Transcript Bond Math

6 September
FNCE 4070
Financial Markets and Institutions
Duration
N
Duration =
CFi
åti 1+ R ti
( )
i=1
N
CFi
å 1+ R ti
)
i=1 (
How interest rates affect duration
• For a single cashflow interest rates do not
affect duration
• For multiple cashflows on different dates
– as interest rates rise duration decreases
– as interest rates fall duration increases
Risk and Duration
DR
DPV » ´ Duration ´ PV
1+ R
Inflation
• Inflation occurs when the prices of goods and services
increase over time.
– Inflation cannot be measured by an increase in the cost of
one product or service, or even several products or
services. Rather, inflation is a general increase in the
overall price level of the goods and services in the
economy (Fed Reserve comment)
• The inflation rate is the percentage change in a price
index.
• General consensus is that an inflation rate of around
2% is reasonable…
– Many countries have adopted an explicit inflation target of
around 2%
Related Terms
• Deflation
– A sustained decrease in the aggregate price level,
which corresponds to a negative inflation rate
• Hyperinflation
– An extremely fast increase in the aggregate price level,
which corresponds to an extremely high inflation rate
• Disinflation
– A decline in the inflation rate, such as from 10% to 5%.
Note, inflation rates remain positive just reduces.
Deflation
• When deflation occurs the value of money
increases.
– Debt contracts are written in fixed amounts means
that real liabilities are increasing.
– Faced with increasing real debt costs a company that
is short of cash will cut its spending, workforce etc.
– Less spending and high unemployment exacerbate the
situation
• Occurred in Great Depression, briefly in US during
2008-9 and periodically in Japan since the late
1990’s
Episodes of Hyperinflation
• It is considered that the basic cause for
hyperinflation is too much money in circulation.
• Germany
– In 1923-24 at the peak prices doubled every 3.7 days
• Yugoslavia
– In January 1994 the monthly inflation rate peaked at
313 million percent
• Zimbabwe
– In November 2008 the monthly inflation rate peaked
at 79.6 billion percent
Episode of Disinflation around the
world
Year
1979
1980
1983
1984
1985
Germany
4.0
5.4
3.3
2.4
2.1
United States
11.3
13.5
3.2
4.3
3.5
United Kingdom
13.4
18.0
4.6
5.0
6.1
Country
Consumer Price Index (CPI)
• It measures the relative cost of a basket of goods
where the basket is changed infrequently
• Problems with CPI
– Three main biases
• Substitution bias - As the price of one good or service rises it may
be substituted with another. This will cause an upwards bias in the
inflation rate
• Quality bias - As the quality of the same product improves over
time it may satisfy peoples needs and wants better. This will cause
an upwards bias in the inflation rate
• New Product Bias - New products are frequently introduced and
these are not adequately reflected in the basket. This will cause
an upwards bias in the inflation rate.
• CPI-U (urban) is used to adjust the notional for TIPS
Personal Consumption Expenditures
(PCE)
• This covers all personal consumption in the US
– Done via business surveys.
– This is the main index that the Fed uses for
targeting inflation.
Explaining Inflation
• Supply-Demand
– The supply of money goes up.
– The supply of goods goes down.
– Demand for money goes down.
– Demand for goods goes up.
Explaining Inflation
• Cost-Push
– Rising costs compel businesses to raise prices
• Wages
• Raw materials
• Demand-Pull
– Increasing demand raises prices which then feeds
back into workers demands for higher wages to
compensate for the rising cost of living
• Increase in the money supply
• Increases in government purchases
• Increases in prices in the rest of the world
Inflation Expectations
• Once inflation becomes embedded in an economy,
businesses, workers, consumers etc all begin to expect
it and build those expectations into their actions.
• This creates an inflation momentum of its own
– Workers may demand larger wage increases to pay for
expected increases in the cost of living which in turn cause
goods to become more expensive.
• Can try to identify expectation through the prices of
TIPs
– But it is viewed that Insurance Companies have used TIPS
to match long-term liabilities and thus have depressed
yields and thus TIPs might underestimate inflation rates.
Distinction Between Real
and Nominal Interest Rates
• Real interest rate
1. Interest rate that is adjusted for expected
changes in the price level
ir = i – pe
2. Real interest rate more accurately reflects
true cost of borrowing
3. When the real rate is low, there are greater
incentives to borrow and less to lend
Distinction Between Real
and Nominal Interest Rates
• Real interest rate
ir = i – pe
We usually refer to this rate as the ex ante real
rate of interest because it is adjusted for the
expected level of inflation. After the fact, we can
calculate the ex post real rate based on the
observed level of inflation.
U.S. Real and Nominal
Interest Rates