Understand age - risk-based allocation models

5.6.3 · Stock-Market › Asset Allocation & Rebalancing

Age/Risk-Based Allocation Models Kya Hote Hain?

Do components hote hain:

• Age: Objective measure → paisa kab chahiye (retirement, goal)
• Risk tolerance: Subjective measure → volatility handle karne ki psychological ability

Yeh Models Exist Kyun Karte Hain?

Age-Based Allocation Ke Peeche Teen Forces

1. Time Horizon Dynamics

First principles se shuru karte hain:

• Equity risk premium exist karta hai: stocks ~7-10% annually return dete hain vs. bonds ~3-5%
• Lekin stocks mein short-term volatility hoti hai (±20-40% annual swings)
• Long periods (20+ years) mein, yeh volatility average out ho jaati hai

Mathematical intuition: Agar annual stock returns normally distributed hain mean μ = 8% aur σ = 18% ke saath, toh n saal ke average return ka standard error hoga:

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

• n = 1 year par: SE = 18% (bahut zyada uncertainty)
• n = 25 years par: SE = 3.6% (8% ke aas-paas kaafi tight)

Yeh step kyun? Denominator mein √n Law of Large Numbers hai — volatility per year constant rehti hai, lekin average volatility shrink hoti hai. Ek 25-year-old ke paas n = 40 saal hain; ek 65-year-old ke paas n = 5 saal.

2. Human Capital as a Bond

Tumhara human capital (future earnings ki present value) ek bond-jaisa asset hai:

• Retirement tak guaranteed income stream (salary)
• Stock market se low correlation
• Age ke saath depreciate hota hai (kam working years bachte hain)

Ek 25-year-old jiska ₹50 lakhs salary × 40 years = ₹20 crore human capital (present value) hai, woh 90% stock portfolio afford kar sakta hai — unka human capital hi "bond" portion hai. Ek 65-year-old ka human capital near-zero hota hai, isliye unke financial portfolio mein bonds honee chahiye.

3. Sequence-of-Returns Risk

Yahi retirees ke liye sabse khatarnak hai:

Yeh step kyun? Jab tum down markets mein withdraw karte ho, tum assets low prices par bechte ho aur woh kabhi recover nahi hote. Bonds isse rokते hain.

Classic Models

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

First principles se derivation:

Assumptions:

1. Retirement age = 65
2. Life expectancy = 85 (retirement mein 20 saal)
3. Minimum safe withdrawal rate = 4% annually
4. Stocks 15+ year periods mein bonds se outperform karte hain

Age A par, retirement tak time = (65 - A). Sequence risk safety ke liye, retirement par tumhare paas kam se kam 5 saal ke expenses bonds mein chahiye.

Agar retirement par tumhara portfolio P hai, aur tumhe 4% × P annually chahiye, toh 5 years = 20% of P bonds mein hona chahiye. 10% buffer add karo → minimum 30% bonds at 65.

Toh age 65 par: 70% stocks, 30% bonds → Stock % ≈ 100 - 65 = 35%?

Ruko, yeh toh bahut conservative hai! Original rule maan ke chalta hai:

• 65 se pehle: growth par focus (zyada stocks)
• 65 par: 100 - 65 = 35% stocks modern lifespans ke liye bahut kam hai

Isliye 110 ya 120 ki taraf shift:

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

Yeh step kyun? Rule ek heuristic hai jo "jab young ho toh growth maximize karo" aur "jab old ho toh capital protect karo" ko balance karta hai.

Model 2: Glide-Path Target-Date Funds

Target-date funds (TDFs) age-based allocation ko glide path ke saath automate karte hain: ek pre-set schedule jo gradually stocks se bonds ki taraf shift karta hai.

Kaise kaam karta hai:

1. Starting allocation (age 25-30): ~90% stocks, 10% bonds
2. Glide slope: Har saal equity ~1% reduce karta hai
3. Landing point (age 65): ~40-50% stocks, uske baad stabilize

Example: Vanguard Target Retirement 2060 (kisi ke liye jo 2060 mein retire hoga):

• 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: 30% stocks, 70% bonds par hold ("to" vs. "through" retirement)

Glide slope angle ki derivation:

Maano

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

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

Yeh step kyun? 1% annual reduction itni slow hai ki equity premium capture ho sake, lekin itni fast ki retirement se pehle derisking ho sake.

Model 3: Risk Capacity Framework

Zyada sophisticated: age ke alawa individual factors ke liye adjust karta hai.

Yeh formula kyun?

• Base 40%: Minimum growth allocation (isse neeche, inflation kha jaayegi)
• +10T: Har decade 10% stocks add karta hai (time = volatility ki tolerance)
• +5I: Stable income (government job) → crashes ride out kar sakte ho
• +2E: Emergency fund ka har month = 2% zyada risk capacity (panic-sell nahi karoge)
• +10F: Flexibility (2 saal aur kaam kar sakte ho) = huge risk buffer

Example:

• Age 35 (T = 30 years), 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

Yeh step kyun? Pure age yeh ignore karta hai ki 55 saal ka ek tenured professor aur 55 saal ka ek gig worker ki risk capacity alag hoti hai.

Common Mistakes & Steel-Manning

Practical Application

Har step kyun?

1. Do models ek range dete hain → psychological comfort ke basis par choose karo
2. Stocks aur bonds ke andar bhi diversify karo sub-asset risk ke liye
3. Threshold rebalancing over-trading se bachata hai
4. Pre-planned glide path emotional decisions hatata hai

Active Recall Flashcards

#flashcards/stock-market

What is the core principle behind age-based allocation models? :: Jaise-jaise age badhti hai, tum stocks se bonds ki taraf shift karte ho kyunki (1) crashes se recover hone ka time kam hota hai, (2) capital preservation ki zaroorat badhti hai, aur (3) human capital (future earnings) kam hota jaata hai.

Connections

• 5.6.01-Understand-strategic-vs-tactical-allocation — Age-based strategic hai (long-term structure), tactical nahi (market timing)
• 5.6.02-Learn-constant-vs-dynamic-rebalancing — Glide paths time axis par dynamic rebalancing hain
• 5.6.04-Calculate-optimal-asset-allocation-ratios — Risk capacity framework optimization mein feed hota hai
• 4.3.02-Compare-debt-equity-hybrid-mutual-funds — Tumhari allocation ke andar equity vs. debt split
• 5.5.01-Define-risk-vs-volatility — Age-based models time diversification se volatility risk manage karte hain
• 5.7.02-Calculate-safe-withdrawal-rates-SWR — Sequence risk SWR ka dushman hai, bonds isse bachate hain
• 2.2.03-Understand-market-cycles-bull-bear — Young investors bear markets ke through khareed sakte hain

Concept Map