Chapter 16
16.1 Expected present discounted values
The expected present discounted value of a sequence of future payments is the value today of this
expected sequence of payments. We can then compare two numbers, the expected present
discounted value and the initial cost. If the value exceeds the cost, we should go ahead and buy the
machine. If it does not, we should not.
But future payments and interest rates are uncertain, so we compute with expected future payments
and expected interest rates.
The present value depends positively on today's actual payment and expected future payments. The
present value depends negatively on current and expected future interest rates.
We can compute the present value of a sequence of real payments in two ways. One way is to
compute it as the present value of the sequence of payments expressed in Euros, discounted using
nominal interest rates, and then divided by the price level today. The other way is to compute it as
the present value of the sequence of payments expressed in real terms, discounted using real interest
rates.
16.2 Bond prices and bond yields
Bonds differ in two basic dimensions:
Default risk: The risk that the issuer of the bond (government or company) will not pay
back the full amount promised by the bond.
Maturity: The length of time over which the bond promises to make payments to the holder
of the bond.
Bonds of different maturities each have a price and an associated interest rate called the yield to
maturity, or simply the yield. Yields on bonds with a short maturity, typically a year or less, are
called short-term interest rates. Yields on bonds with a longer maturity are called long-term interest
rates.
The relation of how the yield depends on the maturity of a bond is called the yield curve, or the
term structure of interest rates.
The vocabulary of bond markets:
Government bonds are issued by the government or government agencies, corporate
bonds are issued by firms (corporations).
Bond ratings, bonds are rated for their default risk, from AAA to C. The difference between
the interest rate paid on a given bond and the interest rate paid on the bond with the highest
(best) rating is called the risk premium associated with the given bond. Bonds with high
default risk are sometimes called junk bonds.
Bond that promise a single payment at maturity are called discount bonds. The single
payment is called the face value of the bond.
Bonds that promise multiple payments before maturity and one payment at maturity are
called coupon bonds. The payments before maturity are called coupon payments The ratio
of coupon payments to the face value is called the coupon rate. The current yield is the
ratio of the coupon payment to the price of the bond. The life of a bond is the amount of
time left until the bond matures.
Bonds are typically nominal bonds: they promise a sequence of fixed nominal payments.
, There are, however, other types of bonds. Among them are indexed bonds, bonds that
promise payments adjusted for inflation rather than fixed nominal payments.
For bonds, we suppose that we and financial investors care only about the expected return. This
assumption is known as the expectations hypothesis. It is a strong simplification: we are likely to
care not only about the expected return, but also about the risk associated with holding each bond.
We use arbitrage to denote the proposition that expected returns on two assets must be equal.
Arbitrage between one- and two-year bonds implies that the price of two-ear bonds is the present
value of the payment in two years, discounted using current and next year's expected one-year
interest rates.
The yield to maturity/n-year interest rate on an n-year bond is defined as that constant annual
interest rate that makes the bond price today equal to the present value of future payments on the
bond.
Long-term interest rates reflect current and future expected short-term interest rates.
The yield curve is the curve formed by all one-year interest rates (?). When the yield curve is
upward sloping (when long-term interest rates are higher than short-term interest rates) this tells us
that financial markets expect short-term rates to be higher in the future. When the yield curve is
downward sloping (when long-term interest rates are lower than short-term interest rates) this tells
us that financial markets expect short-term interest rates to be lower in the future.
16.3 The stock market and movements in stock prices
Firms finance themselves in three ways. First, and this is the main channel for small firms, through
bank loans. Second, through debt finance (bonds and loans). And third, through equity finance
(issuing stocks or shares). Instead of paying predetermined amounts as bonds do, stocks pay
dividends in an amount decided by the firm, paid from the firm's profits.
We use the same arbitrage argument we used for bonds earlier. Assume financial investors care only
about expected rates of return. Equilibrium then requires that the expected rate of return from
holding stocks for one year to be the same as the rate of return on one-year bonds. However, this
ignores the fact that holding a stock is more risky than holding a bond. Arbitrage implies that the
price of the stock today must be equal to the present value of the expected dividend plus the present
value of the expected stock price next year.
Two equivalent ways of writing the stock price:
The nominal stock price equals the expected present discounted value of future nominal
dividends, discounted by current and future nominal interest rates.
The real stock price equals the expected present discounted value of future real dividends,
discounted by current and future real interest rates.
Stock prices follow a random walk: each step it takes is as likely to be up as it is to be down. Its
movements are therefore unpredictable.
A monetary expansion and the stock market: Suppose the central bank decides to adopt a more
expansionary monetary policy (LM curve shifts down). How will the stock market react?
If they fully anticipated the expansionary policy, then the stock market will not react: neither
its expectations of future dividends nor its expectations of future interest rates are affected
by a move it had already anticipated.
If the policy is at least partly unexpected, the stock prices will increase. This is for two
, reasons, first it implies lower interest rates for some time; second, it also implies higher
output for some time (until returns to natural rate). Therefore higher dividends (equation).
To summarise: stock prices depend very much on current and future movements in activity. But this
does not imply any simple relation between stock prices and output. How stock prices respond to a
change in output depends on: (1) what the market expected in the first place, (2) the source of the
shocks behind the change in output, and (3) how the market expects the central bank to react to the
output change.
16.4 Risk, bubbles, fads and asset prices
So far we have assumed that people were risk neutral. In fact, people, including financial
investors, are risk averse. They care both about expected return and risk. Most of finance theory is
indeed concerned with how people make decisions when they are risk averse, and what risk
aversion implies for asset prices.
If people perceive stocks to be more risky than bonds, and people dislike risk, they are likely to
require a risk premium to hold stocks rather than bonds. This risk premium is called the equity risk.
The stock price is still equal to the present value of expected future dividends. But the discount rate
here equals the interest rate plus the equity premium.
So far, we have assumed that stock prices were always equal to their fundamental value, defined
as the present value of expected dividends. But stock prices are not always equal to their
fundamental value, stocks are sometimes underpriced or overpriced.
Stock prices may increase just because investors expect them to. Such movements in stock prices
are called rational speculative bubbles: financial investors might well be behaving rationally as
the bubble inflates. In a speculative bubble, the price of a stock is higher than its fundamental value.
Investors are willing to pay a high price for the stock, in anticipation of being able to resell the stock
at an even higher price.
Chapter 20
20.1 From a housing problem to a financial crisis
Was the sharp housing price increase from 2000 2006 justified? Some increase in prices was clearly
justified:
The 2000s were a period of unusually low interest rates. So mortgage rates were also low,
increasing demand and therefore housing prices.
Mortgage lenders became increasingly willing to make loans to more risky borrowers.
These mortgages, known as sub-prime mortgages, had existed before, but became more
prevalent in the 2000s.
While the trigger of the crisis was indeed the decline in housing prices, its effects were enormously
amplified. Even those economists who had anticipated the housing price decline did not realize how
strong amplification mechanisms would be. To understand them, we must return to the role of
banks.
The role of banks:
What happened in the crisis is a combination of factors. Banks had too little capital. Liabilities were
,very liquid. Assets were often very illiquid. The outcome was a combination of both solvency and
liquidity problems, which quickly paralysed the financial system. We now look at it in more detail:
- Leverage:
Capital ratio: The ratio of capital to assets.
Leverage ratio: The ratio of assets to capital (inverse of capital ratio).
If some of the assets of a bank go bad (e.g. borrowers cannot repay loans), and as a result of that the
liabilities exceed the assets, then the bank is bankrupt. This is indeed what happened during the
crisis: many banks were highly leveraged, so that even limited losses very much increased the risk
of bankruptcy.
Why was leverage so high? Higher leverage means higher expected profit. But leverage also
increases risk: the higher the leverage, the more likely the bank is to go bankrupt. Why did they do
so? First, banks probably underestimated the risk they were taking (were good times). Second, the
compensation system and bonus payments also gave incentives to managers to go for high expected
returns without fully taking risk into account. Third, while financial regulation required banks to
keep their capital ratio above some minimum, banks found new ways of avoiding the regulation
(e.g. SIVs).
SIV stands for structured investment vehicle. Think of it as a virtual bank, created by an actual
bank. To reassure the investors that they will get repaid, the SIV typically has a guarantee from the
actual bank that it will provide funds if needed. They created these to be able to increase leverage,
and thus expected returns. When the crisis hit, it became clear that banks had in effect created a
shadow banking system, and that leverage of the banking system as a whole was much higher than
had been perceived.
AIG stands for American International Group. It is an insurance company, it would sell not only
regular insurance but also insurance against default risk through the sale of credit default swaps, or
CDS. When the crisis hit, AIG had to make good on many of its promises, but it just did not have
the funds to do so. Thus, banks realised that their assets were much riskier than perceived.
Again, leverage of the system (including now banks, SIVs, and CDS issuers such as AIG) was
much higher than had been perceived.
- Complexity:
Another important development was the growth of securitisation. Securitisation is the creation of
securities based on a bundle of assets. For instance, a mortgage-based security, or MBS, is a title
to the returns from a bundle of mortgages (number often in tens of thousands). The advantage is that
many investors, who would not want to hold individual mortgages, will be willing to buy and hold
these securities.
Securisation would seem like a good idea, a way of diversifying risk and getting a larger group of
investors involved in lending to households or firms. And, indeed it is. But it also came with a large
cost. It was a risk that rating agencies, those firms that assess the risk of various securities, had
largely missed: when underlying mortgages went bad, assessing the value of the underlying bundles
in the MBSs in the CDOs (collateralised debt obligations, senior- and junior securities), was
extremely hard to do. These assets came to be known as toxic assets. It led investors assume the
worst and be very reluctant either to hold them or to continue lending to those institution that did
hold them.
- Liquidity:
Another development was the development of other sources of finance than deposit accounts by
banks. Increasingly, they relied on borrowing from other banks or other investors, in the form of
short-term debt, to finance the purchase of their assets, a process known as wholesale funding. It
would again seem like a good idea, giving banks more flexibility in the amount of funds they can
use to make loans or buy assets. But it had a cost, if other banks or investors worried about the
value of the assets held by that bank, they decided to stop lending to the bank, thus resulting in the
, bank finding itself short of funds and to be forced to sell some of its assets. If these assets are
complex and hard to sell, it may have to sell them at very low prices.
- Amplification mechanisms:
As the crisis got worse, solvency and liquidity concerns increased sharply, each reinforcing the
other:
Housing prices declined → some mortgages went bad → high leverage banks → sharp
decline capital banks → banks forced to sell some assets → assets hard to value → sell them
at very low prices (fire price sales) → decreased value of similar assets remaining →
further decline in capital → forcing further sales of assets and further declines in prices
The complexity of the securities (MBSs, CDOs) and of the true balance sheet of banks (and
their SIVs) made it very difficult to assess the solvency of banks and their risk of
bankruptcy. Thus, investors (and banks) became very reluctant to continue to lend to them
(each other), and wholesale funding came to a stop, forcing further asset sales and price
declines.
The difference between the risk less rate (rate of three-month government bonds) and the rate at
which banks are willing to lend to each other (Libor rate) increased. This difference is known as
the Ted spread.
By mid-September, both mechanisms were in full force. The financial system had become
paralysed: banks had basically stopped lending to each other or to anybody else. Quickly, what had
been largely a financial crisis turned into a macroeconomic crisis.
20.2 The use and limits of policy
The immediate effects of the financial crisis on the macroeconomy were twofold: first, a large
increase in the interest rates at which people and firms could borrow (became nearly impossible to
borrow at all); second, a dramatic decrease in confidence (together with lower stock prices resulted
in a sharp decrease in consumption).
Higher interest rates, the inability to borrow, lower stock prices and lower confidence all combined
to decrease the demand for goods. In the face of this large decrease, policy makers did remain
passive. The most urgent measures were aimed at strengthening the financial system, but not every
country had the same initial policy response:
USA: First, to prevent a bank run by depositors they increased the deposit insurance (limited
effect as much of the funding of banks come not from deposits but from short-term debt).
Second, the Fed put in place a number of liquidity facilities to make it easier to borrow
from the Fed to avoid banks having to sell their assets at fire sale prices because of investors
wanting their funds back. The Fed also increased the set of assets that financial institutions
could use as collateral when borrowing from the Fed.
Third, the US government introduced a program, called the Troubled Asset Relief Program, or
TARP, aimed at cleaning up banks. The goal was to increase the capital (ratio) of banks (and thus
decreasing leverage). The goal was to allow them to avoid bankruptcy and, over time, return to
normal.
Europe: To stimulate economic activity, the official interest rates were cut in a sequence of
steps. Also, European banks were granted access to essentially unlimited liquidity at a fixed
interest rate at maturities of up to a year.
Only difference between the purchase by the ECB of covered bonds and the Fed TARP
program is that the Fed would buy mortgage-based securities directly, while the ECB would
buy them indirectly through the banks (and thus being exposed to less risk).
Fiscal and monetary policies were used aggressively as well:
Fiscal policy: During the crisis a lot of governments turned to fiscal policy using a combination of
tax cuts and increases in spending. The effect of these fiscal actions was a large increase on
