Asset Allocation & Rebalancing

Question 1 (10 marks)

(a) Current weights: equity = 680000/1000000 = 68%; bonds = 32%. (2 marks) Deviation: equity 68% − 60% = +8 pp; bonds 32% − 40% = −8 pp. Both exceed ±5 pp band ⇒ rebalance triggers. (2 marks)

(b) Target: equity = 0.60×10,00,000 = ₹6,00,000; bonds = ₹4,00,000. (1) Trade: sell ₹80,000 equity, buy ₹80,000 bonds. (2)

(c) Target equity value = $w^* V$. Amount to sell = current − target: $S = E - w^* V$ Sign convention: $S>0$ ⇒ sell equity (overweight); $S<0$ ⇒ buy equity (underweight). (3) Check: $S = 680000 - 0.6(1000000) = 80000$. ✓

Question 2 (12 marks)

(a) Units = 3000/NAV each month:

• M1: 3000/30 = 100
• M2: 3000/24 = 125
• M3: 3000/20 = 150
• M4: 3000/25 = 120

Total units = 100+125+150+120 = 495. (4)

(b) RCA average cost = total invested / total units = 12000/495 = ₹24.242 per unit. (2) Arithmetic mean of NAVs = (30+24+20+25)/4 = 99/4 = ₹24.75. (1) RCA cost < arithmetic mean because fixed rupee amounts buy more units when price is low and fewer when high, weighting cheap prices more heavily. (1)

(c) With equal rupee $A$ each of $n$ periods at prices $p_i$: Total invested = $nA$; total units = $\sum A/p_i = A\sum 1/p_i$. $\bar c = \frac{nA}{A\sum_{i}1/p_i} = \frac{n}{\sum_i 1/p_i}$ which is exactly the harmonic mean of the prices. (4)

Question 3 (8 marks)

(a) "100 − age": equity % = 100 − age. At 35 ⇒ 65%. (1) "110 − age" ⇒ 75%; "120 − age" ⇒ 85%. (2)

(b) Criticisms (any two, 1.5 each): (i) longer life expectancy means portfolios must last longer, needing more growth; (ii) historically low bond yields make heavy bond allocation drag returns / fail to beat inflation. Variants (110/120) raise equity to reflect longer horizons and higher risk capacity. (3)

(c) Linear glide: slope = (30 − 90)/(65 − 25) = −60/40 = −1.5 per year. $E(a) = 90 - 1.5(a - 25)$ At a=50: $E = 90 - 1.5(25) = 90 - 37.5 = \textbf{52.5\%}$. (2)

Question 4 (10 marks)

(a) Core = low-cost, broadly diversified, passive holdings (index/large-cap) providing stability and market return at low cost; satellite = smaller active/high-conviction tilts (sector, mid-cap, thematic) aiming for alpha while limiting the risk of a mistake to a small sleeve. (3)

(b) Core = 0.75×20,00,000 = ₹15,00,000 (index fund). (1) Satellite = ₹5,00,000, split three ways = ₹1,66,667 each to sectoral, mid-cap, thematic. (2)

(c) Thematic (₹1,66,667) doubles → ₹3,33,333; other satellites & core flat. New total = 20,00,000 + 1,66,667 = ₹21,66,667. (1) New satellite value = 5,00,000 + 1,66,667 = ₹6,66,667. Satellite weight = 6,66,667/21,66,667 = 30.77% ⇒ breaches 30% ceiling. (2) Trim to 25%: target satellite = 0.25×21,66,667 = ₹5,41,667; trim = 6,66,667 − 5,41,667 = ₹1,25,000 (move to core). (1)

Question 5 (12 marks)

(a) Strategic = long-term policy mix based on goals/risk tolerance, held steadily. Tactical = short-term deliberate deviations to exploit expected market moves. Example: overweighting equities to 70% from a 60% policy when valuations look cheap. (3)

(b) FV of annuity: $FV = P\cdot\dfrac{(1+i)^n - 1}{i}$, monthly rate $i = 0.10/12 = 0.008333$, $n = 180$. (2) $(1.008333)^{180} \approx 4.4539$; numerator = 3.4539; /i = 3.4539/0.008333 ≈ 414.47. (2) $P = 4000000 / 414.47 \approx$ ₹9,650 per month (≈₹9,647). (1)

(c) Drift = deviation of current weight from target. Start ₹60/₹40 per ₹100. Equity → 60×1.20 = 72; bonds → 40×1.04 = 41.6; total = 113.6. (2) New equity weight = 72/113.6 = 63.38%; drift = 63.38 − 60 = +3.38 pp. (2)

Question 6 (8 marks)

(a) Asset location = which account holds each asset, given the same overall allocation. Tax-inefficient, high-income assets (bonds/REITs, actively traded funds generating short-term gains) go in tax-advantaged accounts; tax-efficient assets (index equity held long, qualified dividends, growth stocks) go in taxable accounts to exploit lower long-term rates. (3)

(b) (i) Calendar: predictable, may trade unnecessarily → moderate cost; threshold: trades only when needed → cost only on real drift. (ii) Calendar ignores intra-period volatility; threshold responds to it. (iii) Calendar forces realisations on schedule; threshold realises only on breach, more controllable. (3)

(c) Rebalance using new contributions/dividends to top up underweight assets (cash-flow rebalancing), or harvest losses / prefer selling within tax-advantaged accounts — restoring bands without triggering taxable gains. (2)

[
  {"claim":"Q1c sell amount = E - w*V = 80000","code":"E=680000; w=Rational(6,10); V=1000000; result=(E-w*V==80000)"},
  {"claim":"Q2 total units = 495","code":"u=3000/30+3000/24+3000/20+3000/25; result=(u==495)"},
  {"claim":"Q2 RCA cost equals harmonic mean of prices","code":"ps=[30,24,20,25]; rca=Rational(12000,495); hm=len(ps)/sum(Rational(1,p) for p in ps); result=(rca==hm)"},
  {"claim":"Q3c glide equity at 50 = 52.5","code":"E=90-Rational(3,2)*(50-25); result=(E==Rational(105,2))"},
  {"claim":"Q4c satellite weight >30% and trim=125000","code":"tot=2000000+1666667- (1666667); tot=2000000+1666667; sat=500000+1666667; w=Rational(sat,tot); trim=sat-Rational(1,4)*tot; result=(w>Rational(3,10) and abs(float(trim)-125000)<1)"},
  {"claim":"Q5c drifted equity weight approx 63.38%","code":"eq=60*Rational(12,10); bo=40*Rational(104,100); w=eq/(eq+bo); result=(abs(float(w)-0.6338)<0.001)"}
]