# Time-Weighted Rate of Return

Time-weighted rate of return (TWR) is the compound rate of growth over a period on one unit of currency invested at the start of the period. It is called time-weighted because it gives equal weightage to each of the sub-period returns.

It is one of the two methods for calculating rate of return over multiple periods: the other being the money-weighted rate of return which calculates the compound rate such that the rate of return in the periods of high amount of invested *money* is given higher weightage and vice versa.

## Formulas

The basic formula for a time-weighted return for a period is given below:

Time-weighted Rate of Return | |

= | Ending Value − Beginning Value |

Beginning Value |

It is the same as the formula for holding period return. In case of any external cash flows: new investments, withdrawals, dividends, etc., the time-weighted return is calculated for each sub-period and then chain-linked using the following formula:

Time-weighted return for multiple periods

= (1 + 1^{st } period return) × (1 + 2^{nd} period return) – 1

## Example

Guddu Gupta is a client of RAK Asset Management. He started his portfolio with an investment of $10,000 on 1 January 20X9. The value of his portfolio on 31 December 20X9 was $13,050. Impressed with the performance, he invested a further amount of $10,000 on 1 January 20Y0 with the firm. On 31 December 20Y0, he withdrew $5,000. The value of his portfolio before withdrawal was $25,000. The value at the end of 31 December 20Y1 was $22,500.

*Calculate the time-weighted rate of return for his portfolio and tell how it differs from money-weighted return.*

### Solution

We have to calculate the compound rate of return from 1 January 20X9 to 31 December 20Y1. The period has three sub-periods:

- 1 January 20X9 — 31 December 20X9
- 1 January 20Y0 — 31 December 20Y0
- 1 January 20Y1 — 31 December 20Y1

Sub-period rates of return are calculated as follows:

Return for Period 1 | ||

= | 13,050 − 10,000 | = 30.50% |

10,000 |

In Period 2, $10,000 is added because it is a new investment that increased the beginning portfolio value.

Return for Period 2 | ||

= | 25,000 − (13,050 + 10,000) | = 8.46% |

13,050 + 10,000 |

At the start of Period 3, there is a deduction of $5,000 so beginning portfolio value for Period 3 should be $20,000 [= $25,000 minus $5,000].

Return for Period 3 | ||

= | 22,500 − 20,000 | = 12.5% |

20,000 |

The sub-period returns are then chain-linked as follows:

Time-weighted return for the whole period

= (1 + 30.50%) × (1 + 8.46%) × (1 + 12.5%) – 1

= 59.23%

Please note that this is not an annual rate. However, it can be converted to an annual rate using CAGR.

The point to note here is that time-weighted rate of return assigns equal weight to all the periods. The money-weighted rate of return, on the other hand, will weight Period 2 higher because the highest amount of money that remained invested during that period.

Written by Obaidullah Jan, ACA, CFA and last revised on