GIPS Presentation: Time-Weighted Total Return
Suppose you're an investor trying to measure overall return. In a diversified portfolio, you'd own dividend-paying stocks, interest-paying bonds, real estate securities that return capital, and other investments that rely upon capital appreciation, so there are many ways that you can earn a return.
If the GIPS standards strive to capture all of these potential returns, what's the best return measure?
Given that this equation involves just starting and ending values, what can you assume regarding how the cash flows are treated?
That's not it.
Income isn't the only way shareholders earn a return.
No.
Some securities return capital to investors through income.
But this is clearly unrealistic. Why must the calculated return account for cash flows?
No.
Management fees can be paid from the account, so those would be included in the ending value.
Nice try, but no.
Interest can be deposited back into the account.
The best way to calculate the time-weighted rate of return is to geometrically chain link subperiod returns. What might indicate the start of a new subperiod?
No.
External cash flows impact multiple parts of the portfolio.
No, external cash flows are unpredictable, so they're certainly not part of any planning or strategy.
No way.
GIPS standards don't require monthly valuations, so there wouldn't be monthly subperiods.
Since the returns are multiplied, how would you describe the chain-linking equation?
Not quite.
That's a required valuation period, not a required subperiod.
No way.
The return isn't calculated as an inverse.
No.
Adding the returns together wouldn't link the returns so they build off each other.
So if you had to adjust a balance to reflect a contribution made at the beginning of the period, what action would you take if that contribution is included in the ending day's value?
No.
That would lead to the contribution being realized as a gain.
No, actually.
The contribution amount is already included in the ending day's value.
Not quite.
A contribution at the start of the period could lower the return.
No.
If a withdrawal happens at the end of the period, that will lower the manager's return in the calculation.
How would you describe how the cash is spread over the time period?
Not quite.
There's just not enough detail in weekly weightings because managers could change the portfolio's holdings within that one-week timeframe.
No way.
A monthly timeframe is way too long for measuring the impact of an external cash flow.
Nice try, but no.
There's no addition in the modified Dietz method.
Clearly, yes!
The modified Dietz method pro rates the time that the cash flow impacted the portfolio from the time that it did not impact the portfolio.
The other method that estimates the impacts of cash flows is the Modified Internal Rate of Return approach. It solves for _r_ through a trial-and-error procedure for calculating the ending value of the portfolio using the equation
$$\displaystyle V_1 = \sum^{n}_{i=1}[CF_i \times (1 + r)^{w_i}] + V_0(1+r)$$.
No.
There's no averaging in the modified Dietz method.
To sum it up:
[[summary]]
Right!
The total rate of return is the most accurate and inclusive way to represent the client's portfolio performance. GIPS standards therefore calculate the return based upon income and realized and unrealized gains and losses. The simple, single-period return calculation is
$$\displaystyle \displaystyle{r_t= \frac{V_1-V_0}{V_0}}$$
where _r__t_ is the total return for period _t_, _V_1 is the ending value of the portfolio, and _V_0 is the portfolio's beginning value.
Yes!
The basic total return equation assumes that there are no external cash flows because it's based upon the starting and ending values. So it's great for portfolios with no external cash flows or subperiod results that are extrapolated when external cash flows occur.
That's right!
External cash flows are controlled by the client, not the manager, and GIPS standards look for performance calculation based on the portfolio manager's decisions. Therefore, GIPS requires time-weighted rates of return (TWR). This way, the total return isn't impacted by external cash flows and managers can implement their strategy knowing that unexpected external cash flows won't harm performance reporting.
Precisely!
A large external cash flow will necessitate a time-weighted rate of return calculation so the starting/ending balance is adjusted by the cash flow (small cash flows don't trigger this requirement). In order to link these returns, you'll use the equation
$$\displaystyle r_{twr} = (1+r_{t,1}) \times (1 + r_{t,2}) \times ... \times (1+ r_{t,n}) - 1$$
where _r__twr_ is the time-weighted total return for the entire period and _r__t_,1 to _r__t_,_n_ are the subperiod returns.
Right.
The chain-linking equation is a compounding return because it's multiplicative, which makes it the best way to calculate total returns. But again, you'll need to adjust the beginning or ending values to reflect any cash flows.
Exactly!
The contribution amount is already included in the day's ending value and the manager gets penalized by starting with a higher value due to the contribution, so that amount should be subtracted from the ending value. Similarly, withdrawals should be added back to the beginning value so that the manager isn't credited with a gain.
Cash flows need to be weighted daily over the time period that they impacted the portfolio so the manager's performance is known in detail. This also means that the Modified Dietz method or the Modified Internal Rate of Return method can be used.
That's right.
For historical periods, contributions can be assumed to have occurred during the middle of the time period, so the manager isn't harmed or helped by the external cash flow. This allows you to use the original Dietz method for periods prior to 1 January 2005. Its equation is
$$\displaystyle \displaystyle{r_{Dietz} = \frac{V_1 - V_0 - CF}{V_0 + (CF \times 0.5)}}$$.
The Modified Dietz method equation is
$$\displaystyle {r_{ModDietz} = \frac{V_1 - V_0 - CF}{V_0 + \sum^{N}_{i=1}(CF_i \times w_i)}}$$
where $$\sum^{N}_{i=1}(CF_i \times w_i)$$ represents the sum of each cash flow multiplied by its weight; and the weights are
$$\displaystyle{w_i = \frac{CD - D_i}{CD}}$$
where _CD_ is the total number of calendar days in the period and _D__i_ is the number of days from the beginning of the period to the time the cash flow _CF__i_ occurs.
Total return
Income return
Capital gains and losses
That there are no external cash flows
That there are only returns from capital gains
That management fees must be subtracted from the ending value
External cash flows aren't controlled by the manager
External cash flows only impact the liquidity needs of the portfolio
External cash flows are a part of the management strategy and process
The end of a month
A large external cash flow
The end of a calendar year
Inverse
Additive
Compounded
Add the contribution amount to the ending time-period value at the end of the day
Add the contribution amount to the beginning time-period value at the end of the day
Subtract the contribution amount from the ending time-period value at the end of the day
Summed over the period
Pro-rated over the period
Averaged over the period
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