How to evaluate the return on my investments?

Time Weighted Return (TWR) and Money Weighted Return (MWR) are two distinct methods for evaluating and comparing investments or projects.

Time Weighted Returns (TWR):

Definition: Time Weighted Returns measure the compounded growth rate of a portfolio over a specific period. They eliminate the impact of deposits and withdrawals, providing a more accurate picture of the investment manager’s performance.
Calculation: They are calculated by linking the returns of sub-periods and then finding the geometric average of these linked returns. This method is beneficial for evaluating the performance of an investment manager without considering the influence of external flows. It is the “pure” return of the strategy.
Advantages:
1. Eliminates the impact of external flows.
2. Useful for evaluating the performance of a portfolio manager or investment strategy.
Limitations:
1. Does not account for the effects of investor behavior or the timing of cash inflows and outflows.
2. Does not reflect the actual performance achieved by an investor because it does not consider the impact of cash movements.

Money Weighted Returns (MWR):

Definition: Money Weighted Returns (also known as Internal Rate of Return or IRR) represent the timing and size of cash flows entering and leaving an investment. This method takes into account the impact of investors’ deposits or withdrawals on overall profitability.
Calculation: Money Weighted Returns are calculated by solving for the discount rate that equates the present value of cash inflows with the present value of outflows. This measure of profitability is more influenced by the timing and magnitude of investment flows.
Advantages:
1. Reflects the impact of timing and amount of cash flows, providing a more personalized view of an investor’s actual performance.
2. More relevant for individual investors making periodic contributions or withdrawals.
Limitations:
1. Sensitive to the timing and size of cash flows, which can make it difficult to evaluate the skill of an investment manager.
2. May be influenced by investor behavior, which may not accurately represent the performance of the investment manager or the investment itself.

Let’s look at an example:

We have 2 investment portfolios, Portfolio A and Portfolio B. Both achieve the same returns over two consecutive years. We invest USD 100,000 in both funds as follows:

Year 1: We invest USD 100,000 in Fund A

Year 2: We invest USD 0 in Fund A

Year 1: We invest USD 50,000 in Fund B

Year 2: We invest USD 50,000 in Fund B

Portfolios	Return Year 1	Return Year 2
Portfolio A	20%	10%
Investment	100.000	0
Portafolio B	20%	10%
Investment	50.000	50.000

How do we calculate the Time-Weighted Return (TWR) of each fund?:

Fund A:

Year 1 return x Year 2 return, and we find the geometric average of this product

=(1.20 * 1.10)^0.5 – 1 = 14.89%

Fund B:

Year 1 return x Year 2 return, and we find the geometric average of this product

=(1.20 * 1.10)^0.5 – 1 = 14.89%

Both portfolios have the same average annual return.

How do we calculate the Money-Weighted Return (MWR) of each fund?:

Fund A:

100,000 * 1.20 * 1.10 = 132,000

132,000 / 100,000 = 14.89%

Fund B:

50,000 * 1.20 * 1.10 + 50,000 * 1.10 = 121,000

So: ⟮(50,000 x MWR rate) + 50,000⟯ x MWR rate = 121,000. In other words, we find the rate at which the 50,000 invested in year 1, to which 50,000 is added in year 2, and ends up being 121,000 at the end of the period. This can be easily done with an Excel spreadsheet using the IRR formula.

Solving this equation, we get an MWR = 13.40%

As we can see, the timing and amount of the investment in Fund B resulted in a lower final value compared to the investment in Fund A. Even though the same amount was invested, in two strategies with equal returns, different returns were derived. This is because in Portfolio A, the total 100,000 was invested in the year with better returns, while in Fund B it was split evenly. Therefore, the relatively greater “weight” of the return on the 100,000 made the “money” return higher for Portfolio A.

Which of the two measures should we use? Is one better than the other?

The answer to question 1 is “it depends,” and the answer to question 2 is a resounding no!

As we explained at the beginning, each way of measuring return has different objectives and interpretations of different usefulness. If the goal is to evaluate the performance of my investment strategy relative to the market’s performance in general and other investment strategies, it is most correct to compare the TWRs since this measure will not be “contaminated” by either time or the amount of investment.

If the objective is to measure the return of my portfolio specifically by evaluating how I performed with my investments over a given period of time with a certain number and amount of deposits, the MWR will provide me with the actual rate at which my money grew, having invested it in both good and bad years, ultimately, “my reality”.

Ec. Juan Martín Rodríguez, CFA

How to evaluate the return on my investments?

Juncal 1378, Off. 505. Montevideo.

(+598) 98 465 591

contacto@nantas.com.uy

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