© steven j. willis 2006 1 f inancial c alculators for l awyers lesson five-c interest rate...
TRANSCRIPT
© Steven J. Willis 2006 1
FINANCIAL CALCULATORS FOR
LAWYERS
Lesson Five-CInterest Rate Terminology
Yield
FINANCIAL CALCULATORS FOR
LAWYERS
Lesson Five-CInterest Rate Terminology
Yield
© Steven J. Willis 2006 2
Interest Rate Terminology
• At this point, we have defined six terms:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield– Yield to maturity– Internal rate of return
This term is dangerous in that it
has no meaning standing alone
without modifiers.
This term is dangerous in that it
has no meaning standing alone
without modifiers.
CAUTION
© Steven J. Willis 2006 3
Interest Rate Terminology
• At this point, we have defined six terms:
– Interest rate
– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield– Yield to maturity– Internal rate of return
These four are terms of art,
essential for an understanding of
finance.
These four are terms of art,
essential for an understanding of
finance.
© Steven J. Willis 2006 4
Interest Rate Terminology
• At this point, we have defined six terms:
– Interest rate
– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield– Yield to maturity– Internal rate of return
If you do not understand them, you should review the prior materials in Lesson 5-A and you should read the
accompanying text.
If you do not understand them, you should review the prior materials in Lesson 5-A and you should read the
accompanying text.
CAUTION
© Steven J. Willis 2006 5
Interest Rate Terminology
• At this point, we have defined six terms:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate
– Annual percentage rate– Simple yield– Yield– Yield to maturity– Internal rate of return
This is a legal term of art: i.e, it is defined by federal statute and regulation.
It is essential.
It is the subject of Lesson 5-B.
This is a legal term of art: i.e, it is defined by federal statute and regulation.
It is essential.
It is the subject of Lesson 5-B.
© Steven J. Willis 2006 6
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate
– Simple yield– Yield– Yield to maturity– Internal rate of return
Now we define these terms.
© Steven J. Willis 2006 7
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate
– Simple yield– Yield– Yield to maturity– Internal rate of return
These are not terms of art:
definitions may vary.
© Steven J. Willis 2006 8
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield
– Yield to maturity– Internal rate of return
These are terms of art.
They are also closely related.
© Steven J. Willis 2006 9
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate
– Simple yield– Yield– Yield to maturity– Internal rate of return
value market current
naivalue market current
nai
© Steven J. Willis 2006 10
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate (nai)– Periodic rate– Compounding period– Effective rate– Annual percentage rate
– Simple yield– Yield– Yield to maturity– Internal rate of return
value market current
naivalue market current
nai
© Steven J. Willis 2006 11
Interest Rate Terminology
value market current
naivalue market current
nai
• Because this is a function of the current market value, the simple yield varies from day to day, or even minute to minute.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If valued at $1000, the simple yield would be 10%:
– But if the value drops to $950, the simple yield increases to 10.526%:
© Steven J. Willis 2006 12
Interest Rate Terminology
• Because this is a function of the current market value, the simple yield varies from day to day, or even minute to minute.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If valued at $1000, the simple yield would be 10%:
– But if the value drops to $950, the simple yield increases to 10.526%:
value market current
naivalue market current
nai
© Steven J. Willis 2006 13
Interest Rate Terminology
• Because this is a function of the current market value, the simple yield varies from day to day, or even minute to minute.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If valued at $1000, the simple yield would be 10%:
1000
1001000
100
value market current
naivalue market current
nai
© Steven J. Willis 2006 14
Interest Rate Terminology
• Because this is a function of the current market value, the simple yield varies from day to day, or even minute to minute.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If valued at $1000, the simple yield would be 10%:
– But if the value drops to $950, the simple yield increases to 10.526%:
1000
1001000
100
950
100950
100
value market current
naivalue market current
nai
© Steven J. Willis 2006 15
Interest Rate Terminology
• Because this is a function of the current market value, the simple yield varies from day to day, or even minute to minute.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If valued at $1000, the simple yield would be 10%:
– But if the value increases to $1050, the simple yield decreases to 9.5238%:
1000
1001000
100
1050
1001050
100
value market current
naivalue market current
nai
© Steven J. Willis 2006 16
Interest Rate Terminology
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
© Steven J. Willis 2006 17
Interest Rate Terminology
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Value
Simple yield
© Steven J. Willis 2006 18
Interest Rate Terminology
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Value
Simple yield
© Steven J. Willis 2006 19
Interest Rate Terminology
As the value of a
bond drops, the
simple yield
increases.
As the value of a
bond drops, the
simple yield
increases.
9
9.5
10
10.5
11
11.5
12
2005 2006 2007 2008
750
800
850
900
950
1000
1050
YieldValue
Simple Yield
Value
© Steven J. Willis 2006 20
Interest Rate Terminology
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.Value
Simple yield
© Steven J. Willis 2006 21
Interest Rate Terminology
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Did You Notice?
As the value (market price) of a bond drops, the simple
yield increases.
As the value of a bond increases, the simple yield
drops.
Value
Simple yield
© Steven J. Willis 2006 22
Interest Rate Terminology
As the value of a
bond increases, the simple
yield drops.
As the value of a
bond increases, the simple
yield drops.
8
8.5
9
9.5
10
10.5
2005 2006 2007 2008
900
950
1000
1050
1100
1150
1200
YieldValue
Simple Yield
Value
© Steven J. Willis 2006 23
Interest Rate Terminology
• Value and Simple Yield move in opposite directions.
• This is important for a lawyer to know:
– Bond and other investment instruments change value continuously.• As they do so, their respective simple yields change, as
well.
– This can affect valuations in family law or estate planning or tax or corporate law.
© Steven J. Willis 2006 24
Interest Rate Terminology
Value and Simple
Yield move in
opposite directions.
Value and Simple
Yield move in
opposite directions.
0
2
4
6
8
10
12
14
2005 2006 2007 2008 2009 2010 2011 2012
0
200
400
600
800
1000
1200
1400
1600
YieldValue
Value
Simple Yield
© Steven J. Willis 2006 25
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
price purchase
effprice purchase
eff
© Steven J. Willis 2006 26
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate (eff)– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
price purchase
effprice purchase
eff
© Steven J. Willis 2006 27
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
price purchase
effprice purchase
eff
Some people define this as:
value market current
effvalue market current
eff
CAUTION
© Steven J. Willis 2006 28
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
price purchase
effprice purchase
eff
Either definition is acceptable: just be
clear about it.
Either definition is acceptable: just be
clear about it.
value market current
effvalue market current
eff
CAUTION
© Steven J. Willis 2006 29
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
price purchase
naiprice purchase
nai
Some people even use the nai as the numerator and thus interchange “yield”
and “simple yield.”
Some people even use the nai as the numerator and thus interchange “yield”
and “simple yield.”
value market current
naivalue market current
nai
CAUTION
© Steven J. Willis 2006 30
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
CAUTION
Also, some authorities . . . such as the WALL STREET JOURNAL, frequently refer to a “yield” as shorthand
for “yield to maturity.”
Also, some authorities . . . such as the WALL STREET JOURNAL, frequently refer to a “yield” as shorthand
for “yield to maturity.”
© Steven J. Willis 2006 31
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
CAUTION
Also, some authorities . . . such as the WALL STREET JOURNAL, frequently refer to a “yield” as shorthand
for “yield to maturity.”
Also, some authorities . . . such as the WALL STREET JOURNAL, frequently refer to a “yield” as shorthand
for “yield to maturity.”
This is fine . . . Because the term “yield” is not
itself a financial term of art: it means what the
user defines it to mean.
© Steven J. Willis 2006 32
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
CAUTION
Also, some authorities . . . such as the WALL STREET JOURNAL, frequently refer to a “yield” as shorthand
for “yield to maturity.”
Also, some authorities . . . such as the WALL STREET JOURNAL, frequently refer to a “yield” as shorthand
for “yield to maturity.”
This is fine . . . Because the term “yield” is not
itself a financial term of art: it means what the
user defines it to mean.
© Steven J. Willis 2006 33
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield
– Yield– Yield to maturity– Internal rate of return
CAUTION
As cited in a later slide, many federal
regulations interchange the terms “yield” and “yield to
maturity.”
As cited in a later slide, many federal
regulations interchange the terms “yield” and “yield to
maturity.”
© Steven J. Willis 2006 34
Interest Rate Terminology
• Using a common definition of “yield”
price purchase
effprice purchase
eff
© Steven J. Willis 2006 35
Interest Rate Terminology
• Using a common definition of “yield”– the value does not vary from day to day because this is
a function of the purchase price.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If valued at $1000, the simple yield would be 10%:
– But if the value drops to $950, the simple yield increases to 10.526%:
price purchase
effprice purchase
eff
© Steven J. Willis 2006 36
Interest Rate Terminology
• Using a common definition of “yield”– the value does not vary from day to day because this is
a function of the purchase price.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If purchased for $1000, the simple yield would be 10%:
– But if the value drops to $950, the simple yield increases to 10.526%:
price purchase
effprice purchase
eff
© Steven J. Willis 2006 37
Interest Rate Terminology
• Using a common definition of “yield”– the value does not vary from day to day because this is
a function of the purchase price.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If purchased for $1000, the yield would be 10%:
– But if the value drops to $950, the simple yield increases to 10.526%:
price purchase
effprice purchase
eff
1000
1001000
100
© Steven J. Willis 2006 38
Interest Rate Terminology
• Using a common definition of “yield”– the value does not vary from day to day because this is
a function of the purchase price.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If purchased for $1000, the yield would be 10%:
– But if the value increased to $1050, the yield would remain at 10%:
1000
1001000
100
1000
1001000
100
price purchase
effprice purchase
eff
© Steven J. Willis 2006 39
Interest Rate Terminology
• Using a common definition of “yield”– the value does not vary from day to day because this is
a function of the purchase price.
• For example, assume a $1000 bond which pays $25 interest quarterly ($100 annually).– If purchased for $1000, the yield would be 10%:
– But if the value increased to $1050, the yield would remain at 10%:
1000
1001000
100
1000
1001000
100
price purchase
effprice purchase
eff
But the simple yield would have dropped to 9.53%.
But the simple yield would have dropped to 9.53%.
© Steven J. Willis 2006 40
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield
– Yield to maturity– Internal rate of return
These are terms of art.
They are also closely related.
© Steven J. Willis 2006 41
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield
– Yield to maturity– Internal rate of return
These are terms of art.
They are also closely related.
© Steven J. Willis 2006 42
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield
– Yield to maturity– Internal rate of return
These are terms of art.
They are also closely related.
We will treat them as synonymous.
We will treat them as synonymous.
© Steven J. Willis 2006 43
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield
– Yield to maturity– Internal rate of return
The yield to maturity is the nominal annual interest rate at which
the price of an instrument minus the present value of the various cash flows
equals zero.
© Steven J. Willis 2006 44
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield
– Yield to maturity– Internal rate of return
The yield to maturity is the nominal annual interest rate at which
the price of an instrument minus the present value of the various cash flows
equals zero.
© Steven J. Willis 2006 45
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield
– Yield to maturity– Internal rate of return
It is often abbreviated as YTM.
It is often abbreviated as YTM.
© Steven J. Willis 2006 46
Interest Rate Terminology
One federal definition of YTM:
© Steven J. Willis 2006 47
Interest Rate Terminology
(c) Definitions (4) The yield to maturity, or yield, is the annualized rate of return to maturity on a fixed principal security expressed as a percentage.
70 FR 57437 (discussing 31 CFR Parts 356, 357, and 363, sale of T-bills, bonds etc.)
One federal definition of YTM:
© Steven J. Willis 2006 48
Interest Rate Terminology
(c) Definitions (4) The yield to maturity, or yield, is the annualized rate of return to maturity on a fixed principal security expressed as a percentage.
70 FR 57437 (discussing 31 CFR Parts 356, 357, and 363, sale of T-bills, bonds etc.)
One federal definition of YTM:
Notice: it interchanges the terms “yield to maturity” and “yield.”
© Steven J. Willis 2006 49
Interest Rate Terminology
• In this lesson, we will define:
– Interest rate– Nominal rate– Periodic rate– Compounding period– Effective rate– Annual percentage rate– Simple yield– Yield– Yield to maturity
– Internal rate of return
It is often abbreviated as IRR.
It is often abbreviated as IRR.
© Steven J. Willis 2006 50
• Two significant problems exist with these common definitions of YTM:
1. The definition assumes all interest and other payments are reinvested at the same nai.– But this assumption is often unrealistic.
2. The definition states the YTM as a nominal rate.– It thus does not reflect the effective rate on the
instrument.
– BE CAREFUL: users may disagree on this second point – some may define a YTM as as effective rate.
Interest Rate Terminology
© Steven J. Willis 2006 51
• Two significant problems exist with these common definitions of YTM:
1. The definition assumes all interest and other payments are reinvested at the same nai.– But this assumption is often unrealistic.
2. The definition states the YTM as a nominal rate.– It thus does not reflect the effective rate on the
instrument.
– BE CAREFUL: users may disagree on this second point – some may define a YTM as as effective rate.
Interest Rate Terminology
© Steven J. Willis 2006 52
• Two significant problems exist with these common definitions of YTM:
1. The definition assumes all interest and other payments are reinvested at the same nai.– But this assumption is often unrealistic.
2. The definition states the YTM as a nominal rate.– It thus does not reflect the effective rate on the
instrument.
– BE CAREFUL: users may disagree on this second point – some may define a YTM as as effective rate.
Interest Rate Terminology
© Steven J. Willis 2006 53
• Two significant problems exist with these common definitions of YTM:
1. The definition assumes all interest and other payments are reinvested at the same nai.– But this assumption is often unrealistic.
2. The definition states the YTM as a nominal rate.– It thus does not reflect the effective rate on the
instrument.
– BE CAREFUL: users may disagree on this second point – some may define a YTM as as effective rate.
Interest Rate Terminology
© Steven J. Willis 2006 54
• Two significant problems exist with these common definitions of YTM:
1. The definition assumes all interest and other payments are reinvested at the same nai.– But this assumption is often unrealistic.
2. The definition states the YTM as a nominal rate.– It thus does not reflect the effective rate on the
instrument.
– BE CAREFUL: users may disagree on this second point – some may define a YTM as as effective rate.
Interest Rate Terminology
© Steven J. Willis 2006 55
• Two significant problems exist with these common definitions of YTM:
1. The definition assumes all interest and other payments are reinvested at the same nai.– But this assumption is often unrealistic.
2. The definition states the YTM as a nominal rate.– It thus does not reflect the effective rate on the
instrument.
– BE CAREFUL: users may disagree on this second point – some may define a YTM as as effective rate.
Interest Rate Terminology