Section 1 – TSR Calculation Considerations
One of the benefits of using Relative Total Shareholder Return (“RTSR”) as a performance metric is the transparency of the calculation. It is based on empirical stock price data which is published daily from many different objective financial data sources. Nonetheless a wide variance of methodologies for calculating Total Shareholder Return (“TSR”) exist in the marketplace depending on your plan agreements.
Some of the potential decisions for the calculation are summarized below:
- Treatments of dividends – Are they re-invested and when? Are they accumulated?
- The use of an averaging period to smooth out day to day fluctuations in rankings
- The potential use of volume weighted average prices (VWAP’s)
- Foreign exchange rate considerations, if any global peers are selected
Infinite Equity believes it is critical that companies clearly define their methodology for calculating TSR and have it be explicitly written into their grant agreements. Due to the breadth and magnitude of plans that we administer and certify using MyPerformanceAwards, we have published our preferred methodology for calculating TSR. We have selected this methodology – not for simplicity – but as the most theoretically accurate approach that replicates the returns of an investor.
Section 2 of this article provides a simplistic example of this calculation (without looking at VWAPs or currency rate exchanges). Section 3 provides the mathematical algorithms for calculations using this approach. Although we have published the mathematics here, note that any actual calculation or certification will be customized specific to your program, past practices, and legal grant agreement.
Section 2 – Empirical Example of TSR Calculation
The following example assumes that the TSR calculation uses a 20-trading day average with dividends to be re-invested on the ex-dividend date with the following dividend data. Note that the single share (1.0000) accumulates to 1.0853 shares during the performance period.
| Ex-Dividend Date | Dividends Paid | Stock Price | Shares Purchased | Accumulated Shares |
|---|---|---|---|---|
| 1/28/2016 | $1.00 | $126.01 | .0079 | 1.0079 |
| 4/28/2016 | $1.00 | $146.07 | .0069 | 1.0148 |
| 7/28/2016 | $1.00 | $144.42 | .0070 | 1.0219 |
| 10/28/2016 | $1.00 | $144.00 | .0071 | 1.0290 |
| 1/30/2017 | $1.20 | $164.80 | .0075 | 1.0365 |
| 4/27/2017 | $1.20 | $166.55 | .0075 | 1.0439 |
| 7/28/2017 | $1.20 | $174.00 | .0072 | 1.0511 |
| 10/31/2017 | $1.20 | $186.94 | .0067 | 1.0579 |
| 1/31/2018 | $1.30 | $214.38 | .0064 | 1.0643 |
| 4/30/2018 | $1.30 | $193.73 | .0071 | 1.0714 |
| 7/31/2018 | $1.30 | $197.87 | .0070 | 1.0785 |
| 10/31/2018 | $1.30 | $205.28 | .0068 | 1.0853 |
The calculation of TSR of 64.6% can then be seen as follows:
| Beginning of Performance Period | End of Performance Period | |||||||
|---|---|---|---|---|---|---|---|---|
| Day # | Date | Price | Shares | Value | Date | Price | Shares | Value |
| 1 | 12/31/2015 | $132.04 | 1.0000 | $132.04 | 12/31/2018 | $204.18 | 1.0853 | $221.59 |
| 2 | 12/30/2015 | $133.26 | 1.0000 | $133.26 | 12/28/2018 | $202.08 | 1.0853 | $219.32 |
| 3 | 12/29/2015 | $134.14 | 1.0000 | $134.14 | 12/27/2018 | $200.12 | 1.0853 | $217.19 |
| 4 | 12/28/2015 | $133.12 | 1.0000 | $133.12 | 12/26/2018 | $197.57 | 1.0853 | $214.42 |
| 5 | 12/24/2015 | $133.89 | 1.0000 | $133.89 | 12/24/2018 | $187.76 | 1.0853 | $203.77 |
| 6 | 12/23/2015 | $134.15 | 1.0000 | $134.15 | 12/21/2018 | $192.10 | 1.0853 | $208.48 |
| 7 | 12/22/2015 | $133.14 | 1.0000 | $133.14 | 12/20/2018 | $193.58 | 1.0853 | $210.09 |
| 8 | 12/21/2015 | $131.19 | 1.0000 | $131.19 | 12/19/2018 | $195.17 | 1.0853 | $211.82 |
| 9 | 12/18/2015 | $129.53 | 1.0000 | $129.53 | 12/18/2018 | $196.52 | 1.0853 | $213.28 |
| 10 | 12/17/2015 | $133.97 | 1.0000 | $133.97 | 12/17/2018 | $197.92 | 1.0853 | $214.80 |
| 11 | 12/16/2015 | $135.88 | 1.0000 | $135.88 | 12/14/2018 | $200.00 | 1.0853 | $217.06 |
| 12 | 12/15/2015 | $134.88 | 1.0000 | $134.88 | 12/13/2018 | $202.42 | 1.0853 | $219.68 |
| 13 | 12/14/2015 | $132.02 | 1.0000 | $132.02 | 12/12/2018 | $202.48 | 1.0853 | $219.75 |
| 14 | 12/11/2015 | $130.31 | 1.0000 | $130.31 | 12/11/2018 | $202.28 | 1.0853 | $219.53 |
| 15 | 12/10/2015 | $131.71 | 1.0000 | $131.71 | 12/10/2018 | $203.26 | 1.0853 | $220.60 |
| 16 | 12/9/2015 | $131.71 | 1.0000 | $131.71 | 12/7/2018 | $204.88 | 1.0853 | $222.35 |
| 17 | 12/8/2015 | $133.36 | 1.0000 | $133.36 | 12/6/2018 | $207.96 | 1.0853 | $225.70 |
| 18 | 12/7/2015 | $135.60 | 1.0000 | $135.60 | 12/4/2018 | $210.12 | 1.0853 | $228.04 |
| 19 | 12/4/2015 | $136.48 | 1.0000 | $136.48 | 12/3/2018 | $220.81 | 1.0853 | $239.64 |
| 20 | 12/3/2015 | $132.66 | 1.0000 | $132.66 | 11/30/2018 | $218.24 | 1.0853 | $236.85 |
| 20-Trading Day Average | $133.15 | $219.20 | ||||||
| TSR with Dividends Reinvested | 64.6% | |||||||
Section 3 – Mathematical Algorithms (Appendix – For those that just need to know)
Data Necessary
- Stock Prices (
) – On any day i, this will be denoted by
- Dividend Data (
) – On any day i, this will be denoted by
Calculations Necessary
Let x represent the number of days in an x-day averaging period. (All calculations below should begin x-days prior to the beginning of the performance period, and therefore incorporate any dividends that may have been paid during the averaging period).
Total Shares () – Represents the net number of shares owned (including new dividend shares) on any day i. It is calculated as
.
New Shares () – Represents the new number of shares purchased on day i from dividends. It is calculated as
.
Total Value ( ) – Represents the total value of the original share after reinvestment of dividends at any time i. It is calculated as
.
Averaging Period ( ) – Represents the average total value over an x-day averaging period. It is calculated as
. (Note that at the beginning of the performance period, Time 0, this simplifies to
.
Total Shareholder Return () – Represents the total shareholder return over an x-day averaging period on any day i. It is calculated as
.
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