SUMMARY INTRODUCTION FINANCE
Inhoud
Finance...................................................................................................................................................2
Week 1................................................................................................................................................2
Simple Interest...............................................................................................................................2
Compound Interest.........................................................................................................................2
Effective Interest Rate....................................................................................................................2
Interest Rules..................................................................................................................................3
Future Value...................................................................................................................................3
Present Value..................................................................................................................................3
Net Present Value (NPV).................................................................................................................3
Internal Rate of Return (IRR)..........................................................................................................3
Comparison of Multiple Projects....................................................................................................4
Week 2................................................................................................................................................5
Fixed Income Securities..................................................................................................................5
Parties.............................................................................................................................................5
Mortgages......................................................................................................................................5
Bonds..............................................................................................................................................5
Accrued Interest.............................................................................................................................6
Yield to Maturity.............................................................................................................................6
Yield Curves....................................................................................................................................6
Zero Coupon Bonds........................................................................................................................7
Discount Curve...............................................................................................................................7
Stock Index Value...........................................................................................................................7
Distribution Rates of Return...........................................................................................................7
Week 3................................................................................................................................................8
Mean-Variance Portfolio Choice Problem......................................................................................8
Mean-Variance Frontier..................................................................................................................8
Minimum Variance Portfolio Choice Problem................................................................................9
One Fund Result.............................................................................................................................9
Capital Market Line.......................................................................................................................10
Capital Asset Pricing Model (CAPM).............................................................................................11
Security Market Line.....................................................................................................................11
1
, Finance
Based on the book of Luenberger and the lecture slides of Anne Balter.
Week 1
Simple Interest
Under a simple interest rule, money invested for a period different from 1 year accumulates interest
proportional to the total time of the investment. So after 2 years, the total interest due is 2 r times
the original investment ( A ). The total value after n years is equal to;
V =(1+rn)∙ A
Compound Interest
Under yearly compounding, money left in an account is multiplied by (1+r ) after one year. After the
second year, it grows by another factor of (1+r ) to ( 1+r )2 . The difference with simple interest is that
the complete new value of the investment after a year is reinvested. So, in the second year you will
also get interest over the amount of interest you earned in the first year. After n years, such an
account will grow to ( 1+r )n times its original value ( A ). The total value after n years is equal to;
V = A ∙ ( 1+r )n
Note, compounding can be carried out with any frequency The general method is that a year is
divided into a fixed number of equally spaced periods – say m periods. The interest rate for each of
the m periods is thus r /m , where r is the nominal annual rate. After a full year of m periods, the
account will grow by ( 1+r / m )m . So, the total value after n years will be equal to;
mn
V = A ∙ ( 1+r /m )
Consider continuous compounding. We can determine the effect of continuous compounding by
considering the limit of the ordinary compounding as the number m of periods in a year goes to
m r
infinity. We have lim ( 1+r /m ) =e . So, the total value after n years will be equal to;
m→∞
rn
V=A∙e
Effective Interest Rate
The effect of compounding on early growth is highlighted by stating an effective interest rate, which
is the equivalent yearly interest rate that would produce the same result after 1 year without
compounding. For example, an annual rate of 8% compounded quarterly will produce an increase of
( 1.02 )4 =1.0824 ; hence the effective interest rate is 8.24%. The basic yearly rate (8% in this example)
is termed the nominal rate.
2
Inhoud
Finance...................................................................................................................................................2
Week 1................................................................................................................................................2
Simple Interest...............................................................................................................................2
Compound Interest.........................................................................................................................2
Effective Interest Rate....................................................................................................................2
Interest Rules..................................................................................................................................3
Future Value...................................................................................................................................3
Present Value..................................................................................................................................3
Net Present Value (NPV).................................................................................................................3
Internal Rate of Return (IRR)..........................................................................................................3
Comparison of Multiple Projects....................................................................................................4
Week 2................................................................................................................................................5
Fixed Income Securities..................................................................................................................5
Parties.............................................................................................................................................5
Mortgages......................................................................................................................................5
Bonds..............................................................................................................................................5
Accrued Interest.............................................................................................................................6
Yield to Maturity.............................................................................................................................6
Yield Curves....................................................................................................................................6
Zero Coupon Bonds........................................................................................................................7
Discount Curve...............................................................................................................................7
Stock Index Value...........................................................................................................................7
Distribution Rates of Return...........................................................................................................7
Week 3................................................................................................................................................8
Mean-Variance Portfolio Choice Problem......................................................................................8
Mean-Variance Frontier..................................................................................................................8
Minimum Variance Portfolio Choice Problem................................................................................9
One Fund Result.............................................................................................................................9
Capital Market Line.......................................................................................................................10
Capital Asset Pricing Model (CAPM).............................................................................................11
Security Market Line.....................................................................................................................11
1
, Finance
Based on the book of Luenberger and the lecture slides of Anne Balter.
Week 1
Simple Interest
Under a simple interest rule, money invested for a period different from 1 year accumulates interest
proportional to the total time of the investment. So after 2 years, the total interest due is 2 r times
the original investment ( A ). The total value after n years is equal to;
V =(1+rn)∙ A
Compound Interest
Under yearly compounding, money left in an account is multiplied by (1+r ) after one year. After the
second year, it grows by another factor of (1+r ) to ( 1+r )2 . The difference with simple interest is that
the complete new value of the investment after a year is reinvested. So, in the second year you will
also get interest over the amount of interest you earned in the first year. After n years, such an
account will grow to ( 1+r )n times its original value ( A ). The total value after n years is equal to;
V = A ∙ ( 1+r )n
Note, compounding can be carried out with any frequency The general method is that a year is
divided into a fixed number of equally spaced periods – say m periods. The interest rate for each of
the m periods is thus r /m , where r is the nominal annual rate. After a full year of m periods, the
account will grow by ( 1+r / m )m . So, the total value after n years will be equal to;
mn
V = A ∙ ( 1+r /m )
Consider continuous compounding. We can determine the effect of continuous compounding by
considering the limit of the ordinary compounding as the number m of periods in a year goes to
m r
infinity. We have lim ( 1+r /m ) =e . So, the total value after n years will be equal to;
m→∞
rn
V=A∙e
Effective Interest Rate
The effect of compounding on early growth is highlighted by stating an effective interest rate, which
is the equivalent yearly interest rate that would produce the same result after 1 year without
compounding. For example, an annual rate of 8% compounded quarterly will produce an increase of
( 1.02 )4 =1.0824 ; hence the effective interest rate is 8.24%. The basic yearly rate (8% in this example)
is termed the nominal rate.
2
