Chapter 6: Interest Rates
Topics covered
• Cost of Money (Introduction)
• Factors affecting cost of money
– Fundamental factors
– Macroeconomic factors
•
•
•
•
Interest rate levels
Determinants of market interest rates
Term structure of interest rates
What determines the shape of the yield curve?
– Analysis of the impact of different factors (inflation risk,
maturity risk, liquidity risk, default risk) on the shape of yield
curves for treasury and corporate securities
• Risks associated with investment in overseas securities
Answers to selected problems
•
•
•
•
•
•
•
•
6-2 (2.25%)
6-3 (2 yr: 6%, 3 yr: 6.33%)
6-4 (1.5%)
6-5 (0.2%)
6-9 (6.8%)
6-11 (1.55%)
6-12 (0.35%)
6-13 (1.775%)
Self-Test (Page 187 and 188)
• Attempt Self-Test 1 page 187
• Attempt Self-Test 2 page 188
– Answers
a) 2.5%
b) 5.8%
c) 7.6%
d) 6.95%
e) 8.75%
f) 5.5%
•
Hint: Inflation Premium = 26 + x / 9
»
Everything else is given in question just put those values in
formula for calculating interest rate for T-bond and calculate X.
1. INTRODUCTION
Cost of money is the rental price of borrowing
money
Suppose you go to a bank to borrow $10,000 for paying off college
fees, you won’t be able to get this money for free.
The $10,000 come with a price tag attached, i.e. some rate of
interest, consider for example a 10% rate of interest.
This 10% interest rate is the cost of obtaining $10,000. This cost is
also known as the ‘cost of money’.
In a free economy, excess funds of lenders are allocated to borrowers through a
pricing system based on the supply of and demand for funds. This pricing system is
represented by interest rates, ‘i’ or the cost of money.
EXCESS FUNDS
LENDERS
BORROWERS
PRICING SYSTEM (i)
i
Supply of funds
i
Demand of funds
$
So, Now we know!
• Supply and demand of
funds determines the
interest rates (i).
• It is by providing these
rates that the
borrowers make use of
the funds provided by
the lenders.
• Generally interest rates are believed to be the
cost of money.
• However, in case of equity capital,
– Cost of money is called ‘Cost of equity’ and it
consists of dividends and capital gains expected by
the share holders
– Cost of equity = Dividends + Capital Gains
Remember!
Cost of
Money
• Cost from fund
users’ perspective
Cost of
Money
• Return from fund
providers’
perspective
MONEY
DEBT
CAPITAL
BANK
(PROVIDER)
COST OF MONEY (i)
CORPORATION
ABC
(USER)
Return for the funds provider Cost for the user of funds
MONEY
EQUITY
CAPITAL
STOCK-HOLDERS
(PROVIDER)
COST OF MONEY (D+C.G.)
CORPORATION
ABC
(USER)
Return for the funds provider Cost for the user of funds
QUICK FLASHBACK!
• ‘i’ is the cost of obtaining money.
• Supply and demand of funds determines the
interest rates.
2. Factors affecting cost of money, ‘i’
i. Fundamental factors affecting cost of money, ‘i’
The four most fundamental factors affecting the cost of money are:
1. Production opportunities
– Rate of return that producers expect to earn on invested capital.
2.
Time preferences for consumption
– The preferences of consumers for current consumption as opposed to
saving for future consumption.
Preference for current consumption
3.
Supply of funds
Interest rate
Riskiness of loan
– The chance that an investment will provide a low or negative return.
4.
Inflation
– The amount by which prices increase over time.
Expected Inflation
Demand of funds
Interest rate
For highly risky loans
investors expect
high rate of return,
i.e. high ‘i’
ii. Macroeconomic factors affecting
cost of money, ‘i’
1. Monetary policy tools
–
–
Federal Reserve Policies
Open Market Operations
2. Business boom
3. Business recession
4. Government budget deficit and surplus
1. Federal Reserve Policies
– An increase in required reserve ratio by central
bank means reduction in volume of deposits
which raises interest rates.
RRR
Supply of funds
Interest rate
– A decrease in required reserve ratio means
availability of excess deposits which decreases
interest rates.
RRR
Supply of funds
Interest rate
2. Open Market Operations
– Central bank buys back securities from open
market thus injecting money into the system
(increasing supply of money) which decreases
interest rates.
– Central bank sells securities into open market
thus absorbs money from the system (decreasing
supply of money) which increases interest rates.
3. Business booms
Increased demand of funds
Inflationary pressures
i
4. Business recession
Decreased demand of funds
Inflationary pressures
i
5. Government budget deficit
Government needs funds which means demand for funds
i
6. Government budget surplus
Government does not need funds which means demand for funds
i
3. INTEREST RATE LEVELS
• Capital is allocated to borrowers according to interest rates, i.
– Most capital across the world is allocated through the price system (that is,
interest rate).
• As can be seen in the figure below the excess funds of lenders are
allocated to the borrowers through a price system that is the
interest rate.
INTEREST RATE LEVELS
• The firms with the most profitable investment
opportunities are willing and able to pay the most for
capital, so they tend to attract it away from inefficient firms
and firms whose products are not in demand.
• There are many different types of capital markets (for
example, market for high risk securities, market for low risk
securities etc.) and they are all interconnected.
• Interdependence of capital markets
– Capital markets are interdependent, i.e. changes in supply and
demand of funds in one market are going to produce an impact
on the supply and demand of funds in the other market/s.
4. Determinants of Market
Interest Rates
• The interest rate quoted on any debt security is
composed of a real risk-free rate, r* , plus several
premiums that reflect inflation, the security’s
risk, its liquidity (or marketability), and the years
to its maturity. This relationship can be expressed
as follows:
Quoted interest rate = r = r* + IP + DRP + LP + MRP
How is interest rate determined on
debt securities?
• Required Rate of Return
– Nominal rate of return an investor requires to
make an investment worthwhile.
– Made up of 3 components:
• Real risk free rate
• Inflation premium
• Risk premium
Formulas
• Interest rate on short-term govt. security
• Interest rate on long-term govt. security
• Interest rate on corporate securities
• (lecture)
1. Real risk free rate of return, r*
• Definition
– r* is the minimum rate of return an investor
requires. This rate does not take into account
expected inflation.
• Changes in r*
• r* is equal to T-bill rate minus the inflation
premium.
2. Inflation Premium
• Inflation
– Definition: Loss in purchasing power of money
because of increase in prices.
– As inflation increases every dollar we own buys a
smaller percentage of goods and services.
• Why is inflation premium given?
• Impact of inflation on treasury and corporate
securities
• Calculation
Risk Free Rate
• r = r* + IP. It is the quoted rate on a risk-free
security such as a Treasury bill and it includes
a premium for expected inflation.
RF
Difference between Real Risk free interest
rate and Risk free interest rate
• Risk free interest rate = Real Risk free interest rate + Inflation premium
• Real Risk free interest rate = Risk free interest rate – Inflation premium
• What does the term ‘real’ means?
• What does the term ‘risk-free’ means?
3. Risk Premiums
1. DRP = default risk premium. This premium
reflects the possibility that the issuer will not
pay the promised interest or principal at the
stated time.
1. Treasury securities have no chance of default hence
DRP isn’t paid on them.
2. For corporate bonds higher the bonds rating, lower
its default risk and lower will be the interest rates.
3. Risk Premiums
2. LP: Liquidity Premium.
– Liquid asset: An asset that can be converted to
cash quickly at a fair market value.
– Liquidity premium is added to ROI on securities
that aren’t liquid.
– Liquidity premium for treasury and
corporate securities
3. Risk Premiums
3. MRP = Maturity Risk Premium. Longer-term bonds, even
Treasury bonds, are exposed to a significant risk of price
declines due to increases in interest rates; and a maturity risk
premium is charged by lenders to reflect the interest rate risk.
MRP is paid to cover interest rate risk.
– Interest rate risk: The risk of capital losses to which investors are
exposed because of changing interest rates.
While long term bonds are exposed to interest rate risk, short
term bonds are exposed to reinvestment rate risk.
– Reinvestment rate risk: The risk that a decline in interest rates will
lead to lower income when bonds mature and funds are reinvested.
Simple Problems
• If expected inflation during the next year is 2%
and currently the nominal interest rate on T-bills
is 5%, what is the real risk free rate of interest?
• If inflation is expected to average 4% during the
next year and the real risk free rate of interest is
3%, what should be the nominal rate of interest?
• Answers: 3% and 7%
Simple Problem
• Assume that the real risk free rate, r* = 2% and
the average expected inflation rate is 3% for each
future year. The DRP and LP for Bond X are each
1% and the applicable MRP is 2%.
– What is Bond X’s interest rate?
– Is Bond X a treasury bond or a corporate bond?
– Does Bond X more likely to have a 3 month or 20 year
maturity?
– Answers: 9%, corporate, 20 year
5. Term Structure of Interest Rates
• TSIR describes the relationship bond yields and maturities.
• Yield Curve
– Yield curve is actually a graph showing relationship between bond yields
and maturities.
• TSIR enables investors to quickly compare the yields offered on
short-term, medium-term and long-term bonds
• Three different types of Yield Curves:
– “Normal” Yield Curve
• Upward sloping yield curve
• Short term interest rates are low, long term interest rates are high.
– Inverted (“Abnormal”) Yield Curve
• Downward sloping yield curve
• Short term interest rates are high, long term interest rates are low.
– Humped yield curve
• A yield curve where interest rates on medium-term maturities are higher than rates on
both short-and long-term maturities.
• Why does it matter?
6. What determines the shape of the
yield curve?
Factors affecting shape of treasury securities
• Yield on a Treasury bond that matures in t years can be expressed as follows:
–
•
•
T-bond yield = r* + IPt + MRPt
It thus emerges that expected inflation levels and bond’s maturity are the main
factors affecting shape of yield curve of treasury securities. (Value of real risk free
rate of interest, r* varies somewhat over time because of changes in the economy
and demographics, these changes are random rather than predictable, r* thus is
assumed to remain constant.)
Inflation
• Expected inflation has an important effect on the yield curve for treasury securities.
If the market expects inflation to increase in the future, the inflation premium will
be higher on a 3-year bond than on a 1-year bond. On the other hand, if the market
expects inflation to decline in the future, long-term bonds will have a smaller
inflation premium than will short-term bonds.
•
Maturity
• Since investors consider long-term bonds to be riskier than short-term bonds
because of interest rate risk, the maturity risk premium always increases with
maturity.
When inflation is expected to increase
• Long term bonds have higher yields for 2
reasons:
– Inflation is expected to be higher in
future
• If market expects inflation to increase in
future, the inflation premium will be
higher the longer the term to maturity.
– Positive MRP
• MRP always increases with increasing
maturity of bond.
– Refer to table page 177
• When inflation is expected to
decrease
• If market expects inflation to
decline in future, long-term
bonds will have smaller inflation
premium (thus lower rates) than
short-term bonds.
• Such yield curves predict
economic downturn because
weaker economic conditions
generally lead to declining
inflation which leads to lower
long-term interest rates.
Factors affecting shape of Corporate bonds
• Corporate bonds include a default risk premium (DRP) and a
liquidity premium (LP). Therefore, the yield on a corporate
bond that matures in t years can be expressed as follows:
• Corporate bond yield = r* + IPt + DRPt + LPt + MRPt
• The corporate bonds carry additional default and liquidity
risks, this is the reason they pay premium for covering these
risks which is why the ‘i’ (interest rate) paid on corporate
bond, also called the yield, is always higher than that paid on
treasury bonds.
Because of their additional default and liquidity risk, corporate bonds yield more than treasury
bonds with the same maturity and BBB-rated bonds yield more than AA-rated bonds.
• Corporate bond yield can be calculated using the formula:
• r = r* + IPt + DRPt + LPt + MRPt
• LP and DRP of a corporate bond are affected by its maturity
• For example:
– Coca Cola's chances of defaulting on 10 years bond are less
as compared to defaulting on a 100 year bond, so higher
DRP is paid on the bond with ______ years to maturity?
• Long term bonds are also less liquid than short term bonds so
as maturity of bonds increases LP also increases.
7. Risks associated with investment in
overseas securities
• Two main types of risks that an investor,
looking to invest in foreign securities, faces
are: country risk and exchange rate risk.
• Country risk
– Risk that arises from investing or doing business in
a particular country
– This risk depends on a country’s economic, social
and political environment.
– Countries with safer political, social and economic
environment have less country risk and therefore
are safe choices for overseas investment.
• Exchange rate risk
– Risk of losing money in local currency because of fluctuation
in the value of foreign currency (in which investment was
being made).
– Recall example narrated in class (Pakistani earning US dollars
and praying for weak Pakistani rupee relative to US dollar).
– Suppose a US investor purchases Japanese bond. The US
investor gets interest rate in Japanese currency (Yen) which
must then be converted into US dollars whenever he wants
to make a purchase (as the investor resides in the US).
Whenever Yen strengthens in comparison to dollar it means
Yen can be converted into a larger number of US dollars and
the investor will be better off. On the other hand if Yen
weakens relative to dollar, it would mean Yen’s conversion
into dollar will give off fewer dollars and the investor will
have to suffer.
Interest rate determination
• Formula for calculation of interest rate on
short term treasury securities:
– Quoted interest rate = Real risk free rate + inflation premium
– r = r* + IP
t
• Formula for calculation of interest rate on long
term treasury securities:
– Quoted interest rate = Real risk free rate + inflation premium +
maturity risk premium
– r = r* + IP + MRP
t
t
Interest rate determination
• Formula for calculation of interest rate on
corporate securities:
– r = r* + IPt + DRPt + LPt + MRPt
– Quoted interest rate = Real risk free rate + inflation premium + default
risk premium + liquidity premium + maturity risk premium