There can be two major numbers when evaluating the performance of your investment portfolio: the Money Weighted Return(MWR) and the Time Weighted Return(TWR). While both account for the effectiveness of an investment, they do so differently, bringing out different factors. This article discusses the significance of these concepts, how to calculate them, and when it might be more useful to use one over the other.

What is Money-Weighted Return?

The Money Weighted Return, otherwise known as Internal Rate of Return, measures the actual profit you are earning from your investments and also considers when you are putting in and taking out money. This measure gives a perspective by giving more weight to the returns made on periods when you invested more money.

Think of the MWR as telling a story about your investment journey. It isn’t just about the market return; it is how your behavior—for example, ramping up your investment at a certain time—impacts your overall return.

Example 1

Suppose Sarah invests in a mutual fund with the following cash flows and market performance:

• Year 0: Sarah invests $10,000 initially.
• Year 1: The fund grows by 20%, increasing the portfolio value to $12,000. Sarah adds another $5,000, bringing the total investment to $17,000.
• Year 2: The fund suffers a 10% loss. By the end of the year, Sarah’s portfolio value decreases. She withdraws $3,000 for personal reasons.
• Year 3: The fund recovers and grows by 25%.

Cash Flows:

Year	Cash Flow (Contribution/Withdrawal)	Portfolio Value (End of Year)	Net Return (%)
0	-$10000	$10000	Initial investment
1	-$5000	$17000	20%
2	+$3000	$12300	-10%
3	$0	$15375	25%

Calculation:

The MWR is the discount rate (r) that sets the Net Present Value (NPV) of the cash flows to zero. The equation is:

Where:

t is the time period (in years)

r is the Money-Weighted Rate of Return (MWR)

Substituting the cash flows into the equation:

On solving the equation we get MWR =8.43%

These calculations can also be performed using Excel using the =IRR (values) function.

=IRR([-10000, -5000, +3000, +15375])

The MWR as we know will be 8.43%.

Interpretation(MWR)

It reflects Sarah’s actual investment experience, including the timing and impact of her additional investment and withdrawal. 

What is Time-Weighted Return?

The time weighted return gives a sense of how much an investment has grown, regardless of money coming in or going out. It works out the time frame of an investment by splitting it up according to the happening of its cash flows and then combining the returns for each part. It is often used to judge a portfolio’s performance, irrespective of whether an investor is investing more money or withdrawing some from a portfolio.

Example 2

Using the same data from Emma’s investment, let’s calculate the TWR.

Step 1: Calculate the portfolio’s value at the end of each period.

• Year 0: Initial Investment = $10,000
• Year 1: After 20% growth = $12000
• Year 2: Additional investment of $5,000 = $17000 (at the beginning of Year 2)
• Year 2 End: After 10% loss = $15300 and after withdrawing $3000 =$12300
• Year 3 : After 25% growth = $15375.

Step 2: Calculate the holding period returns for each year.

• Year 1 HPR: = ($12000 – $10,000) / $10,000 = 20%
• Year 2 HPR: = ($15300 – $17000) / $17000 = -10%
• Year 3 HPR: = ($15375 – $12300) / $12300 = 25%

Step 3: Calculate the TWR by linking the returns.

To get the time weighted return TWR you would link the returns of the various time periods.

TWR = [(1+0.20) *(1-0.10) *(1+0.25)]-1

TWR = 35%

Interpretation(TWR)

It shows how well the mutual fund itself performed, ignoring the effect of Sarah’s cash flows. It reflects the pure investment performance over the three-year period.

Comparison Between Money-Weighted Return and Time-Weighted Return

Focus:

MWR -This return incorporates the timing of your investments—for instance, when you put in or took out money.
TWR – Is that indicator which says how well the portfolio did, independent of when you made your deposits or withdrawals.

Sensitivity to Cash Flows:

MWR – Responds quickly to when and how much you invest. For example, if you had invested a huge amount of money just before the market fell, then it would show in the MWR.
TWR – Completely ignores cash transactions, which makes it a more reliable measure for judging the performance of different portfolios or fund managers.

Usage:

MWR: This is very good for assessing the performance of your specific investment decisions.
TWR: Very good for analyzing how different portfolios are doing, particularly when you can’t dictate the timing of cash inflows.

Example Comparision

The lower MWR compared to TWR indicates that the timing of Sarah’s cash flows was less than optimal, as she added more money before a loss and withdrew before a significant gain.

This example highlights how different metrics can give different insights into investment performance, emphasizing the importance of understanding both returns in evaluating portfolio performance and making investment decisions.

Conclusion

MWR and TWR have roles but tell stories. MWR shows the results of your specific investment decisions while TWR provides a broader view of how a portfolio performs without considering cash flow impacts. If you want to track your progress MWR is the better option. Conversely TWR is crucial for comparing portfolios or assessing an investment managers effectiveness. Understanding when and how to utilize these metrics can improve your investment planning process.

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