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CFA一級(jí)TWR & MWR知識(shí)點(diǎn)對(duì)比解析
Time-weighted rate of return （時(shí)間加權(quán)的回報(bào)率）
The compound return that $1 initially invested in the portfolio over a stated measurement period.
時(shí)間加權(quán)的回報(bào)率在一個(gè)確定的衡量期間內(nèi)，在期初投入1美元，在期末可以收回金額的復(fù)合回報(bào)率?；蛘哒f，時(shí)間加權(quán)收益率是指在每單位時(shí)間區(qū)間計(jì)算其金額加權(quán)收益率后，計(jì)算整個(gè)時(shí)間區(qū)間收益率的幾何平均數(shù)。時(shí)間加權(quán)類似于幾何平均收益率，考慮了資金的時(shí)間價(jià)值，運(yùn)用了復(fù)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(jì)算方法:
把一個(gè)整體期間按產(chǎn)生現(xiàn)金流的的時(shí)間點(diǎn)劃分為幾個(gè)子區(qū)間，計(jì)算每個(gè)子區(qū)間的持有期收益率，這些子區(qū)間相乘得到整體時(shí)期的收益率。
圖片1
注：N和n不一定相等
Money-weighted rate of return (價(jià)值加權(quán)的回報(bào) MWR)
MWR accounts for the timing and amount of all cash flows into and out of the portfolio.
價(jià)值加權(quán)的回報(bào)率，是在考慮所有的現(xiàn)金流入及流出的情況下，一個(gè)投資組合的內(nèi)部回報(bào)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(xiàn)金流入和流出都會(huì)影響價(jià)值加權(quán)的回報(bào)，且現(xiàn)金流大的所占權(quán)重更大；
Calculation of MWR: similar to IRR.
計(jì)算方法：
圖片2
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(qū)別：
價(jià)值加權(quán)劃分的每一期間都是相等的，時(shí)間加權(quán)的每一期間可以不等；
期間現(xiàn)金流入或流入對(duì)于時(shí)間加權(quán)沒有影響，而會(huì)影響價(jià)值加權(quán)法；
大的現(xiàn)金流在價(jià)值加權(quán)回報(bào)中占據(jù)較大的權(quán)重；因?yàn)閮r(jià)值權(quán)重要求每期的長(zhǎng)度相等，所以劃分時(shí)間區(qū)間時(shí)要以沒有重大現(xiàn)金流的的最小區(qū)間為準(zhǔn)；
例題
考點(diǎn)：一般會(huì)考兩者的計(jì)算，或者比較兩者的大??；
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:
圖片3
TWR = [(1.20)(1.25)(0.8667)(1.0769)]1/4 ? 1 = 8.78%. Or, more simply, (140/100)1/4? 1 = 8.78%。
關(guān)于平均成本，因?yàn)槊磕暧玫攘康呢泿艁碣?gòu)買，應(yīng)該用調(diào)和平均數(shù)來算平均成本，即為
圖片4
