Chapter 7
Interest Rates
Cost of Money and Interest Rate Levels
Determinants of Interest Rates
The Term Structure and Yield Curves
Using Yield Curves to Estimate Future
Interest Rates
7-1
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
What four factors affect the level of interest rates?
•
Production opportunities
•
The more productive a business thought the new investment
would be, the more return (i.e. interest rate) the business could
afford to offer investors for their savings.
Production opportunities
•
➔ Interest rates
Time preferences for consumption
•
If time preferences for current consumption would be high,
savings would be low, interest rate would be high, and capital
formation would be difficult.
Current consumption
➔ Savings
➔ Interest rates
7-2
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
What four factors affect the level of interest rates?
•
Risk
•
The higher the riskiness of the loan, the higher the required rate of
return (interest rate).
Risk
•
➔ Interest rates
Expected inflation
•
The higher the expected rate of inflation, the larger the required
dollar return (interest rate).
Expected inflation
➔ Interest rates
7-3
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Determinants of Interest Rates
r = r* + IP + MRP+ DRP + LP
r
= The “nominal (quoted)” rate of interest on a given security
r*
= The “real” risk-free rate of interest. Like a T-bill rate, if there was no
inflation. r* changes over time and difficult to measure. Typically ranges from 1%
to 5% per year.
IP
= Inflation premium. IP is equal to the average expected rate of inflation
over the life of security.
–
–
–
Treasury Inflation Protected Security (TIPS) whose its value increases with inflation.
See my papers regarding interest rates (Paper#1, Paper#2, Paper#3)
Which alternatives do you prefer? (3% interest rate, $1,000 cash, Heating oil $1 per
gallon at the beginning of the year, Expected inflation 3.5%)
1) Saving money now and buying HO later: You get 1,030/1.035 = 995 gallons.
2) Buying HO now: 1,000/1 = 1,000 gallons.
In real terms, you would be worse off for 1) because interest earned is insufficient to
7-4
offset inflation.
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Determinants of Interest Rates
r = r* + IP + MRP+ DRP + LP
rRF
= the “nominal (quoted)” risk-free rate of interest, such as T-bill, which is
very liquid and free of most types of risk (rRF = r*+IP)
–
Example: If r*=1.7% and the average expected inflation =1.5% over the
next 5 years, the nominal 5-year T-bond rate would be 3.2%.
MRP
= Maturity risk premium (the so-called “term premium”). The longer-term
bonds are exposed to a significant risk of price declines due to increases in inflation
and interest rates
–
–
MRP is time-varying (The MRP rises when interest rates are more volatile
and uncertain)
Long-term rates are generally higher than short-term rates due to MRP.
7-5
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Determinants of Interest Rates
r = r* + IP + MRP+ DRP + LP
DRP
= Default risk premium. DRP reflects the possibility that the issuer will not
pay the promised interest or principal at the stated time.
–
–
–
–
The higher the bond’s credit rating, the lower the default risk and,
consequently, the lower its interest rate.
DRP (“credit spread”) = Corporate bond quoted rate – T-bond quoted rate
(with similar maturity and liquidity) (e.g. ThaiBMA for credit spread)
DRP is time-varying (DRP is high when economy is weaker and borrowers
are more likely to have a hard time paying off their debts)
See my papers regarding credit spreads (Paper#1, Paper#2)
LP
= Liquidity premium. LP reflects the fact that some securities cannot be
converted to cash on short notice at a “fair” market price.
–
–
Liquidity measures: Trading volume (e.g. SET), Bid-Ask spreads (e.g. BOT)
LP is time-varying (The LP soared during the recent financial crisis)
7-6
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Premiums Added to r* for Different Types of Debt
IP
S-T Treasury
✓
L-T Treasury
✓
S-T Corporate
✓
L-T Corporate
✓
MRP
DRP
LP
✓
✓
✓
✓
✓
✓
7-7
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Yield Curve and the Term Structure of Interest Rates
•
•
•
•
Term structure: relationship
between interest rates (or yields)
and maturities.
Yield Curve for May 2011
16
Yield Curve for March
1980
14
The yield curve is a graph of the
term structure.
12
The May 2011 US Treasury yield
curve is shown at the right.
8
10
Yield Curve for
February 2000
6
4
Implications: Corporate treasurers
(Investors) decide whether to borrow
by (invest in) short- or long-term
bonds.
•
Interest
Rate (%)
See yield curve at ThaiBMA
Yield Curve for
May 2011
2
0
0
10
20
30
Years to Maturity
Short
Term
Intermediate
Term
Long
Term
7-8
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Constructing the Treasury Yield Curve: IP
r = r* + IP + MRP
•
•
Step 1: Find the average expected inflation rate over Years 1 to N.
Assume inflation is expected to be 5% next year, 6% the following
year, and 8% thereafter.
N
IP1 = 5% / 1 = 5.00%
INFL t

IP10 = [5% + 6% + 8%(8)] / 10 = 7.50%
t =1
IPN =
IP20 = [5% + 6% + 8%(18)] / 20 = 7.75%
N
When inflation is expected to increase (decrease), longer (shorter)
term bonds have higher IP.
7-9
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Constructing the Treasury Yield Curve: MRP
•
Step 2: Find the appropriate maturity risk premium (MRP).
For this example, the following equation will be used to find a
security’s appropriate maturity risk premium.
MRP1 = 0.1%  (1 − 1) = 0.0%
MRPt = 0.1% (t – 1)
MRP10 = 0.1%  (10 − 1) = 0.9%
MRP20 = 0.1%  (20 − 1) = 1.9%
Notice that since the equation is linear, the maturity risk premium
is increasing as the time to maturity increases, as it should be.
7-10
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Add the IP and MRP to r* to Find the Appropriate
Nominal Rates
Step 3: Adding the premiums to r*.
rRF, t = r* + IPt + MRPt
Assume r* = 3%,
rRF ,1 = 3% + 5% + 0.0% = 8.0%
rRF ,10 = 3% + 7.5% + 0.9% = 11.4%
rRF ,20 = 3% + 7.75% + 1.9% = 12.65%
7-11
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Hypothetical Yield Curve
Interest
Rate (%)
15
Maturity risk premium
•
•
10
Inflation premium
5
Real risk-free rate
0
1
10
An upward-sloping yield
curve.
Upward slope due to (1)
an increase in expected
inflation (IP) and (2) an
increase in maturity risk
premium (MRP).
Years to
Maturity
20
7-12
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Yield Curve When Inflation is Expected to Rise/Drop
The slope of the
yield curve depends
primarily on 2
factors
(1) Expectations
about future
inflation (IP)
(2) Effects of
maturity on
bonds’ risk
(MRP)
7-13
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Relationship Between Treasury Yield Curve and Yield
Curves for Corporate Issues
•
•
•
•
Corporate yield curves are higher than that of Treasury securities,
though not necessarily parallel to the Treasury curve.
The spread between corporate and Treasury yield curves widens as
the corporate bond rating decreases.
Since corporate yields include a default risk premium (DRP) and a
liquidity premium (LP), the corporate bond yield spread can be
calculated as:
r= r* + IP + MRP
r= r* + IP + MRP+DRP+LP
Corporate bond
= Corporate bond yield − Treasury bond yield
yield spread
(LP is less important than DRP)
= DRP + LP
Corporate bonds’ DRP & LP are affected by their maturities. DRP & LP
of short-term corporate bond are lower.
•
•
DRP: There is less chance for firm to go bankrupt over the next few years
LP Investors can buy a short-term bond without doing as much credit checking as
would be necessary for a long-term bond. Thus, investors can buy and sell short7-14
term bond relatively rapidly.
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Representative Interest Rates on 5-Year Bonds in
May 2011
7-15
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Illustrating the Relationship Between Corporate and
Treasury Yield Curves
• Corporate yield curve is
above Treasury yield curve,
but not necessarily parallel.
• The slope of the yield curve
is a good predictor of
RECESSION! (see FRED)
7-16
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Pure Expectations Theory
•
•
•
The pure expectations theory focuses on Treasury bonds.
The pure expectations theory assumes that the maturity risk (term)
premium for Treasury securities is zero (MRP = 0).
The pure expectations theory contends that the shape of the yield curve
depends on investors’ expectations about future interest rates. Put
differently, L-T rates are an average of current and future S-T rates.
•
•
If interest rates are expected to increase, L-T rates will be higher than
S-T rates, and vice-versa. Thus, the yield curve can slope up, down,
flat or even humped.
Information content of the yield curve
•
If the pure expectations theory is correct, you can use the yield curve
to “back out” expected future interest rates.
7-17
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
An Example: Observed Treasury Rates and Pure
Expectations
Maturity
Yield
1 year
6.0%
2 years
6.2
3 years
6.4
4 years
6.5
5 years
6.5
If the pure expectations theory holds, what does the
market expect will be the interest rate on one-year
securities, one year from now? Three-year securities,
two years from now?
7-18
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
One-Year Forward Rate
6.0%
0
x%
1
2
6.2%
1(1+0.062)2 = 1(1+0.060)(1+X)
(1.062)2 = (1.060) (1 + X)
1.12784/1.060 = (1 + X)
6.4004% = X
•The pure expectations theory says that one-year securities will
yield 6.4004%, one year from now.
•Notice, if an arithmetic average is used, the answer is still very
close. Solve: 6.2% = (6.0% + X)/2, and the result will be 6.4%.
7-19
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Three-Year Security, Two Years from Now
6.2%
0
1
x%
2
3
4
5
6.5%
(1.065)5 = (1.062)2 (1 + X)3
1.37009/1.12784 = (1 + X)3
6.7005% = X
7-20
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Conclusions about Pure Expectations
•
•
Some would argue that the MRP ≠ 0, and hence the pure
expectations theory is incorrect.
Most evidence supports the general view that lenders
prefer S-T securities, and view L-T securities as riskier.
– Thus, investors demand a premium to persuade them to
•
hold L-T securities (i.e., MRP > 0).
The Pure Expectations Theory (MRP = 0) ➔ The Expectation
Theory (MRP = Constant) ➔ In reality, MRP = Time-varying!
(See my paper)
7-21
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning
Macroeconomic Factors That Influence Interest Rate
Levels
•
•
•
•
Federal reserve policy
Federal budget deficits or surpluses
International factors
Level of business activity
7-22
Reference: Essentials of Financial Management, 3rd edition, Brigham et al. (2014), Cengage Learning