Probability Weighting and Expected Value
Learning Objectives
Assign consistent probabilities across mutually exclusive scenarios
Calculate expected value for XRP CBDC thesis
Adjust probabilities based on personal analysis and conviction
Apply decision theory frameworks (Kelly criterion, risk-adjusted returns)
Create personal investment decision framework for CBDC thesis
CBDC SCENARIO PROBABILITY SUMMARY
Based on Course Analysis (Lessons 1-16):
Full Adoption (25%+ share): 7.5%
High Partial (15-25%): 7.5%
Mid Partial (10-15%): 12.5%
Low Partial (5-10%): 17.5%
Minimal (<5%): 20%
Failure (0% CBDC share): 35%
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TOTAL: 100%
- These are base case estimates
- Derived from component analysis
- Your estimates may differ
- Should sum to 100%
PROBABILITY DERIVATION METHOD
- Technical requirements
- Regulatory requirements
- Competitive requirements
- Adoption requirements
- Technical: 60-80%
- Regulatory: 40-60%
- Competitive: 30-50%
- Adoption: 20-40%
Step 3: Combination
Combined using rough independence assumptions:
Full Adoption = T × R × C × A
~7.5% = 0.70 × 0.50 × 0.40 × 0.30 × adjustment
- Probabilities sum to 100%
- Relative rankings make sense
- Failure captures remaining probability
PROBABILITY CONSISTENCY CHECKS
Check 1: Sum to 100%
✓ 7.5 + 7.5 + 12.5 + 17.5 + 20 + 35 = 100%
- Full < High Partial < Mid Partial < Low Partial
- Each requires more things to go right
- Failure is largest single category
- Success scenarios (>5%): 45%
- Failure scenarios: 55%
- Consistent with "more likely to fail"
- Similar to Lesson 3-8 estimates
- Incorporates Phase 2 findings
- Liquidity analysis included
PRICE ESTIMATES BY SCENARIO
Scenario Price Range Midpoint
Full Adoption $20-50 $35
High Partial $12-21 $16
Mid Partial $8-12 $10
Low Partial $4-6 $5
Minimal $3-4 $3.50
Failure $1.50-3 $2.25
- Prices are 2035 estimates
- Include CBDC + ODL value
- Failure still has ODL floor
- Current price: ~$2.50
EXPECTED VALUE FORMULA
EV = Σ (Probability × Price)
CALCULATION:
Scenario Prob Price Contribution
Full Adoption 7.5% × $35 = $2.63
High Partial 7.5% × $16 = $1.20
Mid Partial 12.5% × $10 = $1.25
Low Partial 17.5% × $5 = $0.88
Minimal 20.0% × $3.50 = $0.70
Failure 35.0% × $2.25 = $0.79
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EXPECTED VALUE: $7.45
INTERPRETATION:
Current price: $2.50
Expected value: $7.45
Expected gain: $4.95 (198%)
Annualized (10 years): ~11.5%
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EXPECTED VALUE VS. DISTRIBUTION
EV: $7.45
- Failure: 35% probability
- Price: $2.25
- This is the MODE
- 50th percentile falls in Low Partial
- Price: ~$5
- This is the MEDIAN
- Mean (EV): $7.45
- Median: ~$5
- Mean > Median = Right-skewed distribution
IMPLICATION:
Don't expect $7.45.
Most likely outcome is below EV.
EV is pulled up by low-probability high outcomes.
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WHEN YOUR PROBABILITIES MIGHT DIFFER
- More optimistic on regulatory clarity
- Believe mBridge will stall
- See stablecoin weakness
- Have insights on adoption pathway
- Trust Ripple execution more
- More pessimistic on CB adoption
- Believe stablecoins will dominate
- See mBridge expanding faster
- Skeptical of liquidity development
- Concerned about competition
DOCUMENT YOUR REASONING
Don't just feel different—explain why.
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EXAMPLE: OPTIMISTIC ADJUSTMENT
Reasoning: "I believe regulatory clarity will accelerate adoption faster than base case assumes"
Adjusted Probabilities:
Full Adoption: 10% (+2.5%)
High Partial: 10% (+2.5%)
Mid Partial: 15% (+2.5%)
Low Partial: 20% (+2.5%)
Minimal: 15% (-5%)
Failure: 30% (-5%)
Adjusted EV:
10%×$35 + 10%×$16 + 15%×$10 + 20%×$5 + 15%×$3.50 + 30%×$2.25
= $3.50 + $1.60 + $1.50 + $1.00 + $0.53 + $0.68
= $8.81 (vs. base $7.45)
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EXAMPLE: PESSIMISTIC ADJUSTMENT
Reasoning: "I think stablecoins will capture most of the bridge opportunity, limiting XRP to niche"
Adjusted Probabilities:
Full Adoption: 3% (-4.5%)
High Partial: 5% (-2.5%)
Mid Partial: 8% (-4.5%)
Low Partial: 12% (-5.5%)
Minimal: 22% (+2%)
Failure: 50% (+15%)
Adjusted EV:
3%×$35 + 5%×$16 + 8%×$10 + 12%×$5 + 22%×$3.50 + 50%×$2.25
= $1.05 + $0.80 + $0.80 + $0.60 + $0.77 + $1.13
= $5.15 (vs. base $7.45)
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EXPECTED VALUE SENSITIVITY
- Base (7.5%): EV = $7.45
- High (15%): EV = $10.08
- Low (3%): EV = $5.88
- Range: $4.20 swing
- Base (35%): EV = $7.45
- High (50%): EV = $6.23
- Low (20%): EV = $8.67
- Range: $2.44 swing
- Base ($35): EV = $7.45
- High ($50): EV = $8.58
- Low ($20): EV = $6.33
- Range: $2.25 swing
MOST SENSITIVE TO:
Full adoption probability > Failure probability > Prices
Getting success probability right matters most.
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KELLY CRITERION FOR POSITION SIZING
Formula:
f* = (p × b - q) ÷ b
- f* = optimal fraction of capital
- p = probability of winning
- b = win/loss ratio (payout odds)
- q = probability of losing (1-p)
- p = 45% (positive outcome)
- Average win = 150% gain
- q = 55% (negative outcome)
- Average loss = 30%
- b = 150% ÷ 30% = 5
f* = (0.45 × 5 - 0.55) ÷ 5 = 0.34 = 34%
INTERPRETATION:
Kelly suggests 34% of investable capital.
This is AGGRESSIVE.
Most practitioners use half or quarter Kelly.
Half Kelly: 17%
Quarter Kelly: 8.5%
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SHARPE RATIO ANALYSIS
- EV: $7.45 (from $2.50)
- Total return: 198%
- Annualized (10 yr): 11.5%
Risk-Free Rate: 4%
Excess Return: 7.5%
- XRP historical: ~100% annual
- Future estimate: ~80% annual
Sharpe Ratio:
SR = (11.5% - 4%) ÷ 80% = 0.094
INTERPRETATION:
SR < 0.5 is considered poor.
XRP CBDC thesis has low Sharpe.
High volatility reduces risk-adjusted return.
But Sharpe doesn't capture asymmetry.
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SORTINO RATIO ANALYSIS
Sortino focuses on downside volatility only.
- Consider only negative outcomes
- Failure scenarios: ~55%
- Average loss: ~30%
- Downside volatility: ~50%
Sortino Ratio:
= (11.5% - 4%) ÷ 50% = 0.15
- Acknowledges asymmetric upside
- Doesn't penalize positive volatility
- More appropriate for option-like payoffs
CONCLUSION:
Traditional risk metrics undervalue
asymmetric opportunities like XRP CBDC.
Position sizing should account for optionality.
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BUILDING YOUR DECISION FRAMEWORK
- Review course analysis
- Adjust based on your insights
- Document reasoning
- Ensure consistency (sum to 100%)
- Use your probabilities
- Apply scenario prices
- Compute EV
- Maximum acceptable loss
- Time horizon
- Liquidity needs
- Overall portfolio context
- Kelly criterion (aggressive)
- Risk-limited (conservative)
- Blend based on conviction
- When to add
- When to reduce
- Review frequency
- Trigger events
EXAMPLE PERSONAL FRAMEWORK
- Full Adoption: 10%
- High Partial: 10%
- Mid Partial: 15%
- Low Partial: 18%
- Minimal: 17%
- Failure: 30%
My EV Calculation:
10%×$35 + 10%×$16 + 15%×$10 + 18%×$5 + 17%×$3.50 + 30%×$2.25
= $8.55
- Max acceptable loss: 10% of portfolio
- Max XRP drawdown: 80%
- Risk-limited allocation: 10% ÷ 80% = 12.5%
- Time horizon: 7+ years
- Liquidity needs: Low
- Kelly: ~30%
- Risk-limited: 12.5%
- Chosen: 10% (comfortable blend)
- Add if: First CBDC pilot with XRP; probability → higher
- Reduce if: mBridge >20 members; stablecoin dominance
- Review: Quarterly
- Time limit: Reassess fully in 2028
DECISION FRAMEWORK PITFALLS
- Memory is unreliable
- Emotions override logic
- Write it, date it, follow it
- Your probabilities have uncertainty
- Build in margin for error
- Use ranges, not points
- Your estimates should anchor on analysis
- Extraordinary claims need evidence
- Don't just pick optimistic numbers
- Reacting to every headline
- Probabilities shouldn't swing 10%+ often
- Distinguish noise from signal
- If XRP rises, allocation increases
- Discipline to trim at targets
- Or accept higher allocation
✅ Base case EV is ~$7.45: Probability-weighted across all scenarios.
✅ Kelly criterion suggests 17-34% allocation: Depending on full vs. half Kelly.
✅ Traditional risk metrics are low: Sharpe ~0.1 due to high volatility.
✅ Personal framework is essential: Documented rules prevent emotional decisions.
✅ Sensitivity highest to success probability: Getting adoption odds right matters most.
⚠️ Exact probabilities: All estimates have uncertainty bands.
⚠️ Price estimates: 2035 prices are inherently uncertain.
⚠️ Correlation assumptions: Scenarios may not be fully independent.
🔌 Taking Kelly literally: Full Kelly is too aggressive for uncertain estimates.
🔌 Overweighting your views: Humility about probability estimates is wise.
🔌 Not documenting framework: Leads to emotional decisions.
Assignment: Create your personal investment decision framework for XRP CBDC thesis.
Requirements:
Part 1: Your Probability Estimates (300-400 words)
Assign probabilities to each scenario. Explain where and why you differ from base case.
Part 2: Your Expected Value (250-350 words)
Calculate your EV. Show math. Compare to base case and explain difference.
Part 3: Position Sizing (300-400 words)
Determine your recommended allocation using Kelly, risk-limited, and personal factors. Explain your choice.
Part 4: Decision Rules (200-300 words)
Define triggers for adding, reducing, and reviewing. Include time limits.
Total: 1,050-1,450 words
Time investment: 4-5 hours
1. What is the base case expected value for XRP including CBDC thesis?
Correct Answer: ~$7.45, representing 198% expected gain from current $2.50.
2. What does Kelly criterion suggest for XRP allocation?
Correct Answer: 17-34% (half to full Kelly), but most should use quarter to half Kelly given uncertainty.
3. Why is the Sharpe ratio low despite positive expected value?
Correct Answer: High volatility (~80% annually) in the denominator overwhelms the ~7.5% excess return.
4. What is the most important sensitivity in the EV calculation?
Correct Answer: Full adoption probability—small changes have large EV impact due to high scenario value.
5. Why should decision frameworks be written down?
Correct Answer: Prevents emotional decisions, creates accountability, ensures consistency, and enables learning from results.
End of Lesson 17
Total words: ~4,500
Estimated completion time: 55 minutes reading + 4-5 hours for deliverable
Key Takeaways
Base case EV: ~$7.45:
198% expected gain from $2.50 current.
Kelly suggests 17-34%:
But use half or quarter Kelly given uncertainty.
Risk-adjusted returns are modest:
High volatility reduces Sharpe despite positive EV.
Create written framework:
Document probabilities, position size, and decision rules.
Sensitivity analysis matters:
Focus on getting success probability right. ---