Difference Between Time Weighted Returns and Money Weighted Returns

7/29/2019 Difference Between Time Weighted Returns and Money Weighted Returns

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Difference between Time Weighted Returns and Money Weighted

Returns.

Difference between Money Weighted Return and Time Weighted Return?

Very often students of finance are confused between Time Weighted Return and Money Weighted

Return. In this article we have tried to clarify both of them and also show how both these type of returns

differ from each other.

This article highlights how the timing of the returns earned on the portfolio affects the overall financial

position. In other words it is not just the size of the returns that has to be considered but also the timing of

the returns while assessing the overall returns on the portfolio. We would explain this phenomenon with thehelp of examples covering two 2 concepts-Time Weighted Rate of Return and Money Weighted rate of

Return.

Time Weighted Return (TWR)

It allows an investor to directly measure their portfolios true performance and

compare the performances of different money managers over a given time frame. Itcomputes the return for each period and takes the average of the results. It finds theholding period for each period and averages them. If the investment is for more thanone year, the geometric mean of the annual returns is taken to find the time-weighted rate of return for the measurement period.

Let us explain this with an example:

Suppose we have 3 annual returns of -10%, +15% and +5% then the average (timeweighted) return after the 3 years can be calculated as follows:

Average time-weighted = [(1+ r1) (1+r2) (1+r3)]^(1/3)-1

= [(1-10%) (1+15%) (1+5%)]^(1/3)-1

= [0.9 1.15 1.05]^(1/3)-1

= 2.81% per annum

It is interesting to note that when working with time weighted returns, the order inwhich the returns occur does not matter. Let us change r1 and r3 around. Then weget:

Average time-weighted = [(1+5%) (1+15%) (1-10%)]^(1/3)-1

= [1.05 1.150.9]^(1/3)-1

= 2.81% per annum

We get the same answer because we have applied the same weighting to eachreturn item, which in this case, was based on the amount of time it applies to i.e. oneyear. Hence the name time-weighted "returns.


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In general, the arithmetic and time-weighted average returns do not provide thesame answers, because computation of the arithmetic average assumes the initialamount invested to be maintained (through additions or withdrawals) at its initialinvestment value. The time weighted return, on the other hand, is the return on aportfolio that varies in size because of the assumptions that all proceeds arereinvested.

Money-Weighted Return

When it comes to what one actually ends up with in his/her kitty, time-weightedreturns is mostly irrelevant. This is where money-weighted return is the correctmeasure of returns and this is where the timing of the returns affects the final result.It is defined as the internal rate of return on a portfolio taking into account all cashinflows and outflows. The IRR is the discount rate that equates the ending investmentwith the compounded value of the beginning market value as well as all netcontributions made during the life of the investment.

The MWRR can be calculated by solving the expression below for r(T)...

MW(T) = MV(0) {1+r(T)}T + sum [C(t){1+r(T)}{T-t}]

MW(T) : Ending market value portfolio

MW(0) : Beginning market value portfolio

T : Ending time T

r(T) : IRR at time T over time period {0,T}

C(t) : Net contribution at time t

Note that the time period (0,T) is assumed to be divided in n equally spaced timeperiods. Other formulas with different time conventions exist.

Let us look at two different members of the same retirement fund.

Mr. A just started his first job and has started saving towards retirement. His starting assets are therefore Rs0. Let us furtherassume that he contributes Rs10 000 at the end of each of the next 3 years. Mr. B is nearing

retirement and thus far accumulated Rs750 000. He also contributes Rs10 000 at the end of each of the next

3years.Both Mr. A and Mr. B are invested in the same balanced fund.

Scenario 1

Now let us assume the annual returns on the balanced fund over the following 3 years are:

Year 1 -10%

Year 2 +15%Year 3 +5%

What is the average return earned on their assets? And what are the total assets after 3 years?

For Mr. A his total assets are Rs32575.00 which implies an average money-weighted return of 8.35% per

annum.

For Mr. B his total assets are Rs847637.50 which implies an average money-weighted return of 2.88% per

annum.

Scenario 2

Now let us change the annual returns of year 1 and year 3 around and perform the same calculations:

Year 1 +5%


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Year 2 +15%

Year 3 -10%

What is the average return earned on their assets? And what are the total assets after 3 years?

For Mr. A his total assets are Rs29350.00 which implies an average money-weighted return of -2.18% per

annum.For Mr. B his total assets are Rs844412.50 which implies an average money-weighted return of 2.75% per

annum.

Summary of results

Scenario 1 Scenario 2

Time-Weighted Returns 2.81% 2.81%

Mr. A Money-Weighted Returns 8.35% -2.18%

Mr. B Money-Weighted Returns 2.88% 2.75%

The reason for the big difference in money-weighted returns for Mr. A is the fact that he had Rs0 in the

first year and was therefore not affected by the first years' results. When the negative return of -10% wasearned in the 1st year, he was not affected at all and only benefited from the two positive years. However,

when the negative year followed when his accumulated assets was at its highest level i.e. in the last year,

the effect was devastating, bringing his total return into negative zone. This is because now the return is not

based on time, but on the amount of money it is applied to. Hence the name "money-weighted" returns.

As we can see, Mr. B was also affected but not as much as Mr. A. The reason for this is that his assets in

year 3 compared to her assets in year 1 was relatively similar which means that the effect of the returns was

similar, even though it was worse under Scenario 2 when the negative return was applied to a higher asset

value.

Graphical Representation of Calculation of TWRR and MWRR

SNAPSHOT

Point ofDistinction

TWR IRR

Definition Time Weighted Return A Money Weighted Return


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measures the compound rateof return over a given periodfor one unit of money.

measures the compoundgrowth rate in the value ofallfunds invested in the accountover the evaluation period.

Timing of Cash

Flows

TWR is not affected by thetimings of the external cashflows.

MWR is sensitive to the timingof external cash flows

Usage

Time-weighted return is thesuperior measure forevaluating public fundmanagers with no control overthe

size or timing of cash flows.

MWRR is used for private fundmanagers because theytypically exercise a degree ofcontrol over the amount andtiming of fund cash flows.

ADVANTAGES AND DISADVANTAGES OF TIME AND MONEY WEIGHTED RETURNS

Advantages of using Money Weighted Rates of Return:

Investors can easily determine if they are making a consistent month on month return and place an

equivalent interest rate value on the return. If you are not generating a consistent return, your internal rate

of return will fall. There can be no doubt about the importance of making a consistent return over time,

because as time goes by, the value of money depreciates due to the effects of inflation.

Ideal for comparing investment performance over time regardless of the size of the investment or

when you deposit or withdraw money; for example the Internal Rate of Return is ideally suited to

comparing the performance of stocks within a portfolio, or comparing your portfolio with a given market

index such as the NIFTY or SENSEX.

Disadvantages of using Money Weighted Rates of Return:

They are not suited to determining the change in the portfolio value between two consecutive dates within a

given date range.

Advantages of using Time Weighted Rates of Return

It enables investors to determine rates of return independent of when capital is added or withdrawn from

the available investment fund. More commonly this relates to fund managers and not private investors, as

fund managers have limited control over when they receive funds from investors, or when the investor

choose to withdraw their funds.

Ideally suited to environments where you have shared ownership, as they enable ownership to be allocated

based on the value of the assets and the amount invested or withdrawn at any point in time.

Relatively simple to understand and calculate; for example when using the Unit Valuation System the unit

value is the sum of the assets divided by the number of units in circulation. If you want to invest more

money, you simply buy more units at the current unit value. This is primarily used in all mutual fund

schemes.

Disadvantages of using Time Weighted Rates of Return


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They do not factor in how long money has been invested and therefore when it was invested. As an

investor, the Money Weighted Return measures, such as the Internal Rate of Return enable you to track

your performance over time. For example the Unit Value might reflect that you have made a return of

100% but if your unit value does not consistently increase, you can find yourself in a position where your

Internal Rate of Return is falling month after month, which results in your investment capital devaluing

with time.

Time Weighted metrics are not suited to comparing investment performance for different investment

portfolio.

Difference Between Time Weighted Returns and Money Weighted Returns

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