Rate of Return - Time Weighted
Contents
Time Weighted Rate of Return measures the performance of $1 invested in the asset or portfolio for the complete measurement period.
Time Weighted Rate of Return is a calculation method that eliminates the impact of cash flows on the calculation.
Advisors Assistant calculates Time Weighted ROR (Rate of Return) based on the Daily Valuation Method based on formulas provided by the CFA Institute. The Daily Valuation Method is used so that there are not distortions due to large cash flows.
Time Weighted Calculation
A subperiod index is calculated for each cash flow using the formula:
where MVE is the market value at the end of the cash flow period, including any income paid, and MVB is the market value at the beginning of the period.
The Return, R, for subperiods 1 through N is calculated using the formula:
What Is Time Weighted ROR
Think of Time ROR as the return of one share of an investment (or $1 invested) held for the entire reporting period. It measures the Investment's Return because it removes the effect of the timing of the buys and sells.
If you're an advisor, it indicates how good your advice for the investment was, not how good your advice about timing was.
This calculation will be the same whether the investor bought and held for the period or dollar cost averaged during the period.
When Asset Inception Is During Measuring Period
Normally the Beginning and Ending Market Values are measured using the price at the end of the day. However there are two instances when this can provide results that are not intuitive.
1.In the case of a mutual fund with a front end load purchased on or after the beginning date of the measuring period, the beginning market value used by the calculation is the amount invested calculated as the number of shares purchased times the purchase price.
2.In the case of an investment purchased mid day on or after the beginning date of the measuring period, the principal amount invested is also used for the beginning market value.
The "investment" becomes the beginning market value because we are measuring the investment's return.
In the case of the loaded mutual fund, if you measured the return from the purchase date, you would get a considerably lower return than if you measured the return from the day after the purchase date. This is one of the distortions that can happen with Time Weighted Returns.
However, in the case of the front loaded fund, if you ignored the load and used the end of day (NAV), you could have the investment lose value, but if the NAV gained a few cents over the measurement period, the ROR would be positive. This would be a greater distortion and more confusing. You could end up with a beginning investment of $10,000, a 5% load, and an ending value of $9,600 and still show a slightly positive return when the "investment" lost money.
In the case of a regular investment, the market move mid day, so this method takes that into account.
Account Return Exceeding All Individual Asset Returns
Under certain circumstances it is possible for the return on the account for a period to exceed all returns of the assets for that same period. This can happen when an asset is liquidated with substantial gains early in the period and all proceeds of the liquidation are removed from the account.
In the example below, Asset A's Time ROR is 10.0% and Asset B's Time ROR is 15.6%. The account's Time ROR is about 28.9%, and that is higher than either of the assets.
Example of account level January 2 to June 2:
On January 2:
Asset A has a beginning value of $21,856.
Asset B has a beginning value of $5,134
On January 16:
Asset A is sold for $24,053 with a Gain of $2,197 and all proceeds are sent to the client.
Asset B's value declined to $4,944, so the account's value is now $4,944.
Asset A had a gain of about 10%, but Asset B declined, so as of this date, the account (S1) has a gain of about 7.4%. 1.074 becomes S1.
On March 3
Asset B has a $500 dividend reinvested. The value of the account is now $4,825. This is not a flow in or out of the account, so Si is not calculated.
On March 31:
End of Month ROR is calculated. The value of the account (Asset B) is now $5,282, up from $4,944 and the return for the period January 16 to March 31 is about 14.7%. This becomes the Account's S2 . (Actually the S index is 1.147, but we will ignore that for purposes of the explanation.) This is the end of quarter calculation stored by Advisors Assistant.
June 3:
This is the end of the period being measured.
Asset B is liquidated and $5,935 is sent to the client.
The account grew from $5,282 to $5,935 for a incremental return of about 12.3% 1.123 becomes S3 and the last period.
Calculating the return for the periods 1 through 3 using the formula above equals 28.9%.
Why did the account return more than the individual assets?
The answer lies in the fact that the early liquidation of Asset A was removed from the account completely. That 10% gain cannot be ignored and it gets factored in as S1 in the equation.
Where You Can Find More Information
Dollar Weighted and Time Weighted Return are not easy topics. If you do an Internet search on Time Weighted Return, you can find numerous articles written at many different levels.
See Also