Time-Weighted Rate of Return

Time-Weighted Rate of Return

The time-weighted rate of return (TWRR) measures the compound growth rate of an investment portfolio.  Unlike the money-weighted rate of return, TWRR is not sensitive to withdrawals or contributions. Essentially, the time-weighted rate of return is the geometric mean of the holding period returns of the respective sub-periods involved.

Time-weighted Rate of Return Formula

When working out time-weighted measurements, we break down the total investment period into many sub-periods. Each sub-period ends at the point where we have a significant withdrawal or contribution. It could also end after a month, quarterly or even semiannually. We encourage candidates to follow the procedure below when computing TWRR:

  1. Establish the holding period return (HPR) for each sub-period
  2. Add 1 to each HPR
  3. Multiply all the (1 + HPR) terms
  4. Subtract 1 from the final product to get the compounded TWRR

Summarily, compounded TWRR = {(1 + HPR1)*(1 + HPR2)*(1 + HPR3)…*(1 + HPRn-1)*(1 + HPRn)} – 1

Finally, annual time-weighted rate of return = (1 + compounded TWRR) 1/n – 1

Where n is the number of years


An investor purchases a share of stock at t = 0 for $200. At the end of the year (at t = 1) the investor purchases an additional share of the same stock, this time for $220. She then sells both shares at the end of the second year for $230 each. She also received annual dividends of $3 per share at the end of each year. Calculate the annual time-weighted rate of return on her investment.


First, we break down the 2-year period into two 1-year periods:

Holding period 1:

Beginning value  = 200

Dividends paid = 3

Ending value = 220

Holding period 2:

Beginning value = 440 (2 shares * 220)

Dividends paid = 6 (2 shares * 3)

Ending value  = 460 (2 shares * 230)

Secondly, we calculate the HPR for each period:

$$ \text{HPR}_1 =\cfrac {(220 – 200 + 3)}{200} = 11.5\% $$

$$ \text{HPR}_2 =\cfrac {(460 – 440 + 6)}{440} = 5.9\% $$


$$ (1 + \text{annual TWRR})^2 = 1.115 * 1.059 $$


$$ \text {annual TWRR} = (1.115 * 1.059)^{0.5} – 1 = 8.7\% $$

Money-weighted Rate of Return Vs Time-weighted Rate of Return

The money-weighted rate of return is sensitive to the amount and timing of cash flows and could lead to an unfair rating of the fund manager – They have no control over the amount or timing of cash flows. This effect is eliminated by the time-weighted rate of return. The money-weighted rate of return would only be superior to the TWRR if and only if the fund manager had complete control over cash flows and their timings.


A chartered analyst buys a share of stock at time t = 0 for $50. At t = 1, he purchases an extra share of the same stock for $53. The share gives a dividend of $0.50 per share for the first year and $0.60 per share for the second year. He sells the shares at the end of the second year for $55 per share. Calculate the annual time-weighted rate of return.

A. 5.9%

B. 12.24%

C. 7%


The correct answer is A.

We have two 1-year holding periods:


P0 = 50

D= 0.5

P1 = 53


P0= 106

D = 1.2

P1 = 110

We now calculate the holding period returns:

$$ \begin{align*}
\text{HPR}_1 & =\cfrac {(53 – 50 + 0.5)}{50} = 7\% \\
\text{HPR}_2 & =\cfrac {(110 – 106 + 1.2)}{106} = 4.9\% \\
\text{Compounded TWRR} & = 1.07 * 1.049 = 12.24\%
\end{align*} $$


$$ \text {Annual TWRR} = (1 + 0.1224)^{0.5} – 1 = 5.9\% $$

Reading 7 LOS 7d

Calculate and compare the money-weighted and time-weighted rates of return of a portfolio and evaluate the performance of portfolios based on these measures. (Part two)

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep

    Sergio Torrico
    Sergio Torrico
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.