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CA Final · Advanced Financial Management · Portfolio Management

In a single-factor APT world, Rf is 7% and the factor portfolio (beta 1) is expected to return 12%. Share X has beta 1.2 and an expected return of 15%. An arbitrageur buys ₹10,00,000 of X and finances the position by short-selling ₹12,00,000 of the factor portfolio, lending the balance proceeds at the risk-free rate. What is the riskless profit for the year?

The riskless profit is ₹20,000. X earns ₹1,50,000, the short factor position costs ₹1,44,000, and the ₹2,00,000 surplus lent at 7% earns ₹14,000. This equals the 2% excess over the fair APT return of 13% on ₹10 lakh.

  1. A₹20,000Correct
  2. B₹6,000
  3. C₹24,000
  4. D₹14,000

Explanation

The factor exposure is hedged: 1.2 × 10,00,000 = 12,00,000 short. Gain on X = 1,50,000. Cost of short = 12% × 12,00,000 = 1,44,000. The surplus ₹2,00,000 (12L − 10L) lent at 7% earns 14,000. Profit = 1,50,000 − 1,44,000 + 14,000 = ₹20,000, which equals the 2% alpha (15% − 13% fair) on ₹10 lakh. Option ₹6,000 ignores the interest on the lent surplus.

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