Chipotle 3-year relative TSR PSU: grant-date fair value

Hypothetical design on public data. 16 disclosed peers, Monte Carlo, 100,000 trials, valued as of 2026-09-18.

A target share of this award is worth $43.28, which is 129.5% of Chipotle's $33.43 stock price. The award pays nothing about 30% of the time and pays the 200% maximum about 25% of the time, so most of the value sits in the tails. Fair value exceeds the share price because the award pays most when the stock has also done best.
Fair value per target share
$43.28
129.5% of the $33.43 stock price. 95% interval ±$0.34
Expected payout
91%
of target, risk-neutral
Probability of zero
30.5%
below the 25th percentile
Probability of maximum
24.5%
75th percentile or better, TSR positive
Target or better
46.4%
payout of 100% or more

Payout distribution

0%10%20%30%30.5%0%50%62.5%75%87.5%13.3%100%125%150%175%24.5%200%Payout as % of target

Ten possible payouts because 16 peers give 17 discrete rank positions. The guardrail moves 8.3% of trials down to 100%: those are the cases where Chipotle beat most peers while its own 3-year TSR was still negative (Chipotle's TSR is negative in 59% of risk-neutral trials).

Table view
PayoutProbability
0%30.47%
50%6.23%
62.5%6.02%
75%5.58%
87.5%5.31%
100%13.29%
125%2.59%
150%2.76%
175%3.25%
200%24.50%

Sanity checks

PASS
Discounted expected stock price equals today's price
Chipotle: discounted expected price $33.41 vs today $33.43, ratio 0.9995 (standard error 0.0021). Across all 17 companies, the discounted expected total-return price is within 0.37% of today's price (tolerance 0.5%).
PASS
An award that always pays target is worth exactly one share
Forcing the payout to 100% in every trial values the award at $33.41 per target share, which is 0.9995 shares (standard error 0.0021, tolerance 0.5%).
PASS
A company identical to its peers ranks at the 50th percentile on average
Separate run with all 17 companies at 35.5% volatility, uniform correlation 0.289, no dividends: mean percentile 50.00 (standard error 0.10). Each of the 17 rank slots landed within 2.0% of the exact 1/17 share. Expected payout in that world 107.4% of target vs the exact 107.4%.

Inputs

InputValueSourceNote
Grant date / valuation date2026-09-18assumedLast date in the price file and the Treasury file
Performance period3 years, ends 2029-09-18specifiedplan_terms.md
Chipotle close on grant date$33.43measuredprices_split_adjusted.csv, last row
Chipotle 20-day start average$36.57measuredSimple average of the 20 closes ending on the grant date
Risk-free rate4.83% par yield, 4.773% continuousmeasuredrisk_free.csv, 3-year tenor; conversion to continuous compounding is assumed
Chipotle volatility35.5%measuredDaily log returns 2023-09-18 to 2026-09-18, 753 returns, x sqrt(252)
Peer volatilities18.3% to 45.4%measuredSame window and method; per-company values below
Correlation matrix17 x 17, average pairwise 0.289measuredRange 0.11 to 0.85; full matrix used via Cholesky
Dividend yieldsChipotle 0%, peers 0% to 4.38%measureddividend_yields.csv trailing_yield; held constant, reinvested continuously
DriftRisk-neutral: r minus dividend yieldspecifiedSpecified for fair value
Payout curve0% / 50% / 100% / 200% at <25th / 25th / 50th / 75th+specifiedStraight-line between points
GuardrailPayout capped at 100% if Chipotle absolute TSR < 0specifiedplan_terms.md
Percentile conventionPeers beaten / 16assumedSame as Excel PERCENTRANK.INC among 17; gives 17 discrete ranks and 10 payout levels
Trials100,000specifiedRun as 50,000 antithetic pairs; seed 20260918
Trading days per year252assumed756 steps in the period; one exact step to day 736, then 20 daily steps
Settlement valueChipotle close on the final dayassumedNot the 20-day average; no dividend equivalents
Per-company inputs (all measured from the files)
CompanyVolatilityDividend yieldCorr. with CMG20-day start avgClose 2026-09-18Close / start avg
CMG Chipotle35.5%0.00%$36.57$33.430.914
ABNB Airbnb36.2%0.00%0.25$178.34$166.220.932
BKNG Booking30.7%0.98%0.30$189.76$167.900.885
DASH DoorDash42.2%0.00%0.34$214.79$192.940.898
DPZ Domino's29.1%2.62%0.30$329.91$294.200.892
DRI Darden26.1%2.92%0.32$214.47$209.280.976
EBAY eBay31.9%1.09%0.25$106.28$111.841.052
EXPE Expedia45.0%0.66%0.23$302.39$279.350.924
HLT Hilton22.9%0.20%0.37$314.38$305.730.972
LULU lululemon45.4%0.00%0.29$109.30$98.060.897
MAR Marriott25.8%0.83%0.35$341.48$338.920.992
MCD McDonald's18.3%3.00%0.23$258.75$248.240.959
QSR Restaurant Brands23.4%4.38%0.26$77.96$72.880.935
SBUX Starbucks32.6%2.59%0.27$102.94$95.830.931
UBER Uber37.7%0.00%0.19$74.83$70.500.942
ULTA Ulta Beauty35.4%0.00%0.19$541.78$540.980.999
YUM Yum! Brands21.6%2.15%0.32$148.19$137.990.931

Close / start avg below 1.00 means the company begins the period already behind its own TSR starting line. The whole group sold off over the last 20 days, so Chipotle's handicap is mid-pack.

Assumptions not specified in the brief

  1. Grant date is 2026-09-18, the last date in the price file, so the period runs to 2029-09-18. The simulation starts from that day's close.
  2. "Trailing 3 years" means 2023-09-18 to 2026-09-18: 754 closes, 753 daily log returns. The file's earlier two years were not used.
  3. Volatility is the sample standard deviation of daily log returns, annualized with 252 trading days. Correlation is Pearson on the same returns. Both are held constant for the full 3 years (lognormal, geometric Brownian motion).
  4. The 4.83% Treasury par yield was converted to 4.773% continuous (2 x ln(1 + y/2)) and applied flat. No zero-curve bootstrap.
  5. Dividend yields are the file's trailing yields, held constant and reinvested continuously. No dividend growth. Risk-neutral drift per company is r minus its yield.
  6. The start price is the simple average of the 20 closes ending on the grant date, inclusive. Dividends paid inside that 20-day window are ignored (a fraction of one quarterly dividend).
  7. The end price is the average of the total-return index over the last 20 trading days of the period (days 737 to 756).
  8. Percentile rank = number of peers beaten divided by 16. Equivalent to Excel PERCENTRANK.INC among all 17. Ties have zero probability with continuous prices. Because rank is discrete, payout takes only 10 values.
  9. The guardrail tests the same 20-day-average TSR used for ranking, strictly below zero.
  10. Settlement value is Chipotle's closing price on the final day, not the 20-day average, with no dividend equivalents (moot, Chipotle pays no dividend).
  11. No forfeiture, service condition, or retirement-eligibility haircut. Fair value is per target share that vests.
  12. The peer group is fixed at 16 for 3 years. No rule for a peer that is acquired or delisted.
  13. The payout distribution and expected payout are reported under the same risk-neutral measure used for fair value. Real-world expectations would differ (plan item 3 was not requested here and is not shown).
  14. 100,000 paths were run as 50,000 antithetic pairs (variance reduction), seed 20260918. One exact GBM step to day 736 then 20 daily steps, which is exact for this model.
  15. The identical-peer check puts all 17 companies at Chipotle's 35.5% volatility, zero yield, uniform correlation 0.289, the same start price, seed 7.
  16. Pass tolerances: checks 1 and 2 within 0.5% of exact; check 3 mean percentile within 0.5 points of 50 and every rank slot within 6% relative of 1/17.

Built 2026-09-19T17:12:38 in 3.7s. Code: 3-outputs/rtsr_montecarlo.py, results: 3-outputs/results.json. Data: 1-data/prices_split_adjusted.csv, dividend_yields.csv, risk_free.csv. Plan: 2-plan/plan_terms.md.