Factor & Behavioral Finance

Question 1 (14 marks)

(a) Predicted excess return: $R_X - R_f = 0.15 + 1.05(2.0) + 0.60(1.2) + (-0.40)(-0.8)$ $= 0.15 + 2.10 + 0.72 + 0.32 = 3.29\%$

• Correct setup with all four terms: 2
• MKT term 2.10, SMB term 0.72, HML term +0.32 (sign!): 2
• Final 3.29%: 1

(b) (1 mark each, max 4)

• $\beta_{MKT}=1.05$: slightly more market risk than the market itself.
• $\beta_{SMB}=0.60$ (positive): tilts toward small-cap stocks.
• $\beta_{HML}=-0.40$ (negative): tilts toward growth (anti-value) stocks.
• Overall style: small-cap growth manager. (1)

(c) Annualized alpha (compounded): $(1.0015)^{12}-1 = 0.01815 = 1.82\%$

• Formula/compounding: 1; value ≈1.82%: 1
• Positive alpha ⇒ return unexplained by the three factors ⇒ evidence of manager skill / value-add: 1

(d) Small sample / high standard error can make a genuinely positive alpha statistically insignificant; insignificance means we cannot reject zero, not that skill is proven absent. (2)

Question 2 (12 marks)

(a) Earnings yield E/P = EPS/Price:

• A: 5.0/40 = 0.125 (12.5%)
• B: 3.0/60 = 0.050 (5.0%)
• C: 2.5/25 = 0.100 (10.0%)
• D: 2.0/80 = 0.025 (2.5%)
• E: 3.6/30 = 0.120 (12.0%)

Ranking (high→low value): A > E > C > B > D

• All five computed correctly: 3
• Correct ranking: 2

(b) Top 40% = 2 stocks = A and E, equal-weighted ⇒ 50% each. (2)

(c) P/B = Price/Book:

• A: 40/20 = 2.0
• E: 30/18 = 1.667

Both have modest P/B (well below the pricey D at 80/60≈1.33... note D is actually low P/B). Comment: A and E are cheap on E/P; their P/B is moderate, so the value signal is broadly confirmed as reasonable but not extreme — signals can diverge across value metrics (multi-metric value screens exist for this reason).

• P/B values: 2; sensible comment on confirmation/divergence: 1

(d) Smart beta uses rules-based, transparent factor tilts (like passive/index in being systematic and low-cost) but deliberately deviates from market-cap weighting to capture a factor premium (like active in seeking outperformance). (2)

Question 3 (12 marks) — 3 each (bias name 1.5 + justification 1.5)

(a) Anchoring / Loss aversion (disposition). She anchors on the purchase price ₹100 as a reference point and refuses to realize a loss. (Anchoring + loss aversion both acceptable.)

(b) Disposition effect. Selling winners (6) far more readily than losers (1) is the classic pattern of realizing gains and deferring losses.

(c) Confirmation bias. He seeks only information confirming his existing bullish view and dismisses disconfirming evidence (the downgrade).

(d) Herding + recency bias. The crowd follows others (herding) and over-weights the recent 3-month gains, extrapolating them forward (recency).

Question 4 (12 marks)

(a) CAPM predicts a positive relationship between systematic risk (beta/volatility) and expected return — higher risk should earn higher return. Low-vol stocks earning equal/higher returns at lower risk contradicts this, hence an "anomaly." (3)

(b) Sharpe = (Return − Rf)/StdDev:

• Low-Vol: (11−4)/10 = 7/10 = 0.70
• High-Vol: (14−4)/25 = 10/25 = 0.40

Low-Vol has the higher Sharpe (0.70 > 0.40) ⇒ more attractive risk-adjusted.

• Formula: 1; each Sharpe: 1.5, 1.5; conclusion: 1

(c) (2 each)

• Behavioral: Lottery-preference / overconfidence — investors overpay for volatile "lottery-like" high-vol stocks (and shun boring low-vol names), depressing high-vol returns and boosting low-vol returns.
• Limits to arbitrage: Exploiting the anomaly requires shorting overpriced high-vol stocks and/or leveraging low-vol stocks; leverage constraints, shorting costs, and benchmark/tracking-error risk prevent arbitrageurs from eliminating it, so it persists.

Question 5 (10 marks)

(a) When investors sell winners too soon (disposition effect), they create selling pressure that holds a rising stock's price below fair value; the price only adjusts gradually, so it keeps drifting up → underreaction generates continuation (momentum). Similarly holding losers too long delays downward price adjustment. This under-reaction produces the momentum premium. (4) (2 for winner logic, 2 for loser logic / underreaction mechanism)

(b) Any two (2 each):

• Momentum has persisted out-of-sample across markets, asset classes and decades — hard to dismiss as data-mining.
• It may be compensation for a risk factor (crash risk) rather than mispricing, consistent with a rational risk-based premium.
• Behavioral under-/over-reaction plus limits to arbitrage let mispricing persist without contradicting "no free lunch."

(c) Weak = prices reflect past price/volume; semi-strong = + all public info; strong = + private info. Profitable momentum/technical trading contradicts the weak form. (2)

[
  {"claim":"Q1a predicted excess return = 3.29%","code":"a=0.15; bmkt=1.05; bsmb=0.60; bhml=-0.40; mkt=2.0; smb=1.2; hml=-0.8; pred=a+bmkt*mkt+bsmb*smb+bhml*hml; result = abs(pred-3.29)<1e-9"},
  {"claim":"Q1c annualized alpha approx 1.82%","code":"ann=(1+0.0015)**12-1; result = abs(ann*100-1.82)<0.01"},
  {"claim":"Q2 earnings yields select A and E as top two","code":"eps={'A':5.0,'B':3.0,'C':2.5,'D':2.0,'E':3.6}; px={'A':40,'B':60,'C':25,'D':80,'E':30}; ey={k:eps[k]/px[k] for k in eps}; top2=sorted(ey,key=lambda k:-ey[k])[:2]; result = set(top2)=={'A','E'}"},
  {"claim":"Q4b Sharpe ratios 0.70 and 0.40","code":"lv=(11-4)/10; hv=(14-4)/25; result = (abs(lv-0.70)<1e-9) and (abs(hv-0.40)<1e-9)"}
]