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　　Time-weighted rate of return（時間加權的回報率）

　　The compound return that$1 initially invested in the portfolio over a stated measurement period.

　　時間加權的回報率在一個確定的衡量期間內，在期初投入1美元，在期末可以收回金額的復合回報率。或者說，時間加權收益率是指在每單位時間區間計算其金額加權收益率后，計算整個時間區間收益率的幾何平均數。時間加權類似于幾何平均收益率，考慮了資金的時間價值，運用了復利思路。

　　Calculation of TWR:

　　Break the overall *uation period into sub-periods based on the dates of significant cash inflows and outflows;

　　Calculate the HPRs for each sub-periods;

　　Link or compound HPRs to obtain an annual rate of return.

　　計算方法:

　　把一個整體期間按產生現金流的的時間點劃分為幾個子區間，計算每個子區間的持有期收益率，這些子區間相乘得到整體時期的收益率。

　　注：N和n不一定相等

　　Money-weighted rate of return(價值加權的回報MWR)

　　MWR accounts for the timing and amount of all cash flows into and out of the portfolio.

　　價值加權的回報率，是在考慮所有的現金流入及流出的情況下，一個投資組合的內部回報率。

　　If more funds to invest at an unfavorable time,MWR will tend to be depressed;

　　If more funds to invest at a favorable time,MWR will tend to be elevated.

　　所有的現金流入和流出都會影響價值加權的回報，且現金流大的所占權重更大；

　　Calculation of MWR:similar to IRR.

　　計算方法：

　　TWR vs.MWR

　　Time weighted return：

　　Not affected by cash withdrawals or additions;

　　Periods can be any length between significant cash flows.

　　Money weighted return：

　　Assign more weights to the return of larger cash flows;

　　Affected by cash withdrawals or additions;

　　Periods must be equal length.

　　Use shortest period with no significant cash flows.

　　兩者區別：

　　價值加權劃分的每一期間都是相等的，時間加權的每一期間可以不等；

　　期間現金流入或流入對于時間加權沒有影響，而會影響價值加權法；

　　大的現金流在價值加權回報中占據較大的權重；因為價值權重要求每期的長度相等，所以劃分時間區間時要以沒有重大現金流的的最小區間為準；

　　例題

　　考點：一般會考兩者的計算，或者比較兩者的大小；

　　例：Miranda Cromwell,CFA,buys?3,000 worth of Golden shares at the beginning of each year for four years at prices of?100,?120,?150 and?130 respectively.At the end of the fourth year the price of Golden is?140.The shares do not pay a dividend.Cromwell calculates her average cost per share as[(?100+?120+?150+?130)/4]=?125.Cromwell then uses the geometric mean of annual holding period returns to conclude that her time-weighted annual rate of return is 8.8%.Has Cromwell correctly determined her average cost per share and time-weighted rate of return?

　　Average cost Time-weighted return

　　A.Correct Correct

　　B.Correct Incorrect

　　C.Incorrect Correct

　　答案：選C

　　解析：Because Cromwell purchases shares each year for the same amount of money,she should calculate the average cost per share using the harmonic mean.Cromwell is correct to use the geometric mean to calculate the time-weighted rate of return.The calculation is as follows: