Range Accruals - Income from Volatility

Level 1: Beginner | Module 1.4 | Time: 2 hours

🎯 Learning Objectives

By the end of this module, you will:

Understand range accrual mechanics and daily accrual concepts
Learn optimal market conditions (sideways, low volatility)
Master range selection strategy
Calculate yield and probability
Identify barrier risks and manage them

Prerequisites: Principal Protected Notes

What is a Range Accrual?

A structured product that pays yield for each day the underlying asset trades within a specified price range.

The Core Concept

Think of it as a "parking meter" for your money:

Traditional parking meter:
- Pay $2/hour while parked
- No payment when you leave

Range Accrual:
- Earn 0.15% per day Bitcoin stays in range ($45k-$55k)
- Earn nothing when Bitcoin breaks out of range
- Your capital is still invested, just not earning

Perfect for: Sideways markets, low volatility environments, income seekers.

How Range Accruals Work

Basic Structure

Step 1: Define the Range

Lower Barrier: $45,000
Upper Barrier: $55,000
Range: $45,000 - $55,000 (±10% from $50k center)

Step 2: Set the Daily Accrual Rate

Daily rate: 0.15%
If in range: Earn 0.15% that day
If out of range: Earn 0% that day

Step 3: Count Days in Range

30-day period
Bitcoin in range: 22 days
Bitcoin out of range: 8 days

Yield = 22 days × 0.15% = 3.3% (in 30 days!)
Annualized: ~40%+ if repeatable

Complete Range Accrual Example

Initial Setup

Date: March 1, 2025
Investment: $100,000
Underlying: Bitcoin (currently $50,000)
Range: $45,000 - $55,000 (±10%)
Daily Accrual Rate: 0.15%
Term: 30 days (expires April 1)

Daily Tracking

Scenario: Typical Month

Day 1 (Mar 1): BTC = $50,200 ✅ In range → Earn $150 (0.15% of $100k)
Day 2 (Mar 2): BTC = $51,000 ✅ In range → Earn $150
Day 3 (Mar 3): BTC = $52,500 ✅ In range → Earn $150
Day 4 (Mar 4): BTC = $54,800 ✅ In range → Earn $150
Day 5 (Mar 5): BTC = $55,500 ❌ Out of range → Earn $0
Day 6 (Mar 6): BTC = $56,000 ❌ Out of range → Earn $0
Day 7 (Mar 7): BTC = $54,000 ✅ Back in range → Earn $150
...

Days in range: 22 out of 30
Total earned: 22 × $150 = $3,300

Return: 3.3% in 30 days
Annualized: ~40% (if repeatable)

Visual Representation

Price Chart with Barriers:

$60k |
     |                    •
$55k |--------------------•---------- Upper Barrier ❌
     |         •    • •   |  • •
$50k |   • • •  •  •   • •    •  •   Center
     |  •               •
$45k |-------------------------------- Lower Barrier ❌
     |
     +----> Time (30 days)

Green zone (between barriers): Earning days ✅
Red zone (outside barriers): Non-earning days ❌

Range Selection Strategy

How to Choose Your Range

Factor 1: Historical Volatility

Look at past 30-day price movements:

Bitcoin Historical Ranges (30-day):
- Low vol period: $48k - $52k (±4% range)
- Medium vol: $45k - $55k (±10% range)
- High vol: $40k - $60k (±20% range)

Strategy:
- Use historical data to set realistic ranges
- Wider range = higher probability but lower yield
- Narrower range = lower probability but higher yield

Factor 2: Volatility Regime

Check current market conditions:

Low Volatility (VIX < 20, BTC IV < 60%):
→ Set tighter ranges (±5-8%)
→ Higher accrual rates available
→ More days in range expected

High Volatility (VIX > 30, BTC IV > 80%):
→ Set wider ranges (±15-20%)
→ Lower accrual rates but safer
→ Fewer days out of range

Factor 3: Risk Tolerance

Conservative: ±15-20% range
- High probability of staying in range
- Lower accrual rates (~0.10%/day)
- Annualized: ~30%

Moderate: ±10-12% range
- Medium probability
- Medium accrual rates (~0.15%/day)
- Annualized: ~40%

Aggressive: ±5-8% range
- Low probability of full month in range
- High accrual rates (~0.25%/day)
- Annualized: ~60%+ (if you win)

Yield Calculation Methods

Method 1: Fixed Daily Rate

Most Common Structure

Daily rate: 0.15%
30-day term
Days in range: Variable

Best case (30/30 days): 30 × 0.15% = 4.5%
Expected (22/30 days): 22 × 0.15% = 3.3%
Worst case (0/30 days): 0 × 0.15% = 0%

Method 2: Fixed Total Yield (Divided by Days)

Total yield offered: 4%
Term: 30 days

Daily rate = 4% / 30 = 0.133% per day

If in range 25 days:
Yield = (25/30) × 4% = 3.33%

Method 3: Tiered Ranges (Multiple Barriers)

Range 1 (narrow): $48k - $52k → 0.25%/day
Range 2 (medium): $45k - $55k → 0.15%/day
Range 3 (wide): $40k - $60k → 0.08%/day

Example month:
- 10 days in Range 1: 10 × 0.25% = 2.5%
- 15 days in Range 2 only: 15 × 0.15% = 2.25%
- 5 days in Range 3 only: 5 × 0.08% = 0.4%
- Total: 5.15% (excellent!)

Method 4: Digital Range (All or Nothing)

Stay in range ALL 30 days → 6% total
Break range ONCE → 0% total

High risk, high reward
Not recommended for beginners

Probability Calculation

Estimating Success Probability

Using Historical Volatility

Current Bitcoin price: $50,000
Range: $45,000 - $55,000 (±10%)
Historical 30-day volatility: 50% annualized

Daily volatility = 50% / √365 = ~2.6%

Probability of staying in ±10% range for 30 days:
- Rough estimate: ~60-70%

Formula (simplified):
P(stay in range) ≈ 1 - (Daily Vol / Range Width)^Days

Using Implied Volatility

Check option prices:
- $45k put premium: $2,000
- $55k call premium: $2,500

Market is pricing ~30% chance of breaching range

Therefore:
- 70% chance of staying in range
- Expected days in range: 30 × 0.70 = 21 days
- Expected yield: 21 × 0.15% = 3.15%

Expected Value Calculation

Scenario A (60% probability): 25 days in range
Yield: 25 × 0.15% = 3.75%

Scenario B (30% probability): 18 days in range
Yield: 18 × 0.15% = 2.7%

Scenario C (10% probability): 10 days in range
Yield: 10 × 0.15% = 1.5%

Expected Value:
(0.60 × 3.75%) + (0.30 × 2.7%) + (0.10 × 1.5%) = 3.21%

Expected annualized: ~38%

Optimal Market Conditions

✅ Perfect for Range Accruals

1. Low Volatility Environments

Characteristics:
- VIX < 20 (stocks) or BTC IV < 60%
- Tight trading ranges
- Lack of major catalysts
- "Boring" markets

Example:
Bitcoin consolidating $48k-$52k for weeks
→ Perfect for tight range accrual
→ High probability of success

2. Post-Crash Recovery (Stabilization Phase)

Timeline:
- Major crash happens (BTC $60k → $40k)
- Panic subsides
- Price stabilizes around $42k-$48k for months

Strategy:
Set range at new equilibrium ($40k-$50k)
Earn yield during consolidation phase

3. Bull Market Pause

Scenario:
- Strong uptrend (BTC $30k → $50k)
- Hits resistance at $50k
- Consolidates for 2-3 months

Strategy:
Range accrual at $48k-$53k during pause
High income while market decides direction

4. Sideways Markets

Multi-month ranging:
- No clear direction
- Support at $45k, resistance at $55k
- Bouncing between levels

Result:
Multiple range accrual cycles at $45k-$55k
Consistent monthly income (3-5%)

❌ Avoid Range Accruals When

1. High Volatility Events

Upcoming:
- Bitcoin halving (next week)
- Major regulation announcement
- FOMC meeting
- Earnings (for stocks)

Problem: Huge price swings likely
Solution: Wait until after event

2. Strong Trending Markets

Clear uptrend or downtrend:
- BTC making new highs weekly
- Or crashing continuously

Problem: Will break out of range quickly
Solution: Use directional strategies instead

3. Major News Pending

Examples:
- Spot Bitcoin ETF decision
- Major exchange hack
- Regulatory clarity expected

Problem: Binary outcomes → big moves
Solution: Stay on sidelines

Barrier Risks

Understanding Barrier Dynamics

Continuous Monitoring (Most Common)

Range: $45,000 - $55,000

Intraday breach counts!

Example:
- Opens at $50,000 ✅
- Spikes to $55,500 during day ❌
- Closes at $53,000

Result: NO accrual for that day (touched barrier)

Daily Close Monitoring (Investor Friendly)

Only closing prices matter

Example:
- Opens at $50,000 ✅
- Spikes to $55,500 intraday
- Closes at $53,000 ✅

Result: ACCRUAL earned (closed in range)

Note: This structure pays higher yields

Barrier Types

1. Soft Barriers (Warning Zone)

Main range: $45k - $55k (earn 0.15%/day)
Warning zone: $43k - $57k (earn 0.05%/day)
Hard barrier: $40k - $60k (earn 0%)

More forgiving structure

2. Hard Barriers (Binary)

In range: 0.15%/day
Out of range: 0%/day

Simple but unforgiving
One bad day = no accrual

3. Knock-Out Barriers (Termination)

Range: $45k - $55k
Knock-out: If touches $40k or $60k → structure terminates

High risk!
Could lose all future accrual potential

Real-World Case Study: 2019 Bitcoin Sideways Year

Background

Investor: Sarah (income seeker)
Capital: $200,000
Date: April 2019
Market: Bitcoin consolidating after 2018 bear market
BTC Price: ~$5,000 (range-bound $4,000-$6,000)

Strategy: 12-Month Range Accrual Campaign

Structure per month:
Range: $4,000 - $6,000 (±20% from $5k center)
Daily rate: 0.12%
Investment: $200,000
Term: Monthly rolling (12 cycles)

Month-by-Month Results

Month 1 (Apr): BTC $4,800-$5,200 → 28/30 days in range
Earned: 28 × 0.12% × $200k = $6,720 (3.36%)

Month 2 (May): BTC $5,500-$6,200 → 22/31 days (breached upper)
Earned: 22 × 0.12% × $200k = $5,280 (2.64%)

Month 3 (Jun): BTC $5,800-$7,500 → 15/30 days (broke out upward)
Earned: 15 × 0.12% × $200k = $3,600 (1.8%)

Month 4-10 (Jul-Jan): Back to ranging $6,000-$8,000
Adjusted range to $5,500-$8,500
Average: 25/30 days per month
Earned: ~$6,000/month average

Month 11-12: Volatility increased, ended strategy

Final Results (10 months)

Total earned: ~$58,000
Return: 29% in 10 months
Annualized: ~35%

Compared to:
- Holding BTC: $5k → $7.5k = +50% (better)
- But: Sarah had INCOME each month (no volatility stress)
- Could have used range accrual + held BTC separately

Key Lesson: Range accruals excel in consolidation periods, underperform in strong trends.

Advanced Range Accrual Structures

1. Multiple Underlying Assets

Basket Range Accrual:
- Bitcoin in range $45k-$55k: 0.15%/day
- Ethereum in range $2,500-$3,500: 0.15%/day

Earn BOTH if both in range: 0.30%/day
Earn ONE if only one in range: 0.15%/day
Earn ZERO if both out of range: 0%

Diversification benefit

2. Asymmetric Ranges

Bullish bias:
Lower barrier: $45,000 (10% below)
Upper barrier: $60,000 (20% above)

Wider upside room reflects bullish view
Still earn income in expected path

3. Memory Features

Standard: Miss one day → lose that day's accrual

Memory feature:
- If BTC breaks range but returns within 3 days
- "Catch-up" accrual for missed days
- Costs more (lower daily rate) but more forgiving

4. Autocall + Range Accrual Hybrid

Year 1:
- Range accrual $45k-$55k (0.15%/day)
- Autocall trigger: If BTC > $65k anytime, product calls

If autocalled early:
- Get all accrued yield + principal + bonus
- Exit with profits

If not called:
- Continue earning monthly accruals

Practical Implementation Strategy

Step 1: Analyze Market Conditions

Check:
1. Historical 30-day ranges
2. Current implied volatility
3. Upcoming events calendar
4. Support/resistance levels

Decision: Is market range-bound? Yes/No

Step 2: Set Your Range

Conservative approach:
- Take 60-day historical range
- Add 20% buffer
- Example: If BTC traded $46k-$54k → set $44k-$56k

Aggressive approach:
- Use 30-day historical range
- Tighter bounds for higher yield

Step 3: Calculate Expected Return

Expected days in range: ____ / 30
Daily rate: ____%
Expected yield: (Days × Rate)

Compare to:
- Risk-free rate (bonds)
- Other strategies
- Opportunity cost

Proceed if yield justifies risk

Step 4: Monitor Daily

Daily checklist:
☐ Check if price in range today
☐ Track cumulative accrual
☐ Monitor volatility changes
☐ Watch for upcoming events
☐ Consider early exit if conditions change

Step 5: Roll or Exit

At expiration:
Option A: Roll to new range accrual (market still sideways)
Option B: Exit and reassess (market trending)
Option C: Switch strategies (volatility changed)

Common Mistakes to Avoid

Mistake 1: Ignoring Volatility Regime Changes

❌ Wrong:
Set range accrual during low vol
Volatility spikes (news event)
Stay in position, lose accrual days

✅ Right:
Monitor volatility continuously
Exit early if IV spikes significantly
Accept small loss to avoid large opportunity cost

Mistake 2: Range Too Tight (Greed)

❌ Wrong:
BTC at $50k, historical range $45k-$55k
Set range at $49k-$51k for 0.30%/day rate
BTC hits $51.5k on day 3 → most month wasted

✅ Right:
Use wider, realistic ranges
Better to earn 0.15%/day for 25 days
Than 0.30%/day for 8 days

Mistake 3: Not Accounting for Event Risk

❌ Wrong:
Bitcoin halving in 2 weeks
Enter 30-day range accrual
Halving causes 20% spike → range broken

✅ Right:
Check event calendar BEFORE entering
Wait until after major events
Or set much wider ranges to accommodate

Mistake 4: Assuming Linear Probability

❌ Wrong thinking:
"Bitcoin in range 80% of last 30 days,
so next 30 days will be 80% too"

✅ Right thinking:
Markets change regimes
Past performance ≠ future results
Use probability as GUIDE, not certainty

Mistake 5: Neglecting Opportunity Cost

❌ Wrong:
Bitcoin clearly breaking out upward
Stay in range accrual earning 3%/month
Miss 40% rally

✅ Right:
Exit range accrual when trend becomes clear
Switch to directional strategies
Range accruals are for UNCERTAINTY, not trends

Practice Exercise: Design a Range Accrual

Your Scenario

Date: Today
Asset: Ethereum
Current Price: $3,000
Your Capital: $50,000
View: Sideways for next 60 days
Historical 30-day range: $2,700 - $3,300
Current IV: 65% (moderate)
Risk Tolerance: Moderate

Design a 60-day range accrual strategy

Click for suggested solution

Recommended Structure:

Range Selection:
Lower barrier: $2,600 (13% below current)
Upper barrier: $3,400 (13% above current)

Rationale:
- Historical range was $2,700-$3,300 (±10%)
- Add buffer for safety → ±13%
- Moderate IV supports moderate range

Daily Accrual Rate:
Target: 0.13% per day (moderate for moderate range)

Expected Outcomes:

Best case (55/60 days in range):
Yield = 55 × 0.13% = 7.15%
Annualized: ~43%

Expected case (45/60 days in range):
Yield = 45 × 0.13% = 5.85%
Annualized: ~35%

Worst case (25/60 days in range):
Yield = 25 × 0.13% = 3.25%
Annualized: ~20%

Decision:
Proceed if:
- Expected 35% annualized beats alternatives
- Comfortable with 20% worst-case scenario
- No major ETH events in next 60 days

Key Takeaways

1. Range accruals earn yield when assets trade sideways

Perfect for low volatility periods
Daily accrual for each day in range
3-6% monthly in ideal conditions

2. Range selection is critical

Too tight → frequently breach, low total yield
Too wide → low daily rate, low total yield
Sweet spot: ~10-15% ranges in moderate vol

3. Optimal in specific market conditions

Sideways markets (consolidation)
Low volatility environments
Post-crash stabilization
Avoid trending markets

4. Barrier types matter

Continuous monitoring (stricter)
Daily close monitoring (friendlier)
Soft vs hard barriers
Knock-out features (risky)

5. Calculate expected value, not just best case

Use probability-weighted scenarios
Compare to alternatives
Monitor and adjust continuously

What’s Next?

You’ve mastered all Level 1 structures! You now understand:

✅ What structured products are
✅ Covered calls (income generation)
✅ Principal protected notes (capital safety)
✅ Range accruals (sideways income)

Ready for intermediate pricing and risk?

Continue to: Black-Scholes Model →

Learn how to mathematically price options and understand what drives premiums.

Tools & Resources

Practice Tools:

Structure Tool - Design range accruals with live pricing
Volatility Analyzer - Check if market is range-bound
Probability Calculator - Estimate success odds

Next Steps:

Paper trade range accruals in different market conditions
Track historical ranges for your preferred assets
Build a range accrual watchlist

Next Module: Black-Scholes Model →

Related Content:

Volatility Analysis - Understand when to use range accruals
Autocallables - Advanced range-based structures
Case Studies - More real-world examples