Note: Take 365 days in a year and value of e 0.005942 = 1.005960, e 0.001849 = 1.001851. AB Ltd.'s equity shares are presently selling at a price of…

CA Final · Advanced Financial Management · RTP · May 2025
Note: Take 365 days in a year and value of e 0.005942 = 1.005960, e 0.001849 = 1.001851. AB Ltd.'s equity shares are presently selling at a price of 500 each. An investor is interested in purchasing AB Ltd.'s shares. The investor expects that there is a 70% chance that the price will go up to 650 or a 30% chance that it will go down to 450, three months from now. There is a call option on the shares of the firm that can be exercised only at the end of three months at an exercise price of 550. Calculate the following: (i) If the investor wants a perfect hedge, what combination of the share and option should he select? (ii) Explain how the investor will be able to maintain identical position regardless of the share price. (iii) If the risk-free rate of return is 20% p.a. for the three months period, what is the value of the option at the beginning of the period? (iv) What is the expected rate of return for the option buyer?

Suggested Answer and Working Notes:

(a) (i) To compute perfect hedge we shall compute Hedge Ratio (Δ) as follows: Δ = (C1-C2) / (S1-S2) = (100-0) / (650-450) = 100 / 200 = 0.50 The investor should purchase 0.50 share for shortening every 1 call option Or, the investor should purchase 1 share for shortening every 2 Call Option. (ii) How the investor will be able to maintain his position if he purchase 0.50 share for 1 call option written. (a) If price of share goes upto 650then value of purchased share will be: Sale Proceeds of Investment (0.50 x 650) = 325 Loss on account of Short Position (₹ 650 - 550) = 100 = 225 (b) If price of share comes down to 450 then value of purchased share will be: Sale Proceeds of Investment (0.50 x 450) = 225 (iii) The Value of Option, say, P at the beginning of the period shall be computed as follows: (250 – P) 1.05 = 225 262.50 - 1.05P = 225 37.5 = 1.05P P = 35.71 (iv) Expected Return on the Option Expected Option Value = (₹ 650 - 550) × 0.70 +0 × 0.30 = 70 Expected Rate of Return = (70 - 35.71) / 35.71 × 100 = 96.02%

Topics: Derivatives Analysis & Valuation

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