Score
0.80
Kelly
35.6%
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Buying a first home
Property / major purchase · 120-month horizon
Score 0.80 · worth doing, but scale the stake to your risk budget (GO_REDUCED)
With the resources you committed ($54,020 of equivalent capital) over a 120-month horizon, the prior win rate is 64.3%, the payoff ratio is b=1.24, giving an expected value of EV=$23,925 and a risk-adjusted return of RAROC=1.27. The expected value is positive, so the arithmetic supports acting. The Kelly-optimal stake of 35.6% exceeds the 20% risk budget for your Working professional profile, so the platform caps its recommendation at that ceiling.
A 10% first-time-buyer down payment plus closing costs on the median existing home, held ten years. The win rate is the share of ten-year windows with positive *real* appreciation; the nominal figure would read above 90%. Mortgage interest, ownership costs and forgone rent are all excluded.
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The three numbers
Win rate, payoff ratio and expected value decide most of the recommendation; Kelly, RAROC and score turn them into an action.
Win rate p
64.3%
Prior probability of success
Payoff ratio b
1.24 ×
b = E[win] / E[loss]
Expected value
$23,925
EV = capital × (p × b − (1 − p))
Kelly
35.6%
(b·p − (1 − p)) / b
RAROC
1.27
EV / (capital × σ)
Score
0.80
score = p × b
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What you are committing
Equivalent capital $54,020, converted from five kinds of resource.
This opportunity carries $54,020 of equivalent capital. The largest single component is cash, at 90% of the total ($48,700). Cash has a clear floor, but keep 30% in reserve. Never put every liquid resource behind one decision.
How non-cash resources are priced
One hour of your own time is priced at $38 and one person-month of hired labour at $8,080. These are market shadow prices, not what you personally earn; changing them changes only the scale, not the ranking.
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How this compares with the category
Your assumptions against the Beta(α, β) prior for this kind of decision.
Category mean win rate
63.3%
Beta(α=19, β=11)
Category payoff P50
1.25 ×
P90 2.50×
Your win rate of 64.3% is in line with the category baseline of 63.3%. The payoff ratio of 1.24× is close to the baseline median of 1.25×. Baseline source: Case-Shiller national index, real 10-year windows (US-RE-10..15) + NAR buyer profile (US-RE-01..05).
Baseline source: Case-Shiller national index, real 10-year windows (US-RE-10..15) + NAR buyer profile (US-RE-01..05)
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Action plan
Sized to the risk budget of your profile: Working professional.
Recommendation: GO_REDUCED — the expected value is positive and this is worth doing, but the Kelly-optimal stake exceeds your risk budget. Scale the commitment down to the risk_budget ceiling shown below.
- Kelly's stake clearly exceeds your risk budget, which means the opportunity is good but large relative to your resources today. Fund it to the risk-budget ceiling and no further.
- Replace one all-in commitment with staged funding: run a pilot or MVP first, then add capital once the metrics hold.
- Consider whether a partner can carry half the cash or time. That halves your effective position without halving the upside.
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Sensitivity analysis
How much the expected value moves when each variable is swung ±20%, ranked by impact. The top two are the ones worth researching before you commit.
- · The tornado analysis identifies Win rate (p) as the variable the conclusion is most sensitive to: a ±20% swing moves the expected value by $31,178. Spend your research budget here first.
- · The second most sensitive variable is Payoff ratio (b) (expected value swings $17,284); the remaining inputs matter markedly less.
- · A quick test for whether to keep researching: buy the information only if it costs less than one fifth of the expected-value swing it would resolve.
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Monte Carlo distribution
10,000 simulated outcomes, seed demo-tier1-property — rerunning with the same inputs gives the same distribution.
P5
-$64,794
Median (P50)
$51,822
P95
$110,759
Probability of a positive outcome
64.5%
Across 10,000 Monte Carlo runs: P5 = -$64,794, P50 = $51,822, P95 = $110,759, and the probability of a positive outcome is 64.5%. The distribution is roughly symmetric — gains and losses are balanced.
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Scenarios
Bull, base and bear, moving win rate and payoff ratio together by ±15%.
Scenario analysis (win rate and payoff ratio moved together by ±15%): bull = $43,071, base = $23,925, bear = $6,724. The $36,347 gap between bull and bear measures how fragile your assumptions are — the wider it is, the more due diligence pays for itself.
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Counterfactual matrix
What the expected value becomes at other combinations of win rate and payoff ratio — how wrong your assumptions can be before the answer changes.
The counterfactual grid shows that expected value turns non-negative once the win rate reaches 20%, or once the payoff ratio reaches 0.5×. Treat those two lines as the minimum bar any further evidence has to clear.
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Assumptions
Every input behind the numbers above, in one place.
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Reproducibility appendix
Everything needed to recompute this report yourself.
Core formulas
EV = capital × (p × b − (1 − p)) f* = (b·p − (1 − p)) / b RAROC = EV / (capital × σ)Python
from models.feasibility_model import expected_value, kelly_fraction, raroc, go_no_go
p, b, sigma, capital = 0.643, 1.244, 0.35, 54020
ev = expected_value(p, b, capital)
kelly = kelly_fraction(p, b)
rr = raroc(ev, capital, sigma)
print(ev, kelly, rr, go_no_go(ev, kelly, 0.20, rr))TypeScript
import { expectedValue, kellyFraction, raroc, goNoGo } from "decision-lab/lib/feasibility";
const p = 0.643, b = 1.244, sigma = 0.35, capital = 54020;
const ev = expectedValue(p, b, capital);
const kelly = kellyFraction(p, b);
const rr = raroc(ev, capital, sigma);
console.log(ev, kelly, rr, goNoGo(ev, kelly, 0.20, rr));Both implementations are in the repository and are kept in agreement by golden-parity tests: models/feasibility_model.py and lib/feasibility/.
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Sources and disclaimer
- · Kelly J.L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal.
- · Markowitz H. (1952). Portfolio Selection. The Journal of Finance.
- · Sharpe W.F. (1966). Mutual Fund Performance. The Journal of Business.
- · Kahneman D. & Tversky A. (1979). Prospect Theory. Econometrica.
- · Industry baseline: Case-Shiller national index, real 10-year windows (US-RE-10..15) + NAR buyer profile (US-RE-01..05)
- · Decision Lab methodology
- · Full business plan (PDF)