唯學(xué)網(wǎng)小編提醒：特許金融分析師考試CFA知識(shí)點(diǎn)，定量投資作為一種投資制度定量投資在國(guó)內(nèi)被引進(jìn)的時(shí)間并不長(zhǎng)，作為一種投資方法市場(chǎng)對(duì)其理論和模型尚有爭(zhēng)論。投資者對(duì)定量投資的認(rèn)識(shí)普遍存在幾個(gè)誤區(qū)，解開(kāi)這些疑惑，就不難理解定量投資方法在今天中國(guó)的市場(chǎng)仍然適用，并且是對(duì)傳統(tǒng)定性投資方法非常好的有效補(bǔ)充。希望考生認(rèn)真復(fù)習(xí)，順利通過(guò)特許金融分析師考試。

二、Investment Tools: Quantitative Methods

1.A.: Time Value of Money

a: Calculate the future value (FV) and present value (PV) of a single sum of money.

Future Value:

FV = PV(1 + I/Y)N

Where PV = the amount of money invested today, I/Y = the rate of return, and N = the length of the holding period.

Example: Using a financial calculator, here's an example of how you would find the FV of a $300 investment (PV), given you earn a compound rate of return (I/Y) of 8% over a 10-year (N) period of time:

N = 10, I/Y = 8, PV = 300; CPT FV = $647.68 (ignore the sign).

Present Value:

PV = FV / (1 + I/Y)N

Example: Using a financial calculator, here's an example of how you'd find the PV of a $1,000 cash flow (FV) to be received in 5 (N) years, given a discount rate of 9% (I/Y).

N = 5, I/Y = 9, FV = 1,000; CPT PV = $649.93 (ignore the sign).

b: Calculate an unknown variable, given the other relevant variables, in single-sum problems.

Example 1: Solving for I/Y

In this example, you want to find the rate of return (I/Y) that you'll have to earn on a $500 investment (PV) in order for it to grow to $2,000 (FV) in 15 years (N). This very same problem could also be set up in terms of growth rates - e.g., what rate of growth (I/Y) is necessary for a company's sales to grow from $500 per year (PV) to $2,000 per year (FV) in 15 years (N).

N = 15, PV = -500, FV = 2,000; CPT I/Y = 9.68%

Example 2: Solving for N

In this example, you want to find out how many years (N) it will take for a $500 investment (PV) to grow to $1,000 (FV), given that we can earn 7% annually (I/Y) on your money.

I/Y = 7, PV = -500, FV = 1,000; CPT N = 10.24 years.

c: Calculate the FV and PV of an regular annuity and an annuity due.

Calculate the FV of an ordinary annuity:

Example: Find the FV of an ordinary annuity that will pay $150 per year at the end of each of the next 15 years, given the investment is expected to earn a 7% rate of return.

N = 15, I/Y = 7%, PMT = $150; CPT FV = $3,769.35 (ignore the sign).

Calculate the FV of an annuity due:

Example: Find the FV of an annuity due that will pay $100 per year for each of the next three years, given the cash flows can be invested at an annual rate of 10%.

Note: When solving for a FV of an annuity due, you MUST put your calculator in the beginning of year mode (BGN), otherwise you'll end up with the wrong answer.

N = 3, I/Y = 10%, PMT = $100; CPT FV = $364.10 (ignore the sign).

Calculate the PV of an ordinary annuity:

Example: Find the PV of an annuity that will pay $200 per year at the end of each of the next 13 years, given a 6% rate of return.

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