# How to Calculate Money-weighted Returns

In the previous article, we learned about arithmetic returns and geometric returns. However, the problem with these measures is that they do not consider the amount of investment made in each period. For example, in the first year, we may have an investment of USD 5,000 while in the second year, the investment may only be $2,000. So, the returns when looked at along with how much money was invested will make a huge difference to our actual return on investment. This will be called money-weighted return on internal rate of return.

Let’s say we had the following investments and returns in the past 3 years:

In the first year, we made an investment of $1000, and we had a 100% return in the first year. By the end of the year, our investment has grown to $2000. Then at the beginning of the second year we invested $2000 more making a total investment of $4000. The returns in the second year were -50%, and our investment value reduced to $2000. Then assume we withdrew $500 from the investment fund, leaving only $1500 invested. In the third year there was no new investment, and our returns were 35%, making our investment grow to $2025. The cash flows are shown in the table below.

The money-weighted returns can be calculated using the same formula as that of the Internal rate of Return (IRR).

Our cash flows are as follows:

CF0 = -$1,000

CF1 = =$2,000

CF2 = +$500

CF4 = $2,025

Applying the above formula and solving for IRR we get:

IRR or money-weighted returns = -8%

This tells the investor about what she actually earned on the money invested for the entire three year period. Note that this return is negative because a significantly large amount of money was invested in the year of negative returns compared to other years.

#### Course Downloads

- Major Types of Return Measures
- How to Calculate the Holding Period Returns
- Portfolio Risk & Return - Part 1A - Video
- Portfolio Risk & Return - Part 1B - Video
- Arithmetic Returns Vs. Geometric Returns
- How to Calculate Money-weighted Returns
- How to Calculate Annualized Returns
- How to Calculate Portfolio Returns
- Gross and Net Returns Calculations
- How to Calculate Leveraged Returns
- Nominal Returns and Real Returns in Investments
- Calculate Variance and Standard Deviation of an Asset
- Standard Deviation and Variance of a Portfolio
- Efficient Frontier for a Portfolio of Two Assets
- Effect of Correlation on Diversification
- Risk Aversion of Investors and Portfolio Selection
- Utility Indifference Curves for Risk-averse Investors
- Capital Allocation Line with Two Assets
- Selecting Optimal Portfolio for an Investor
- How to Calculate Portfolio Risk and Return
- Portfolio Risk and Return - Part 2A - Video
- Portfolio Risk and Return - Part 2B - Video

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