What is the P&L Rate of Return？
The P&L rate of return ("RoR") is the ratio of cumulative profit to initial cost over a period of time. A simple way to calculate it is:
RoR=(Ve/Vs-1)*100%
*Ve and Vs refer to the ending value and starting value of a certain period respectively.
However, this method is not valid if an investor makes frequent deposits and withdrawals during the investment period. For example, if an investor's starting value of total assets is $10,000 cash, then they deposit another $5,000 cash but still don't make any trades, their end value of their total assets becomes $15,000. According to the simple method, the rate of return of their portfolio is ($15,000/$10,000-1)*100%=50%. However, this investor has yet to make any investments. The reason for this outcome is because this simple method doesn't take an investor's deposits & withdrawals into account when assessing the change in the total value of their portfolio.
Tiger's P&L Rate of Return Calculation
Time-Weighted Return
A commonly used concept --Time Weighted Method is available on the Tiger Trade App. First, calculate the value-weighted rate of return per unit time, then calculate the geometric mean of each period's rate of return over the entire time interval. Deposits made on a certain day are assumed to be available to participate in the transactions of that day, hence are included in the assets at the beginning and the end of the period. On the other hand, withdrawals made on a certain day are assumed to be not available to participate in the transactions of that day. The calculations are as follows:
P's RoR=(Ve-Vs-Cd+Cw)/(Vs+Cd)
Time Weighted RoR ("TWR")=((1+P1's RoR)*(1+P2's RoR)*...*(1+Pn's RoR)-1)*100%
Vs for Period 2 = Ve for Period 1. Cd includes cash deposits, inward stock transfers, etc. Cw includes cash withdrawals, stock transfers, etc.
For example, when each period is 1 trading day:
Date | Vs | Ve | Cd | Cw | P's RoR |
01/12 | 50,000 | 50,000 | 0.00% | ||
02/12 | 50,000 | 70,000 | 12,000 | 12.90% | |
03/12 | 70,000 | 65,000 | 2,000 | -4.29% | |
04/12 | 65,000 | 72,000 | 11,000 | 3,000 | -1.32% |
02/12's RoR=(70,000-50,000-12,000)/(50,000+12,000)*100%=12.90%
03/12's RoR=(65,000-70,000+2000)/70,000*100%=-4.29%
04/12's RoR=(72,000-65,000-11,000+3,000)/(65,000+11,000)*100%=-1.32%
After we have calculated each period's rate of return for December 1st to December 4th, we can then calculate the time-weighted rate of return for the entire period from December 1st to December 4th.
TWR=（(1+0%)*(1+12.90%)*(1-4.29%)*(1-1.32%)-1）*100%=6.64%
Please note that the TWR will be the same even if we change any or all of the 4 intervals, all else being equal (e.g. If the end of P3 is changed to the end of 10/12 and the beginning of P4 becomes the start of 11/12).
"Money-Weighted Return"
The approximation of the Money-Weighted Return method - the Modified Dietz method is also available on the Tiger Trade App. Whereby only one calculation for the whole period is made after all net cashflows are weighted. The calculation formula is as follows:
Modified Dietz RoR ("MDR") = Cumulative P&L for the period / [Initial Total Assets + ∑(Net Cashflow * Time Weight)]
Where:
Net cashflow ("NCF") = Cd - Cw
Time Weight = 1 - (Days that a certain Net Cashflow affected the valuation of the whole Period / Total Days of the whole Period)
Example:
Date | Vs | NCF | Daily P&L | Ve | Time Weight | NCF*Time Weight |
01/12 | 50,000 | 50,000 | 1 | 0 | ||
02/12 | 50,000 | 12,000 | 8000 | 70,000 | 0.75=1-(1/4) | 9000 |
03/12 | 70,000 | -2,000 | -3000 | 65,000 | 0.5=1-(2/4) | -1000 |
04/12 | 65,000 | 8,000 | -1000 | 72,000 | 0.25=1-(3/4) | 2000 |
And so on, calculate the Money-Weighted Rate of Return from December 1st to December 4th.
MDR = (8000-3000-1000)/(50000+9000-1000+2000)= 6.67%
Simple Dietz Return
The Simple Dietz Return method is a simplified way to calculate rate of returns when compared to the MDR method, since it does not "weigh" the occurrences of the cash flows according to their time, but "even" them out as if they all occurred in the middle of an investment period. It is relatively simple to come up with a rate of return with such a method. The formula is as follows:
Simple Dietz RoR ("SDR") = Cumulative P&L for the period / [Initial Total Assets + ∑(Net Cashflow * Time Weight)]
Whereby:
The time weight for each Net Cashflow is fixed at 0.5.
Using the same cashflow example above:
Date | Vs | NCF | Daily P&L | Ve | Time Weight | NCF*Time Weight |
01/12 | 50,000 | 50,000 | 0 | |||
02/12 | 50,000 | 12,000 | 8000 | 70,000 | 0.5 | 6000 |
03/12 | 70,000 | -2,000 | -3000 | 65,000 | 0.5 | -1000 |
04/12 | 65,000 | 8,000 | -1000 | 72,000 | 0.5 | 4000 |
So, if we choose to use the Simple Dietz Rate of Return from December 1st to December 4th.
SDR = (8000-3000-1000)/(50000+6000-1000+4000) = 6.78%
3. Q&A
Is the data of the account analysis page updated in real-time?
To better assist our investors in having a comprehensive overview of their latest asset trends, the account analysis page provides near real-time data analysis for total assets, asset trends, P&L analysis, P&L calendar, and other functions.
Total Assets: near real-time data updated every minute*, and displayed in the selected currency after conversion based on real-time exchange rates.
Asset trends, P&L analysis and P&L calendar and others:
Today/Last 5 days: near real-time data updated every 5 minutes*. The cut-off time is 9:00 am in Beijing Time/Sydney Time/Wellington Time, whichever applies to the time zone a client has set in their Tiger Trade platform.
Other time periods or customised time intervals: settled data's display is consistent with the data of statements, but is only updated daily. Yet to settle transactions will be updated with near real-time data until they are settled.
*Due to the different cut-off times, the analyses displayed for that very day and up to the last 5 days can be different from your statement's. Please go by your statement. The frequencies of near real-time updates mentioned are for reference only. Please refer to the actual market data.
Why is the daily P&L on the portfolio page different from that on the account analysis page?
Different data scope: the daily P&L on the portfolio page only contains current holding investments' P&L, while the daily P&L on the account analysis page includes not only the P&L of the current holdings but also the changes of total assets caused by interest deductions and other factors.
Different data period: the daily P&L of the portfolio page is calculated from 0:00 am local time of each exchange and summed up based on real-time exchange rates, while the daily P&L on the account analysis page is calculated based on the real-time asset's cut-off time, which is 9:00 am in Beijing Time/Sydney Time/Wellington Time.
Why is Tiger's rate of return different from mine? Did you get it wrong?
The rate of return is used as a reference indicator for analysing investment performance. There are several commonly used calculations like ROI, time-weighted, IRR, analyst test, etc. Different assets and different investment scenarios may apply different yield calculation methods. Among all these methods, the time-weighted concept adopted by Tiger is one of the more common methods used by various investment institutions and evaluators to measure the investment performance of investment managers. In the absence of external cash flow impact, the results of each formula should be consistent. When affected by external cash flow (deposits, withdrawals, transfer of shares, etc.), the results of various formulas may deviate. In special cases, the deviation will be relatively large, mainly due to different assumptions about time, capital, or assets' return processing methods. Clients can also calculate their ROI based on their own formulas.
Why are the signs of my total P&L and RoR calculated by Tiger opposite？
The time-weighted calculation adopted by Tiger has the same weight for all time periods regardless of the investment amount. This is usually due to a relatively short term presence (inflow) of a sizable capital, and the absolute figure of the profit or loss for that period of time is "diluted" after it is converted into a percentage, hence one's change from loss to profit, or vice versa, is not reflected with a change of sign in one's RoR. Under special circumstances, there may be asymmetry of signs. Please try other calculation methods.
If you have questions about RoR, please contact us for assistance.