2、time-weighted return : It is the rate at which $1 compounds over a specified performance horizon. 

     时间加权回报率计算步骤：1）在收入与支出之前计算投资组合的价值；2）计算每个子时期的持有期收益率（HPR）；3）计算每个子时期的（1+HPR）,再计算总的回报率（所有子时期的1+HPR相乘），若总周期大于1年，则需进行几何平均以计算总的时间加权回报率。

Example:

An investor purchases a share of stock at t=0 for $100. At the end of the year, t=1, the investor buys another share of the same stock for $120. At the end of Year 2, the investor sells both shares for $130 each. At the end of both years 1 and 2, the stock paid a $2 per share dividend. What is the money-weighted rate of return? What is the annual time-weighted rate of return for this investment?

货币加权回报率计算：t=0， perchase of the first share         = -$100  outflow to the account

                                    t=1 ,   perchase of the second share   =  -$120  outflow to the account

                                               dividend from the first share    =  +$2     inflow to the account

                                              subtotal ,  t=1                                  -$118   outflow to the account

                                    t=2 ,   proceeds from selling shares    = +$260  inflow to the account

                                               dividend from two shares          =  +$4     inflow to the account

                                               subtotal , t=2                                   +$264  inflow to the account

                                   PV (inflow) = PV (outflow)

                                    100+118/(1+r) = 264/(1+r)平方   ——r = 13.68%

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时间加权回报率计算：Break the evaluation period into two subperiods based on timing of cash flows.

                                    Holding period 1:   Begining value            = $100

                                                                     Dividends paid            = $2

                                                                     Ending value                = $120

                                    Holding period 2:   Begining value            = $240 (two shares)

                                                                     Dividends paid            = $4 ($2 per share)

                                                                     Ending value                = $260 (two shares)

                                   Calculate the HPR for each subperiod.

                                   HPR1 = (120+2)/100 - 1 = 22%

                                   HPR2 = (260+4)/240 - 1 = 10%

 

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若投资的资金是在收益率较低的时期前，则货币加权回报率一般会低于时间加权回报率；反之，若投资的资金是在收益率较高的时期前，在货币加权回报率一般会高于时间加权回报率。时间加权回报率不受此影响，因此更有利于投资者在投资项目间做出选择。若投资者可以完全控制资金的流入流出，则使用货币加权回报率会更有利于投资者项目的选择