Understand age - risk-based allocation models

What Are Age/Risk-Based Allocation Models?

The two components:

• Age: Objective measure → time until you need the money (retirement, goal)
• Risk tolerance: Subjective measure → psychological ability to handle volatility

Why Do These Models Exist?

The Three Forces Behind Age-Based Allocation

1. Time Horizon Dynamics

Starting from first principles:

• Equity risk premium exists: stocks return ~7-10% annually vs. bonds ~3-5%
• But stocks have short-term volatility (±20-40% annual swings)
• Over long periods (20+ years), this volatility averages out

Mathematical intuition: If annual stock returns are normally distributed with mean μ = 8% and σ = 18%, the standard error of the average return over n years is:

$\text{SE}_n = \frac{\sigma}{\sqrt{n}} = \frac{18\%}{\sqrt{n}}$

• At n = 1year: SE = 18% (massive uncertainty)
• At n = 25 years: SE = 3.6% (much tighter around 8%)

Why this step? The √n in the denominator is Law of Large Numbers—volatility per year stays constant, but the average volatility shrinks. A 25-year-old has n = 40 years; a 65-year-old has n = 5 years.

2. Human Capital as a Bond

Your human capital (present value of future earnings) is a bond-like asset:

• Guaranteed income stream (salary) until retirement
• Low correlation with stock market
• Depreciates as you age (fewer working years left)

A 25-year-old with ₹50 lakhs salary × 40 years = ₹20 crore human capital (present value) can afford90% stock portfolio—their human capital is the "bond" portion. A 65-year-old has near-zero human capital, so their financial portfolio must hold bonds.

3. Sequence-of-Returns Risk

This is the killer for retirees:

Why this step? When you withdraw during down markets, you sell assets at low prices and they never recover. Bonds prevent this.

The Classic Models

Model 1: Rule of 100 (or 110/120)

Derivation from first principles:

Assumptions:

1. Retirement age = 65
2. Life expectancy = 85 (20 years in retirement)
3. Minimum safe withdrawal rate = 4% annually
4. Stocks outperform bonds over 15+ year periods

At age A, time until retirement = (65 - A). For sequence risk safety, you need at least 5 years of expenses in bonds when you retire.

If your portfolio is P at 65, and you need 4% × P annually, then 5 years = 20% of P should be in bonds. Add a 10% buffer → 30% bonds minimum at 65.

So at 65: 70% stocks, 30% bonds → Stock %≈ 100 - 65 = 35%?

Wait, that's too conservative! The original rule assumes:

• Before 65: focus on growth (higher stocks)
• At 65: 100 - 65 = 35% stocks is too low for modern lifespans

Hence the shift to 110 or 120:

• 110 - Age: At 30 → 80% stocks; at 65 → 45% stocks
• 120 - Age: At 30 → 90% stocks; at 65 → 55% stocks

Why this step? The rule is a heuristic that balances "maximize growth when young" with "protect capital when old."

Model 2: Glide-Path Target-Date Funds

Target-date funds (TDFs) automate age-based allocation with a glide path: a pre-set schedule that gradually shifts from stocks to bonds.

How it works:

1. Starting allocation (age 25-30): ~90% stocks, 10% bonds
2. Glide slope: Reduces equity by ~1% per year
3. Landing point (age 65): ~40-50% stocks, stabilizes thereafter

Example: Vanguard Target Retirement 2060 (for someone retiring in 2060):

• 2025 (age ~25): 90% stocks, 10% bonds
• 2040 (age ~40): 80% stocks, 20% bonds
• 2055 (age ~55): 60% stocks, 40% bonds
• 2060 (age ~60): 50% stocks, 50% bonds
• Post-2060: Holds at 30% stocks, 70% bonds ("to" vs. "through" retirement)

Derivation of glide slope angle:

Assume

• S₀ = 90% stocks at age 25
• S₆₅ = 45% stocks at age 65
• Linear glide: Sₐ = S₀ - k × (A - 25)

Solve for k: $45 = 90 - k \times (65 - 25)$ $k = \frac{90 - 45}{40} = 1.125 \approx 1\% \text{ per year}$

Why this step? The 1% annual reduction is slow enough to capture equity premium but fast enough to derisk before retirement.

Model 3: Risk Capacity Framework

More sophisticated: adjusts for individual factors beyond age.

Why this formula?

• Base 40%: Minimum growth allocation (below this, inflation eats you)
• +10T: Each decade adds 10% stocks (time = tolerance for volatility)
• +5I: Stable income (government job) → can ride out crashes
• +2E: Each month of emergency fund = 2% more risk capacity (won't panic-sell)
• +10F: Flexibility (can work 2 more years) = huge risk buffer

Example:

• Age 35(T = 30years), software engineer (I = 3), 6 months emergency (E = 6), flexible (F = 0.5)

• Stock % = 40 + 10(3) + 5(3) + 2(6) + 10(0.5) = 40 + 30 + 15 + 12 + 5 = 102% → cap at 90%

• Age 55 (T = 10 years), freelancer (I = 1), 3 months emergency (E = 3), inflexible (F = 0)

• Stock % = 40 + 10(1) + 5(1) + 2(3) + 0 = 61% stocks

Why this step? Pure age ignores that a tenured professor at 55 has different risk capacity than a gig worker at 55.

Common Mistakes & Steel-manning

Practical Application

Why each step?

1. Two models give a range → choose based on psychological comfort
2. Diversify within stocks and bonds for sub-asset risk
3. Threshold rebalancing avoids over-trading
4. Glide path pre-planned removes emotional decisions

Active Recall Flashcards

#flashcards/stock-market

What is the core principle behind age-based allocation models? :: As you age, you shift from stocks to bonds because (1) time to recover from crashes decreases, (2) need for capital preservation increases, and (3) human capital (future earnings) decreases.

Connections

• 5.6.01-Understand-strategic-vs-tactical-allocation — Age-based is strategic (long-term structure), not tactical (market timing)
• 5.6.02-Learn-constant-vs-dynamic-rebalancing — Glide paths are dynamic rebalancing on a time axis
• 5.6.04-Calculate-optimal-asset-allocation-ratios — Risk capacity framework feeds into optimization
• 4.3.02-Compare-debt-equity-hybrid-mutual-funds — The equity vs. debt split within your allocation
• 5.5.01-Define-risk-vs-volatility — Age-based models manage volatility risk via time diversification
• 5.7.02-Calculate-safe-withdrawal-rates-SWR — Sequence risk is the enemy of SWR, bonds protect it
• 2.2.03-Understand-market-cycles-bull-bear — Young investors can afford to buy through bear markets

Concept Map

Hinglish (regional understanding)