總體框架

Time Value

Interest Rate

rf: 無風險收益率 (CFA中一般認為是美國短期國債T-bill的收益率)

Nominal risk-free rate: 名義無風險稅率

Real risk-free rate: 實際無風險利率

Liquidity premium: 流動性風險溢價

Maturity premium: 到期風險溢價

Risk premium: 風險溢價

費雪效應

Nominal interest rate和Stated Interest rate是一個概念

Effective annual rate(EAR)

For discrete compounding

Where: m is the compounding frequency

............. r is the noinal/quoted/stated annual interest rate

............. r/m is periodic interest rate

For continuous compounding

時時刻刻分分秒秒在計息.

例: 算名義年利率是8%, 求連續計算情形下的EAR.

....計算器按法: 0.08 --> 2ND --> LN ==>結果: 1.083287

Conversion of PV/FV

Present Value (PV)

The value of an initial investment.

Future Value (FV)

The value of an initial investment would be worth n period from today.

Conversion of PV/FV:

compounding:

continuous compounding:

站在今天去推測未來會價值幾何: PV --> FV : 復利

站在未來推測今天需要存入多少: FV --> PV :折現

Annuity

Ordinary annuity

all constant cash flows occuring at the end of each period(END), 後付年金

Annuity due

all constant cash flows occuring at the beginning of each period(BEG), 先付年金

Prepetuity

a set of constant never-ending sequential cash flows occuring at the end of each period, 永續年金

PV = A/R

where A: the periodic payment

......r: the periodic return

推薦用第三種方式, 就不用再把計算器在END和BGN模式之間去轉換.

QM1_Time value of Money