CFA考试《定量方法》习题练习：时间加权收益率 贴现率
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1、The time-weighted rate of return:
A 、results in a lower return when compared with the money-weighted rate of
return.
B 、is affected by the amount and timing of cash flows to and from a portfolio.
C 、calculates multi-period cash flows mirroring a portfolio’s compound growth
rate.
2、Given a discount rate of 10%, the net present value (NPV) of the following
investment is closest to:
Time 0 1 2 3 4 5 6
Cash flow –1,500 300 600 1,000 200 500 300
A 、605.
B、 578.
C 、636.
C is correct. Time-weighted rate of return reflects the compound rate of growth of one unit of currency invested over a stated measurement period, and it removes the effects of timing and amount of withdrawals and additions to the portfolio.
A is incorrect. Time-weighted rate of return can be the same, higher, or lower than money-weighted rate of return.
B is incorrect because this is in fact the explanation for money-weighted return.
C is correct. The given cash flows are inserted into a financial calculator along with the 10% discount rate: CF0 = –1,500, CF1 = 300, CF2 = 600, CF3 = 1,000, CF4 = 200, CF5 = 500, CF6 = 300, I = 10. Computing NPV the result is 636.32 ~ 636. Alternatively, the net present value of the project is found by discounting each cash flow by the time at which it arises, at the appropriate discount rate。
B is incorrect; 578 occurs when the cash flows are discounted by one period too many (i.e., Year 0 is discounted as if it were Year 1, Year 1 is discounted as if it were Year 2, etc.): CF1 = –1,500, CF2 = 300, CF3 = 600, CF4 = 1,000, CF5 = 200, CF6 = 500, CF7 = 300, I = 10. Computing NPV the result is 578.
A is incorrect; the mistake is to use the average cash flow across the six years (483.33). Using a financial calculator: PMT = –483.33, N = 6, I/Y = 10, FV = 0. Computing PV (PV = 2,105.03) and subtracting 1,500: 2,105.03 – 1500 = 605.03 ~ 605
