CFA(4) Quantitative Methods CFA(5) CFA(6)

• The time value of Money.
• Discounted cash flow Applications.
• Statistical Concept and Market Return
• Probability Concepts.

Stated(Nominal) vs. Effective Annual Interest Rate

• The stated rate of interest=the nominal rate=contractual rate
• Effective annual rate(EAR) is the rate of interest that investors actually realize as a result of compounding and may be determined as follows:

              EAR=(1+periodic rate)^m-1

              where:

               periodic rate=nominal rate/m

               m=the number of compounding periods per year

             计息周期越短越好，ear极限为e^stated rate-1

 

CFA(5)

Future Value(FV) of a Single Sum

• FV=PV(1+1/Y)^N

         ---PV=amount of money invested today(the present value)

        ----1/Y=rate of return per compounding period

          ---N=total number of compounding periods

          ---FV=amount to whitch an investment grows to\

Present Value(PV) of a single Sum

• PV=FV/(1+1/Y)^N

Ordinary Annuity(年金) and Annuity Due

• Annuity: a series of equal cash flows that occur at evenly spaced intervals over time.
• Ordinary annuity: cash flows occur at the end of each time period
• Annuity due: cash flows occur at the beginning of each time period
• Perpetuities: annuities with an infinite life. 

Future Value of an Ordinary Annuity

• FVAo=PMT*[(1+1/Y)^N-1]/(1/Y)

         PMT:payment

Future Value of an Ordinary Annuity

• FVAD=FVAO*(1+1/Y)

CFA(6)

Present Value of an Ordinary Annuity

• PVAO=PMT*{[1-1/(1=Y)^N]/(1/Y)}

• PVAD=PVAO*(1+1/Y)
• PV of a perpetuity
• PVperpetuity=PMT/(1/Y)