should
not be able to consistently beat the market. It means that buying the shares they suggest
should not be better than just buying a basket of the market as a whole.
Insider trading:
Proven method to beat the market. Insiders are company’s officers, directors and any beneficial
owners with substantial share of ownership. In the US it is illegal to trade such information, as in
most countries now, but in Europe it came in late.
Foreign exchange rates:
EMH is often applied in the context of stocks, but it works for all financial assets. EMH predicts
the FX rates should be unpredictable and that is exactly what empirical test shows, but FX rates
are not very predictable, they follow a random walk. All the evidence in favor of EMH led its
father and most prominent advocate, Eugene Fama, the 2013Nobel prize in Economics, to declare
in 1970: “The evidence in support of EMH is extensive and, somewhat uniquely in economics,
contradictory evidence is sparse”. This view is not shared by another 2013 Nobel prizewinner,
Robert Shiller, he wrote a book called “Irrational Exuberance” and one called “Animal Spirits”.
Evidence against EMH:
- January effect→ stock prices fall in December and rise in January, abnormal positive return
in the month of January that is predictable, and hence, inconsistent with random walk
behavior.
- Small firm effect→ many empirical studies have shown that small firms have earned
abnormally high returns over long periods of time, even when the greater risk for these
firms has been considered. This is a challenge for EMH because no stock should
consistently exhibit excess returns.
- Market overreaction and momentum→ sometimes stock prices continue to rise for quite
some time after a positive news (momentum). Momentum strategies: sell stocks that have
had bad returns and buy those with high returns in the last 3-12 months.
- Excessive volatility→ EMH implies that prices basically reflect all and only market
fundamentals (PV of future dividends). However, stocks appear to have excessive volatility
compared to volatility of fundamentals.
Behavioral finance: concepts from psychology, sociology and other social sciences are applied to
understand the behavior of securities prices. Richard Thaler won the Nobel prize for his
contribution to the field in 2017. Behavior theories include psychological aspects such as “loss
aversion” to understand investors. Other behavior analysis points to investor overconfidence as
perpetuating stock price bubbles.
INDIRECT FINANCE:
Why do financial institutions (FI) exist? The two primary functions of indirect fiance are:
1. Lower transaction costs
2. Reduce asymmetric information
The reason for their existence is that, at least in principle, indirect finance is better equipped than
financial markets to solve these problems. By doing 1 + 2 FI engage in risk sharing (asset
transformation/diversification).
Talking about transaction costs we can say that they influence the financial structure. Certain types
of investments are only available in large denominations. For small transactions, commissions and
fees represent a high percentage of investments and as a result small individual investments are
not well diversified. Indirect finance can reduce transaction costs through:
- Economies of scale: average cost per $ of investment decreases as the size scale increases
(fixed cost in buying share)
- Economies of scope: average cost decreases as number of products offered increases
→ direct vs indirect finance:
Throughout the world, non-financial businesses mostly use indirect finance as a source of external
funds, which are all those funds that do not come from the business itself through retained earnings.
Small firms do not issue bonds + stocks, there is more debt (bonds + loans) than equity around the
world or bank loans often require collateral (secured), all mainly due to asymmetric information.
Asymmetric information happens when one counterparty lacks crucial information about another
party, impacting decision making. The market may break down in the presence of asymmetric
information, causing market failure. Asymmetric information problems are often categorized into
adverse selection and moral hazard.
1. Adverse selection: can happen before transaction occurs (ex-ante). Before agreeing to a
transaction, one party has more information, such as a bank doesn’t know the
creditworthiness of a potential borrower, to which the bank could respond by charging a
higher interest rate. Large well-established firms should have less asymmetric information
with financial markets. Hence these firms can more easily issue stocks and bonds.
Meanwhile small firms have hard time issuing stocks and bonds directly, causing adverse
selection.
2. The party that knows more about the transaction most likely produces the undesirable
adverse outcome→ famous lemon market problem of Akerlof in the market for secondhand
cars.
How can we solve adverse selection?
1. Private collection of information: private production of info creates a free riding problem,
once info is out in the market, it is hard to keep it
2. Government regulation: reduce asymmetric information by having true company’s
information revealed.
3. Screening ex ante from FI: especially banks, like private collection of information, but
rather than selling it, FI make private loans that other investors cannot observe, they also
repeatedly lend to same businesses.
4. Collateral and net worth: ask ex ante to borrowers to have some “skin in the game”,
collateral: house for a mortgage, car for car loan, and net worth (assets – liabilities).
Adverse selection can explain why small firms are shut out of capital markets and use banks, and
why bank loans are usually collateralized. One fact still remains unexplained, why so little equity
as a source of external finance? Why so much debt (bonds + loans), moral hazard can explain
that, as it is a situation where one party has the incentive to engage in undesirable (immoral)
activities after the transaction has occurred (ex post). An example could be employee can become
lazy right after a promotion.
Principal-agent problem is the result of separation of ownership by stockholders (principals) from
control by managers (agents), or agents can act in their own rather than principals’ interest.
Problem arises because the agents know more about the company than principals, which could
monitor agents’ activities but that’s costly. It arises especially with equity contracts.
To this problem there are 3 main solutions:
1. Monitoring→ ex post screening. Shareholders can observe the level of effort of the
manager. The problem is that monitoring is costly, and FI are goods at this, for example
venture capitalists do constant, active monitoring and receive equity share in startup that is
not tradable.
2. Government intervention→ enforce the laws on fraudulent behavior.
3. Debt contracts→ the principal agent problem arises with equity because equity is a claim
on all profits of the firm. Thus, the principal needs to make sure no profit is diverted away
by the agent. It requires monitoring. A debt contract can reduce monitoring costs as it only
needs to monitor in some state of the world. If the firm has high profits, the lender receives
the fixed payment, as agreed, and doesn’t monitor. Important result in theoretical finance
is that debt is the optimal security if moral hazard is present.
Moral hazard can explain why debt is much more prevalent than equity. But debt itself is not
immune from moral hazard and to overcome it, debt contracts often have collateral (car for loan)
and covenants, to prevent undesirable behavior. FI usually require and enforce both.
Commercial banking and bank balance sheet:
What are commercial banks? Are institutions that accept deposits (liabilities) and make loans
(assets). They are traditionally the large financial intermediary by asset size, while investment
banks are not depository institutions and mutual funds are also not accepting deposits, but issue
shares and invest them in other securities.
→ the balance sheet is a list of bank’s assets and liabilities.
𝑡𝑜𝑡 𝑎𝑠𝑠𝑒𝑡𝑠 = 𝑡𝑜𝑡𝑎𝑙 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 + 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
A bank’s balance sheet lists sources of bank funds (liabilities) and uses to which they are put
(assets). Book value, which is what you read on the balance sheet, is different from market value,
as evaluated by the market using prices).
Assets:
1. Reserves and cash (16%): accounts held at the federal reserve, + physical cash in bank’s
vault.
2. Securities (22%): only debt, commercial banks are not allowed to hold equity. Mostly US
government debt and mortgage-backed securities.
3. Loans (53%): mostly in real estate and business loans to firms.
4. Other assets (9%): buildings, IT infrastructure…
Liabilities:
1. Deposits (71%): from households and firms, there are two main types, the first one is the
checking deposits, which allows to withdraw at any time, and the second one non
transaction deposit, which are limited withdrawals.
2. Other short-term borrowing (18%): fed funds (overnight from other banks), interbank
offshore dollar deposits, repurchase agreements and commercial paper and notes.
3. Capital (11%): difference between assets and liabilities.
Off balance sheet:
Not everything is on the balance sheet, in the past two decades banks have greatly expanded their
fee income generating off balance sheet activities, they may include:
1. Securitization: sell loans and repackage them into securities to free up space in balance
sheet.
2. Loan commitments: provide up to $X to borrower.
3. Trading/hedging: derivatives, options, futures, interest rate swaps.
Banks have an obvious incentive to bring assets onto the balance sheet and conceal liabilities at
the same time. These activities do not show up in book equity, but are taken into consideration for
market equity, and it also depends on how much the market knows about OBS.
It is helpful to understand some of the simple accounting associated with the process of banking.
Banks engage in asset transformation, which a bank uses as deposits to make a loan. Therefore,
banks tend to borrow short an lend long, in term of maturity.
Remember that when a bank receives deposits, reserves increase by equal amount and when bank
loses deposits, reserves decrease by equal amount.
The bank has 4 primary concerns:
1. Liquidity management:
The need for liquidity management arises because the maturity of banks’ assets is generally longer
than the maturity of their liabilities. Therefore, a bank may have to pay its creditors before it
receives the proceeds from its assets. Liquidity management ensures that there is enough cash to
pay depositors, when they wish to withdraw their money. Furthermore, banks need to have enough
reserves to satisfy the minimum reserve requirements. With ample excess reserves no changes
needed in balance sheet. In case of no excess reserves, you can borrow from other banks (cost
federal funds rate), or you can sell securities (cost transaction costs). You could also borrow from
fed (cost discount rate, higher than fed funds rate), or you could call in or sell off loans (cost low
liquidity in secondary markets for loans).
We can way that excess reserves are insurance against above 4 costs from deposit outflows. Banks
are willing to hold excess reserves in order to avoid these costs. However, large excess reserves
holdings substantially reduce the profitability of the bank, so less loans. Liquidity management
involves the choice of assets, which can be liquid short-term securities that are easy to convert into
cash if liquidity problems occur (deposit outflows), but they yield less than long term illiquid
assets.
2. Asset management (managing credit risk, managing interest rate risk):
Represent the attempt to earn the highest possible return on assets while minimizing the risk and
holding enough liquid assets.
3. Liability management:
Represent the managing of the source of funds, from deposits to CDs to other debt. Large banks
now manage asset and liabilities at the same time, and this is known as asset and liability
management.
4. Managing capital adequacy:
Capital/equity/net worth is the difference between assets and liabilities. Funds supplied by bank
owners, shareholders, either directly via purchases of shares or through retention of retained
earnings, which is a portion of profits that are not distributed through dividends.
When losses occur, they first get subtracted from the bank’s net worth, before other creditors get
affected. If assets drop below the value of liabilities, the bank’s net worth (book value) becomes
negative, negative net worth means that the bank is insolvent.
Banks need to manage the amount of capital held for two main reasons, the first one is a strong
capital stock protects from bank failure and second one the capital stock affects the bank’s
profitability, negatively.
Bank capital is a cushion that prevents banks failure, as a low capital bank is insolvent. Insolvency
means that even if the bank sells all its assets, it will not be sufficient to pay all creditors. Such
banks go bankrupt unless, the owner provide new funds, or new owners step in or also, buying an
insolvent bank is cheap.
Also, capital reduces profitability, so banks may not want to naturally hold high level of capital,
even if it improves solvency.
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑛𝑜𝑛 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 = 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠 + 𝑛𝑜𝑛 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠 = 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠
𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒 + 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠 = 𝑛𝑒𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒
Return on assets gives a broad idea of how well the bank is using its assets to generate income.
𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
𝑅𝑂𝐴 =
𝑎𝑠𝑠𝑒𝑡𝑠
Return on equity is what owners ultimately care about, this is the return they get on the capital they
provided to the bank.
𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
𝑅𝑂𝐸 =
𝑒𝑞𝑢𝑖𝑡𝑦
Bank performance: the two are of course linked, and the link is the equity multiplier. Also note
that 𝐸𝑀 > 1, so that 𝑅𝑂𝐸 = 𝑅𝑂𝐴 ∙ 𝐸𝑀. The smaller the ratio of capital to assts, the greater the
ROE, for a given net income and equity holders prefer to have less capital with more leverage and
all else equal.
𝑎𝑠𝑠𝑒𝑡𝑠
𝐸𝑀 =
𝑒𝑞𝑢𝑖𝑡𝑦
Net interest margin measures how well the bank generates income from its primary core function,
which is issuing liabilities and investing in interest earning assets. It is the spread between what
the bank earns in interest income and what it has to pay.
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 − 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠
𝑁𝐼𝑀 =
𝑎𝑠𝑠𝑒𝑡𝑠
Central
banks
and
monetary
policy:
central banks are the government authorities in charge of monetary policy, they have to do with
interest rates, money supply and inflation but they also have effects on bank credit. Actually, most
of what central banks do goes through the commercial banking system.
We have the federal reserve assets, which divide in two main asset classes:
- Securities: which before 2008 mostly short-term T bills and nowadays long-term treasuries
and MBS.
- Loans to financial institutions (discount window) or other liquidity facilities, there are
provision of credit to help financial institutions and calm markets in crisis times, while in
normal times these are not used, but in 2008-2010 they were frequently used.
Talking about federal reserve liabilities, we can divide it into two main liabilities:
- Currency in circulation: these are banknotes and coins, that grow at a constant rate with
economy.
- Reserves: fund banks hold in an account with the fed, which also divide in required
reserves, required by law (minimum 3-10% of checkable deposits in US), and any reserves
beyond this is called excess reserves.
𝑡𝑜𝑡𝑎𝑙 𝑟𝑒𝑠𝑒𝑟𝑣𝑒𝑠 = 𝑅𝑅 + 𝐸𝑅
In normal times therefore we use open market operations, and it is clear that the fed balance sheet
has expanded a lot in the last 10 years, but the basic structure of assets (securities + loans to banks)
and liabilities (currency in circulation + reserves) has not changed. The scale and type of securities
held is different and it is useful to start from what the fed used to do in normal times to conduct
monetary policy→ open market operations.
The open market operations refer to either purchase/sale of securities by the fed from a set of banks
(primary dealers) and discount loans to financial institutions. The objective is to influence the
amount of money supply, and bank reserves can be exchanged by banks in the federal funds
market, a money market, which means safe, short-term instrument.
Supply and demand in the market for reserves:
We will examine how this change in reserves affects the federal funds rate, the rate banks charge
each other for overnight loans. We will also examine other tools available to the fed, for example
the ability to set the required reserve ratio for deposits held by the banks.
There are 3 rates to keep in mind:
1. Discount window rate: rate at which banks can borrow directly from the fed
2. The fed funds target rate: rate the fed wants, which is the effective at which banks lend and
borrow from each other equilibrium, may be different from target from time to time, but
very close.
3. The interest rate on excess reserves: rate the fed pays on excess reserves.
The
graph on the right represents the response to the open market purchase. In fact, with the open
market purchases, the fed increases the number of reserves and lowers the fed target rate, and with
the open market sales, the opposite happens. For this to work, the supply curve needs to intersect
the demand curve on its downward sloping part, this is what happens in normal times when
reserves are scarce.
Monetary policy recently: abundance of reserves makes clear that open market operation would
not work now, in fact the fed funds rate has been close to zero since 2008. The fed increased the
number of reserves to purchase securities and sustain
the economy. Securities holdings have been
declining recently, the fed is letting securities mature
without rolling-over funds into new securities. Part
of monetary policy normalization after crisis, but it
will take a few years before both reserves and
securities are back to pre-crisis level.
The fed also is raising rates: how can they do so with
many reserves?
The fed has several tools at its disposal to increase
fed funds rates even with large reserves.
- Increase interest on excess reserves
- Increase reserve requirements
- Reverse repos (more technical)
Mutual funds:
Are financial intermediaries that pool the investors’ resources by selling them shares and using the
proceeds to buy securities. They have been growing in number and importance since 1980, in the
US and worldwide. They are now as large as commercial banks in terms of total assets.
Mutual funds are the pooling resources that reduce the transaction cost and bring better
diversification to small investors and the majority of mutual funds continuously sells new shares
to investors and allows redemption of outstanding shares at market price. They are five principal
benefits of mutual funds, which explains why they are so popular:
1. Liquidity intermediation: investors can quickly convert investments into cash.
2. Denomination intermediation: investors can participate in equity and debt offering that,
individually, require more capital than they possess.
3. Diversification: even for small investments. Its benefits come with the ability to invest in
large denomination and lower average transaction costs
4. Cost advantages: the mutual funds can negotiate lower transaction fees than would be
available to the individual investor.
5. Managerial expertise: many investors prefer to rely on professional money managers to
select their investments.
→ in order to make money, mutual funds charge fees.
Net asset value (NAV): total market value of the mutual fund’s stocks, bonds, cash and other assets
minus any liabilities (such as accrued fees), divided by the number of shares outstanding. The
open-end fund agrees to buy back shares from the investors at any time at the NAV.
There are four primary classes of mutual funds available to investors by asset class and they invest
in (index funds and hedge funds do not fit these categories):
- Stock equity funds
- Bond funds
- Hybrid funds
- Money market funds
Money market mutual funds:
Open end funds that invest only in money market securities. Traditionally thought to be very safe
and yield higher returns than bank deposits. That’s why they are so popular and net assets increased
dramatically since 1980. Some of these MMMFs went in trouble during the 2007 crisis.
MF often have fees, in fact there can be one-time fees on the amount of. Shares you purchase, and
you can have the load, which is a funds charge an upfront fee (%of total sale) for buying shares,
or deferred loads, for funds charge a fee (% of original sale) when the shares are redeemed. If the
particular fund charges no front or back-end fees, it is referred to as no-load.
Index funds: a special class of mutual funds that is not actively managed. The fund contains the
stock of the index, and it is mimicking. It offers benefits of traditional mutual funds with lower
fees. Only recently popular, until the advent of computing technology, it was quite costly to
manage an index portfolio.
A special type of index funds are the exchange traded funds, which are open end investment
companies that replicate an index. They are different from index funds and the ETFs trade
continuously during the trading day.
→ structure of ETF:
The ETF manager enters into a legal contract with one or several authorized participants, typically
large financial institutions. The ETF manager can issue or redeem shares with APs in large blocks,
called creation units, in exchange for a basket of securities and or cash. Another characteristic is
that only authorized participants in turn interact with the markets. The mechanism by which the
shares of the ETF are adjusted in response to supply and demand is known as creation/redemption
mechanism, where creation means increase in the number of shares outstanding, while redemption
means decrease in the number of shares outstanding.
ETF price:
ETF managers have to publish a NAV too, but in contrast to MFs, investors in ETFs mostly do not
trade the fund directly. Deviations of price from the announced NAV are arbitraged away, thanks
to the creation redemption mechanism, by for example switching the basket of securities for EFT
shares, which in turn it could sell, to lock in intraday profits (done by the AP).
The creation mechanism thus works through arbitrage to help keep the price of an ETF close to
the intrinsic value of its holdings. Market data vendors calculate and publish the NAV based on
past prices and provide an intraday indicative value (every 15 seconds). The intraday tradability
of ETFs allows to have the price of the fund determined by the market through the interaction of
buyers and sellers. In contrast, for MFs liquidity is offered only at the close and only at NAV.
Other advantages of ETFs are great transparency (ETF investment are specified in advance and
their holding are listed daily), and lower fees (their cost are externalized).
→ the sellers of the fund will transact directly with buyers at a market determined price without
the interaction with capital markets.
Hedge funds:
Are a special type of mutual fund, and are different from typical mutual funds, as the high
minimum investment (average 1M), only wealthy investors (with annual income > 200k and net
worth >1M). Also, there are high fees (typically 1% of assets + 20% of profits), they are highly
levered and there is little current regulation (rich can take care of themselves). Hedge funds do
speculation as they are the best arbitrageurs in the market. They employ sophisticated trading
strategy, and they try to take advantage of unusual spreads between security prices.
Smooth functioning of securities markets requires financial institutions such as investment banking
firms, and these firms help buy and sell stocks, raise financing through equity and bonds issues
there are many types, such as investment banks, brokers, venture capitalists and private equity.
→ investment banks are financial intermediaries that:
1. Underwrite the initial sale of stock and bonds
2. Deal maker in mergers, acquisitions and spin offs
3. Private broker and bank to the very wealthy
So, they do not collect deposits and make loans like commercial banks do, but they intermediate
the flows of funds in primary and secondary market, and their main revenue are the fees they
receive.
Investment banks were created by the Glass-Steagall act in 1933. Before, investment banks were
part of the universal banks, but during the great depression 10000 banks failed. Therefore, the idea
behind it was to separate the normal banking activities, such as deposits and loans, from the risky
activities, such as trading or underwriting of securities.
In 1999 the glass Steagall was repealed by the Gramm-Leach-Bliley act (under President Clinton
and was considered one of the factors that contributed to the crisis). In 2010 the Dodd-Frank act
(under President Obama) partly reintroduced some separation between central banks and
investment banks.
- Volcker rule: prohibits “proprietary trading” at central bank, so bank cannot trade for profit
with its own money, only on behalf of clients.
- Again, the logic is separate traditional banking from riskier activities.
Although this, it doesn’t really mean that they cannot trade anymore. In fact, in 2018 president
trump eased some of the rules.
In Europe instead, there is no distinction between investment banks and central banks, in fact there
are universal banks (commercial banks could become investment banks by expanding into
investment banking activities).
The main traditional business area of investment banks is underwriting stocks and bonds, basically
investment banks help firms get listed and issue bonds. A firm would need this service because
they don’t do it often and there are high transaction costs. Investment banks also give advice on
when to issue, what to issue and what price, they also know potential buyers and provide implicit
guarantee about the issuance quality.
Talking about transaction costs we can affirm that the rules are complicated, there are inaccurate
registration statements that can result in lawsuits, debt issues require a credit rating and for equity
issues, they decide where the stock will be eventually traded.
Investment banks can also advise on type, price and date of issuance.
What type to issue?
Q: if PE industry ratios are high and interest rates are high, should you issue bonds or stocks?
A: stocks (high P) rather than bonds (low P)
When to issue? Explain current market conditions
At what price? For a Seasoned Equity Offering (SEO) it’s easy:
Look at current price in the secondary market. For an Initial Public Offering (IPO): not so easy
The investment bank can also help solve an asymmetric information problem when a firm issues
stocks and bonds. In fact, investors don’t know the true value of the firm. They could research the
company, but it is costly, and they do not trust the company itself to reveal honest and accurate
information. Instead, they trust the investment banks. The firm contracts the IB about the initial
interest in the issue of a particular security, and if the IB says yes, it is implicitly guaranteeing the
quality of the issue to the public.
So IB have reputational capital at stake, in fact it is a repeat business, so their income also depends
on costumers returning and on investors’’ trusting the IB judgment.
The IB is incentivized to do due diligence on the issues they distribute to the public, while if IB
lose investors’ confidence, their ability to make deals is severely impaired.
There are two main types of underwriting:
1. Traditional underwriting: if IB buys full issue at a pre-determined price and then distributes
the issue, the firm is guaranteed a price for its shares. The IB profit is the difference
between the price paid to the issuer, purchase price, and the price receive in the secondary
market, offer price. Because it is quite risky, usually IB ask other IB to join ad form a
syndicate.
2. Best effort underwriting: no price guarantee, only distribution. In this case the firm is not
guaranteed a price because the IB does not purchase the entire issue. The IB gets a
commission for selling securities and the IB has less incentives to do due diligence because
it is not putting its reputation at risk. In best effort, underwriting the IB is no longer
certifying the issuance quality. do you think that best-effort underwriting is mostly used
for IPO or SEOs? SEO. There is a price already on the secondary market and symmetric
info less of an issue than with IPO.
The goal of underwriting is to fully subscribe, however this may not occur, because of
undersubscription, that means underwriting syndicate unable to generate interest in all of the
available shares (so IB needs to resell at a lower price), or because of oversubscription, which
means that interest in more share than are available, which is not good either, as IB should have
set a higher price. Reputation as incompetent underwrite.
→ private placements: the entire issue is sold to a small, select group of investors. Advantages are
that there is no need for SEC registration. For this to work you need buyers with large pockets,
insurance companies, commercial banks, mutual funds…
Mostly private placement of bonds, rarely done with equity issues, and Goldman Sachs is the most
active IV in private placements.
Another traditional business area for IB: mergers and acquisitions deal making. A merger is the
combination of two firms into one, and management at both firms agree and shareholders simply
convert their stocks into the new firm stocks. In an acquisition one firm takes over another by
buying its stocks. This can be a friendly takeover, in fact often time a company in financial distress
will seek out a buyer, while a deal may be a hostile takeover, where the target does not wish to be
acquired.
Conflict of interest is a type of moral hazard that arises when there are multiple interests and
serving one interest is detrimental to the other.
IB research (provide analysis on) companies they also help underwrite.
Where is the conflict of interest? What are the multiple interests the IB is serving?
There are two party’s interest: investors and the company. The public investors want an unbiased
review of the company. The company benefits from an optimistic review.
Another common practice was that of spinning, place underpriced share to company executives
who promise future business to the IB, then executives can re-sell at a higher price on secondary
market. IB loses today but gains business with the company’s futures SEOs.
Pricing the IPO:
Technically hard but also inherent tension between IB profits and the interest of the company, a
conflict of interest. On the one hand, the IB wants to buy the issue at the lowest possible price and
then sell it at a high price to the public. On the other hand, they need to ensure that the issuer is
satisfied with the price.
Usually, IPOs are underpriced, and prices rise significantly right after the stocks start trading in
the secondary market. This means that the issuer potentially leaves significant amounts of money
on the table. IPOs are underpriced by about 17% on average in the US and UK, and markets have
come to like underpriced IPOs as a signal of quality of IPO.
Risk management:
Not all risk can be hedged, there is no way of getting rid of every possible risk, nor is this
necessarily desirable (hedging is costly), but FI must be careful not to be exposed to too much risk
(or they will be bankrupt). They hence to analyze very well how risks interact with each other and
avoid most severe ones. This is the central idea behind risk management, and all FI have a separate
risk management department.
→ credit risk is the risk that promised cash flows from loans and securities are not paid in full.
Credit risk arises for two reasons:
- Loans were made to people who shouldn’t have received them→ adverse selection and
moral hazard.
- Adverse events, such as general economic downturn, caused people to default on their
obligations.
FI can only try to fix the first one.
In order to manage credit risk, you can use the screening, which is essential for identifying high
quality borrowers and denying to unreliable borrowers (it is done ex ante). You can also do
monitoring, especially of outstanding loans which prevent borrowers from engaging in more risky
actions (it is done ex post. Once a loan is obtained, since the payment is fixed in case of no default,
incentive to take more risk, and loan contracts often ask the borrower to give up collateral in case
of default).
→ collateral: can induce self-selection of borrowers. The high-risk borrowers may realize that
they will lose the collateral with high profitability and may refrain from applying for a loan.
Collateral may also reduce moral hazard, in fact borrowers have something they might lose, and it
helps banks to reduce losses in case default occurs.
However, research also suggests that when collateral is too valuable, bank may screen too little.
Lending standards may vary over the cycle, in a boom, lax lending standards in a crisis instead
banks screen more.
Does charging a higher interest rate on loans always increase the bank’s profits? No because the
borrowers willing to pay a high interest rate are exactly those the bank would like to avoid (adverse
selection): better to do credit rationing.
Credit rationing means either refusing loans to some customers (even if they are willing to pay a
high interest rate) or restricting the size of the loan.
It may be optimal for the bank to do credit rationing:
→The bank knows that by changing the interest rate it changes the average quality of the pool of
borrowers asking for credit.
Screening: it can be achieved by using:
1. Hard information→ information that can be encoded in number, such as credit store
2. Soft information→ subjective aspects that can’t be processed automatically
3. Specialization in lending→ by specializing in a particular type of lending FIs can screen
more, but it has a negative side such as the lack of diversification.
But FI do not just screen and monitor to alleviate asymmetric information problems.
Their business model also helps:
Long term relationships with their customers (repeated interactions alleviate asymmetric info)
and loan commitments (provide up to $X at pre-specified interest rate, a credit line). Customer
will come back when it needs more money, but agrees to provide info continuously, even when it
does not ask for credit.
Interest rate risk:
Financial institutions, banks in particular, specialize in earning a higher rate of return on their
assets relative to the interest paid on their liabilities. Although it may seem simple, you have to
manage many risks, and we will look at interest rate risk.
What happens to an FI if the interest rate change?
- Changes in income: interest income on variable-interest loans and other securities will
change, and also interest rate paid on liabilities will change→ income gap analysis.
- Changes in net worth: values of assets and liabilities on the balance sheet will readjust,
depending on their duration→ duration gap analysis.
Remember that there is a distinction between income and change in value, as we will use book
values for income gap and market values for duration gap.
Income gap analysis: the idea is to look at the balance sheet and go over the asset side, collect all
items whose income flow will adjust with the interest rate: rate-sensitive assets (RSA, and the
items left are rate insensitive assets). You than do the same for the liability side: rate sensitive
liabilities (RSL, the items left are the rate insensitive liabilities).
The difference between these two positions will be an indicator by how much your income will
change.
𝑖𝑛𝑐𝑜𝑚𝑒 𝑔𝑎𝑝 = 𝑅𝑆𝐴 − 𝑅𝑆𝐿
Here we only define it for change in 1 year interest rates, but you can calculate one income gap for
each maturity bucket instead.
→RSA is a measure of the amount of assets that either reprice or mature within one year. It is the
number of dollars of assets (liability) that will pay (cost) variable interest rate.
→RSL is the amount of the liabilities that mature or reprice within a year.
The income gap can be positive or negative, depending on the exact composition of the FI’s
balance sheet.
If NII denotes, net interest income ∆𝑁𝐼𝐼 = 𝑖𝑛𝑐𝑜𝑚𝑒 𝑔𝑎𝑝 ∙ ∆𝑖, so interest rate changes can
negatively or positively affect net interest margin, depending on the sign of the income gap, and it
is greater than 0, banks make more money if interest rates rise, but loses out if interest rates fall.
It is generally complicated to determine the RSA and the RLS, therefore we need to find those
assets and liabilities whose income will change, because the interest rates will be reset within the
year. Some items are obvious, such as those with maturity less than one year for example), but
others also may be affected.
Determine the RSA:
Any asset with a maturity below 1 year, will change its interest income if interest rate changes, so
securities and commercial loans with maturity < 1 year. Some assets have 𝑚𝑎𝑡 > 1𝑌 but are
adjusted automatically, variable rate mortgages (𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑟𝑠 𝑝𝑎𝑦 𝑥% + 𝐿𝐼𝐵𝑂𝑅). But also,
income on 30-year fixed rate mortgages, even if they do not mature within 1 year, they can change,
in fact homeowners can decide to repay early by selling their homes or refinance mortgage at lower
rate.
Finally, income from securities with a term to maturity of > 1 year will not change.
Determine the RSL:
Any liability with a maturity < 1Ywill changes its interest income, expense for the bank, if interest
rate changes. Money market deposits, variable rate CDs and CDs below 1 year, Fed Funds or other
short borrowings. Checking and savings account have interest rate that can be changed at any time
by the bank, although usually banks keep them constant, partially RSL.
Pitfalls of income gap analysis, the main problems with income gap analysis are:
1. Short term focus: < 1 𝑦𝑒𝑎𝑟. A security with 1.5 years residual maturity could be a nonRSA.
2. If interest rates rise, the asset values of bonds, loans and securities with long maturities will
fall. Particularly relevant for mar-to-market accounting and if securities fall in value the
corresponding amount will have to be written off, reducing the bank’s net worth. And
duration gap analysis will help with this.
Duration gap analysis:
The idea is to calculate the duration of the FI’s assets, do the same for
liabilities and then compare the two to determine the duration of the
bank’s net worth. Recall the formulas, and
that if the change in interest is small then the formula is
We have a similar approach here, but %∆𝑃 is replaced with changes in
the bank’s net worth.
Recall that the duration is additive, so that the duration of a portfolio 𝑃 = 𝐴 + 𝐵 is just a market
value weighted average of duration of each asset:
𝑀𝑉𝐴
𝑀𝑉𝐵
𝐷𝑈𝑅𝑝 = 𝑀𝑉 +𝑀𝑉
× 𝐷𝑈𝑅𝐴 + 𝑀𝑉 +𝑀𝑉
× 𝐷𝑈𝑅𝐵 , by definition 𝑁𝑊 = 𝐴 − 𝐿, so 𝐴 = 𝑁𝑊 + 𝐿.
𝐴
𝐵
𝐴
𝐵
Hence if you see assets as a portfolio of net worth + liabilities:
𝐴
𝐿
𝐷𝑈𝑅𝑁𝑊 = 𝑁𝑊 × (𝐷𝑈𝑅𝐴 − 𝐴 × 𝐷𝑈𝑅𝐿 )
𝐿
𝐴
We can define 𝐷𝑈𝑅𝐺𝐴𝑃 ≡ 𝐷𝑈𝑅𝐴 − 𝐴 × 𝐷𝑈𝑅𝐿 so we have 𝐷𝑈𝑅𝑁𝑊 = 𝑁𝑊 × 𝐷𝑈𝑅𝐺𝐴𝑃 , finally since
∆𝑁𝑊
𝑁𝑊
∆𝑖
≈ −𝐷𝑈𝑅𝑁𝑊 × 1+𝑖 and we arrive at
∆𝑁𝑊
∆𝑁𝑊
𝐴
∆𝑖
≈ −𝐷𝑈𝑅𝐺𝐴𝑃 × 1+𝑖.
𝐿
∆𝑖
You have to remember that 𝐴 ≈ − (𝐷𝑈𝑅𝐴 − 𝐴 × 𝐷𝑈𝑅𝐿 ) × 1+𝑖. Hence DURgap (thing between
brackets) measures the sensitivity of a bank’s net worth, relative to the total value of assets in
response to changes in interest rates. An important assumption is that ∆𝑖 is the same for all assets
and liabilities, regardless of maturity structure.
Duration gap can be positive or negative, depending on the exact composition of the FI’s balance
sheet, so interest rate changes can be negatively or positively related to changes in net worth. In
either case the duration gap measures FI’s net worth exposure to interest rate risk.
If 𝐷𝑈𝑅𝑔𝑎𝑝 > 0 the FI’s liabilities have relatively shorter duration than its assets. In order to
change this, the FI may sell assets with high duration and convert them into assets with lower
duration.
Targeting duration gap:
Note that if an FI matched the duration of assets and liabilities then it would have little IRR
(𝐷𝑈𝑅𝑔𝑎𝑝 ≈ 0), but banks earn from the natural mismatch between long duration assets and short
duration liabilities. Thus, for a bank hedging IRR by altering the balance sheet can be costly, lose
profit margin.
Alternatively, the bank hedges by taking an opposite position in the derivatives market, interest
rate futures/forwards or interest rate swaps.
Financial regulation:
The financial system is one of the most heavily regulated industries in our economy. Today and
tomorrow, we will develop an economic analysis of why regulation of banking takes the form that
it does. Again, the two key concepts of adverse selection and moral hazard, provide the rationale
for government regulation. Regulation does not always work and actually it can have perverse
effects by increasing both moral hazard and adverse selection.
The areas of government regulation:
1. Government safety net (with deposit insurance and lender of last resort):
Panic of 1907 due to the failure of Knickerbocker trust. Widespread bank failures were quite
common in the nineteenth and early twentieth century: 1819, 1837, 1857, 1873, 1884, 1907, 193033, and in the last dates indicated over 10000 banks failed during the great depression. The number
was then drastically reduced after 1934, since which the US government is guaranteeing
depositors’ money (up to a certain limit), if the bank defaults.
→ deposit insurance:
Why does deposit insurance prevent bank failures? Because it prevents bank runs, which is a
systemic event where many depositors withdraw their money at the same time. The bank can
sustain some deposit outflows if they have ample reserves and once reserves are depleted, they
need to sell other assets to raise money, or borrow from others, but many assets are illiquid like
loans.
A perfectly solvent bank may go bankrupt because of a liquidity problem created by massive
withdrawals.
If you suppose deposit insurance doesn’t exist, and suddenly 5% of all banks become insolvent
(losses), depositors are unable to tell bad and good banks apart (there is asymmetric information
between creditors and borrowers). Remember that bank solve asymmetric information between
creditors and borrowers by making private loans, thus banks’ creditors do not know the quality of
the loan portfolio. Bank runs at both good and bad banks, failure of one hastens failures at other
banks (contagion effect), there is a “first come, first served” model which gives incentives to
withdraw first.
With DI, no incentive to withdraw at first sign of weakness from banking system. But why should
the government prevent bank failures and no other firms? Because banks are different, a bank
failure has consequences that are more socially undesirable than any other business, as people lose
their savings, contagion effects to other banks, borrowers lose access to credit or information on
borrowers’ credit worthless is lost.
Bank runs have been around for as long as there have been banks. But at the heart of the 2007
crisis was a run on the shadow banking system, and not depositors lining up in front of the ATM,
but sophisticated creditors not rolling over funds.
In the US the federal deposit insurance commission is the government agency that guarantees
deposits up to 250000$.
Insurance fund paid by banks themselves, like an insurance premium, and a similar system is
applied in Italy. Interestingly, they have never actually used taxpayers $, but if money runs out,
the government pays. DI can stop bank failures with no need for $, it prevents runs by acting on
expectations.
DI therefore is a great thing, as it can stop bank failures by stopping run and it doesn’t cost
taxpayers anything in practice or at least the cost was the lack of market discipline. The problem
is if your money is insured by the government, you will not worry about bank solvency. The banks
covered by DI face less scrutiny from creditors and the gamble with depositors’ money and take
on more risks: moral hazard.
In general, the presence of DI can remove the disciplining effect of bank runs on bank managers
and shareholders, especially problematic in countries with weak institutions. Moral hazard is why
deposit insurance is limited in scope (< 100𝑘, < 250𝑘).
Another problem with the government safety net is the creation of the “too big to fail” problem
which meant some FIs became so large that they play a systematically important role in the
economy, and they are too big for the government to let them fail. FI knows this and take
advantage, they grow in size and take on excessive risks, moral hazard. The first time this term
was used in Continental Illinois in 1984. All deposits, even greater than insurance and all bond
holders were fully repaid but this sets a dangerous precedent.
→ lender of last resort:
Deposit insurance is not the only form of the government safety net. It implicitly guarantees to
support banks in cases of failure are another common form and sometimes the central bank stands
ready to provide cheap lending to banks, acting as the lender of last resort.
The government safety net is necessary for stability of banking system (prevents bank runs),
however its presence creates moral hazard itself and this motivates further regulation to prevent
excessive risk raking by FIs.
2. Capital requirements:
The interests of depositors and bank owners are misaligned, the more so the less capital the bank
has. Higher capital performs two functions:
- Cushion against bank failure
- It aligns interest of bank owners with those of depositors/creditors, it reduces ROE
FIs with a lot of capital have more to lose if they fail and are less likely to engage in excessive risk
taking.
Minimum capital requirements: help solve the moral hazard problem induced by deposit insurance.
How much capital is enough? Hard to know in practice. Through most of the 1980’s, regulators
𝐸
used a simple minimum leverage ratio: 𝐴. There is a simple scale depending on the leverage ratio,
where > 5% means well capitalized, > 4% means adequately capitalized, < 4% means
undercapitalized and < 2% means critically undercapitalized.
The leverage ratio had a major shortcoming. It ignored the riskiness of assets; a risky commercial
loan would require same amount of capital as safe treasury bonds. A committee of central bankers
from many nations spent a long time in Basel searching for solutions.
- Basel I: (1988) 26 pages
- Basel II: (1999) > 500 pages, implemented in 2008 for all EU, but in US only for the 12
largest banks
- Basel III: 2013 last update, > 500 pages and 78 equations that was implemented in 2019
What is Basel all about? Risk weights applied to all assets and off-balance sheet activities. These
weights reflect the degree of risk and are used to calculate risk weighted assets. RWA are
calculated by multiplying each asset by its risk weight and then adding them up.
𝑁
𝑅𝑊𝐴 = ∑ 𝑅𝑊𝑖 ∙ 𝐴𝑖
𝑖=
Bank capital requirements are then specified as a percentage of its RWA, rather than total assets:
𝐸
𝐶𝑎𝑝𝑅𝑒𝑞 =
≥ 8%
𝑅𝑊𝐴
Basel I just assigned a RW to each category, where 0% (no capital needed) on reserves and
government debt of advance economies, 20% on securities from corporates rated ≥ 𝐴𝐴 −, the
50% on municipal bonds, residential mortgages and 100% on loans to consumers and
corporations.
The rule is simple, but what’s the problem? Banks engaged in regulatory arbitrage, invest in the
riskiest asset within the same risk weight class.
Basel II tried to fix the regulatory arbitrage by changing how RW are calculated, and banks can
use two methods:
- A standardized approach like Basel I, but with refined buckets of risks
- Or internal model-based approach, banks use their own models to determine the RW. The
models need to be validated by regulators. IRB is very complicated, only the largest banks
can afford to use the IRB
2007-2009 crisis revealed further problems of Basel II, as it didn’t require enough capital to
weather the financial crisis, as many banks were insolvent), also it relied on credit ratings for
weights, which proved unreliable during the crisis and finally it had a procyclical requirement,
since the RW increases during a bad time, it requires more capital from the bank exactly when it
is most short.
Basel III again is trying to fix these issues, as it put emphasis on quality of capital, on numerator
rather than denominator, it is less procyclical and risk-weighted requirement + leverage ratio +
liquidity ratios.
3. Restrictions on asset holdings:
Regulations limit the type of assets FI may hold:
- US commercial banks that may not hold common equity
- Pension funds can only hold AAA securities
Does this work? In 2007-2009 financial crisis the risk was not in equity, rather with subprime
related securities (AAA), but it is hard to know in advance. Sovereign debt in Europe, maybe now
it will be risk-weighted or there will be limits on % of assets.
4. Assessment of risk management:
Historically, regulation focused on the quality of assets. Even though the quality of assets may be
deemed acceptable at one point in time, it can deteriorate if the bank is unable to deal with
emerging risks. The quality of assets is still important, but there has been a shift towards
monitoring risk management systems of FIs.
As part of assessing FIs’ risk management, regulators require stress tests, which calculate the
bank’s losses under extreme circumstance, such as a 10% drop in the GDP or a 2-year recession
and if a bank fails a stress test usually a big deal.
VaR is the minimum potential loss a bank may have with a certain probability over a period of
time, for example a one day 1% VaR of 10M: a 1% probability of at least 10M loss over one day
period. GS has an average daily 1% VaR of 80M.
5. Macro-Prudential vs micro-Prudential:
→ micro-prudential:
regulation focuses on the solvency of individual institutions using the tools we have seen so far
such as stress testing, VaR and capital requirements.
→ macro-prudential:
Instead focuses on the solvency of the entire financial system. This is very difficult to do, but the
crisis has emphasized that looking at only individual institutions is not enough, the financial system
is more than the sum of its parts because they are all interconnected.
6. Prompt corrective action:
If the amount of a financial institution’s capital falls to low levels, two serious problems result.
First, the bank is more likely to fail because it has a smaller capital cushion if it suffers loan losses
or other asset write-downs. Second, with less capital, a financial institution has less “skin in the
game” and is therefore more likely to take on excessive risks. In other words, the moral hazard
problem becomes more severe, making it more likely that the institution will fail, and the taxpayer
will be left holding the bag.
Banks in the United States are now classified into five groups based on bank capital. Group 1,
classified as “well capitalized,” comprises banks that significantly exceed minimum capital
requirements and are allowed privileges such as the ability to do some securities underwriting.
Banks in group 2, classified as “adequately capitalized,” meet minimum capital requirements and
are not subject to corrective actions but are not allowed the privileges of the well-capitalized banks.
Banks in group 3, “undercapitalized,” fail to meet capital requirements. Banks in groups 4 and 5
are “significantly undercapitalized” and “critically undercapitalized,” respectively, and are not
allowed to pay interest on their deposits at rates that are higher than average. In addition, for group
3 banks, the FDIC is required to take prompt corrective actions such as requiring them to submit
a capital restoration plan, restrict their asset growth, and seek regulatory approval to open new
branches or develop new lines of business. Banks that are so undercapitalized as to have equity
capital that amounts to less than 2% of assets fall into group 5, and the FDIC must take steps to
close them down.
7. Chartering and examination:
Overseeing who operates financial institutions and how they are operated, referred to as financial
supervision or prudential supervision, is an important method for reducing adverse selection and
moral hazard in the financial industry. Because financial institutions can be used by crooks or
overambitious entrepreneurs to engage in highly speculative activities, such undesirable people
would be eager to run a financial institution. Chartering financial institutions is one method for
pre- venting this adverse selection problem; through chartering, proposals for new institutions are
screened to prevent undesirable people from controlling them. Regular on-site examinations,
which allow regulators to monitor whether the institution is complying with capital requirements
and restrictions on asset holdings, also function to limit moral hazard. Bank examiners give banks
a CAMELS rating. The acronym is based on the six areas assessed: capital adequacy, asset quality,
management, earnings, liquidity, and sensitivity to market risk. With this information about a
bank’s activities, regulators can enforce regulations by taking such for- mal actions as cease and
desist orders to alter the bank’s behavior or even close a bank if its CAMELS rating is sufficiently
low. Actions taken to reduce moral hazard by restricting banks from taking on too much risk help
reduce the adverse selection problem further because with less opportunity for risk taking, riskloving entrepreneurs will be less likely to be attracted to the banking industry. Chartering is similar
to the screening of potential borrowers, regulations restricting risky asset holdings are similar to
restrictive covenants that prevent borrowing firms from engaging in risky investment activities,
capital requirements act like restrictive covenants that require minimum amounts of net worth for
borrowing firms, and regular examinations are similar to the monitoring of borrowers by lending
institutions.
8. Disclosure requirements:
To ensure that better information is available in the marketplace, regulators can require that
financial institutions adhere to certain standard accounting principles and disclose a wide range of
information that helps the market assess the quality of an institution’s portfolio and the amount of
its exposure to risk. More public information about the risks incurred by financial institutions and
the quality of their portfolios can better enable stockholders, creditors, and depositors to evaluate
and monitor financial institutions and so act as a deterrent to excessive risk taking. Disclosure
requirements are a key element of financial regulation. Basel 2 puts a particular emphasis on
disclosure requirements, with one of its three pillars focusing on increasing market discipline by
mandating increased disclosure by banking institutions of their credit exposure, amount of
reserves, and capital. The Securities Act of 1933 and the Securities and Exchange Commission
(SEC), which was established in 1934, also impose disclosure requirements on any corporation,
including financial institutions, that issues publicly traded securities. In addition, the SEC has
required financial institutions to provide additional disclosure regarding their off- balance-sheet
positions and more information about how they value their portfolios. Regulation to increase
disclosure is needed to limit incentives to take on excessive risk and to upgrade the quality of
information in the marketplace so that investors can make informed decisions, thereby improving
the ability of financial markets to allocate capital to its most productive uses. Particularly
controversial in the wake of the global financial crisis is the move to so-called mark-to-market
accounting, also called fair-value accounting, in which assets are valued in the balance sheet at
what they could sell for in the market.
9. Consumer protection:
The existence of asymmetric information also suggests that consumers may not have enough
information to protect themselves fully in financial dealings. Consumer protection regulation has
taken several forms. The Consumer Protection Act of 1969 (more commonly referred to as the
Truth in Lending Act) requires all lenders, not just banks, to provide information to consumers
about the cost of borrowing, including the disclosure of a standardized interest rate (called the
annual percentage rate, or APR) and the total finance charges on the loan. The Fair Credit Billing
Act of 1974 requires creditors, especially credit card issuers, to provide information on the method
of assessing finance charges and requires that billing complaints be handled quickly.
10. Restrictions on competition:
Increased competition can also increase moral hazard incentives for financial institutions to take
on more risk. Declining profitability as a result of increased competition could tip the incentives
of financial institutions toward assuming greater risk in an effort to maintain former profit levels.
Thus, governments in many countries have instituted regulations to protect financial institutions
from competition. These regulations have taken two forms in the United States in the past. First
were restrictions on branching, which are described in Chapter 19, which reduced competition
between banks, but these were eliminated in 1994. The second form involved pre- venting nonbank
institutions from competing with banks by engaging in banking business, as embodied in the GlassSteagall Act, which was repealed in 1999. Although restrictions on competition propped up the
health of banks, they also had serious disadvantages: They led to higher charges to consumers and
decreased the efficiency of banking institutions, which did not have to compete as vigorously.
Thus, although the existence of asymmetric information provided a rationale for anticompetitive
regulations, it did not mean that they would be beneficial.
The theory of financial crises:
Financial crises are major disruptions in financial markets characterized by:
- Sharp declines in asset prices
- Failures of financial institutions
- Some government policy intervention afterwards
Although this financial crisis is different from a recession. A recession indicates an economic
contraction, in fact usually a financial crisis leads to a recession, but a recession cannot lead to a
financial crisis.
A recession can be caused also by a supply stock (the 1973 oil crisis), a trade/political shock
(collapse of the URSS) or a natural disaster (Japan tsunami).
Financial crises are a prevalent feature of our economies and have a lower frequency event
compared to recessions and over the last 120 years, banking crises worldwide have lasted 2-3 years
and cost 5-10% of GDP on average.
Since history tends to repeat itself, by studying financial crises we can learn from past mistakes
and try to prevent/contain future crises, as financial crises seem to have a similar pattern. They are
typically preceded by credit booms and asset price bubbles (many of those booms happened in real
estate). The seeds are often planted with financial liberalization or innovation and every single
financial crisis happened because of excessive debt, one way or another.
Stage 1: initiation (Debt Build-up)→ we have a credit boom and then a bust, an asset price boom
which is often accompanied to a bust and finally the increase in uncertainty, caused by the failure
of some major FI, such as Lehman. Talking about the credit boom we can say that it is an aggregate
amount of credit in the economy is higher than its long-rum trend, in other words, banks lend a lot
maybe “too much”. The additional credit increases demand for other assets, which appreciate
substantially in price (asset price boom). Often credit booms follow a financial liberalization, more
competition between banks, introduction of new types of loans or financial products and the
country liberalizes international capital flows. It’s not that all credit booms lead to a recession,
often credit booms are simple expansions of credit with no follow up problems and are good for
economic development.
A bubble: the price of an asset is well above the fundamental value, that is an unrealistic price,
unjustified by current conditions or predicted earnings and we saw that this can happen with stocks
fairly easily because of overconfident investors, but it can also happen with other assets, such as
housing.
Financial liberalization or innovation leads to new types of loans or other financial products.
Government safety net creates moral hazard and eventually, loan losses accrue, and asset values
fall leading to a reduction in capital. Financial institutions cut back in lending a process called
deleveraging. During a financial crisis, banks deleverage rather than increase capital. Since
𝐸
𝐶𝑎𝑝𝑅𝑒𝑞 = 𝑅𝑊𝐴, banks decrease denominator rather than increase numerator, because issuing
equity is especially costly during a crisis, stock prices are low. With less credit available, firms
can’t finance their growth but as a result economic activity decline.
Stage 2: banking crisis (real economy)→ as banks reduce lending, the economy suffers, the decline
in economic activity deteriorates bank balance sheets further as more borrowers are likely to
default and this is how a banking crisis starts.
If severe enough, these factors lead to a bank panic/run. As cash balances fall, FIs must sell assets
quickly and when assets need to be sold quickly, fire sales occur prices at which assets are sold
tend to be low as there is an excessive and quick sell off. Fire sales further deteriorate balance
sheets of banks because the value of remaining assets falls, and net worth decreases.
Stage 3: debt deflation but doesn’t always happen→ if the crisis also leads to a sharp decline in
overall prices, debt deflation occurs. A deflation is an episode of declining prices and expecting
more decreases in the future. A debt deflation means that with deflation, asset prices falls but debt
levels do not adjust therefore there is an overall increasing debt burden. This is the worst possible
outcome because it prolongs the stagnation for a long time.
Deflation is bad for the macro economy, as agents postpone consumption of durable goods, and
this makes consumption decrease and therefore also GDP decreases. Deflation is bad for finance
too and debt contracts are typically fixed in nominal terms. Hence, when prices fall, the value of
those fixed payments increases in real terms. Deflation therefore is good for lenders but bad for
borrowers, so the real value of debt becomes bigger and asset values do not rise, as it actually falls
in recession, and real value of liabilities increases and therefore the real value of net worth
decreases.
→ Japanese crisis:
Japan in the 1990s experienced a financial crisis that had all the 3 stages, including a long,
prolonged episode of deflation and stagnation. Japan was an incredible success story of strong
economic growth since WWII, like China today.
The economy was based on keiretsu, which is a conglomerate of companies around a bank who
provides the funding. Financial liberalization:
- Deregulation of interest rates on deposits, banks paid interest on deposits but did not
increase interest on loans, due to competition.
- Basel rules allowed Japanese banks to count unrealized stock gains (up to 45%) for equity,
and on euro dollar markets, Japanese banks borrowed extensively
Much of bank lending went into real estate, where prices skyrocketed and for a long time, the bank
of Japan kept interest rates low and the boom went on, but in 1990, the bubble reached its peak
and burst. In most extreme areas, current real estate value is around 1% of their previous levels.
Falling asset prices eroded bank capital, but banks were quite good at hiding their losses initially.
Eventually, undercapitalized banks kept lending to risky borrowers at good rates so not to
recognize losses on their balance sheet: zombie lending/loan evergreening.
→ The great depression of 1929:
The great depression was another example of a financial crisis followed by debt deflation, it has
been called the mother of all financial crises and its timing varied across nations but in most
countries, it started in 1930 (in the US 1929). The world economy did not fully recover until after
WWII.
→The 2007-2009 financial crisis:
is sometimes called the great recession and like the great depression of 1929 it originated in the
United States and then it affected the entire world. Actually, it affected some countries much more
than the US, as it did not lead to a debt deflation stage, in fact the US GDP and employment
recovered relatively quickly.
Lecture 22: exercises