CASE STUDY Akhil, the manager of Bharat Hedge Funds, uses derivative securi- ties extensively to reduce the risks. When he started studying op- tions, he learnt that hedging using options is not simple. There are a number of Greek letters used, and these cannot be understood easily. Furthermore, he has learnt that it is necessary to go for a dy- namic hedging strategy in order to preserve the gains. He is won- dering how he can hedge his portfolio of stocks and options. His portfolio is currently worth INR 3 billion. Of this, INR 200 million is invested in stocks. The stock portfolio is highly correlated with the Nifty index, with a correlation of 0.88. On September 1, the Nifty index is at 4,800 and index call options and put options are available with an exercise price in the range of INR 4,700 to INR 5,000 with expiry on October 29. The prices of these options are as shown in Table 1. There is also an October index futures with a futures price of INR 4,637 expiring on October 29. The volatility of the Nifty index is estimated as 24%, and the risk-free rate is 8%. Bharat Fund also received money from foreign investors for USD 1 million, and these investors are paid a dividend of 10% every three months, with the next payment due on December 31. Since the amount is to be paid in U.S. dollars, Akhil would like to hedge the exchange rate risk by buying U.S. dollar options. The exercise price of December options is INR 46.85, and the options are selling for INR 1.28. The volatility of the USD-INR exchange rate is 18%. Akhil is worried about a possible downside risk and wants to hedge the value of the portfolio. Table 1 Discussion Questions Exercise Price (INR) Call Price (INR) Put Price (INR) 4,600 267 247 4. 4,700 217 286 1. Explain the risks associated with the use of options for hedg- ing 2. Explain how Akhil can delta-hedge the portfolio. 3. How can Akhil make the portfolio gamma-neutral? How can Akhil make the portfolio vega-neutral? 5. How can Akhil make the portfolio gamma-neutral as well as vega-neutral? 6. How can Akhil create a put option synthetically in order to hedge the portfolio? 7. How can Akhil make the U.S. dollar option gamma-neutral and vega-neutral? 4,800 173 358 4,900 135 400 5,000 105 474 CASE STUDY Akhil, the manager of Bharat Hedge Funds, uses derivative securi- ties extensively to reduce the risks. When he started studying op- tions, he learnt that hedging using options is not simple. There are a number of Greek letters used, and these cannot be understood easily. Furthermore, he has learnt that it is necessary to go for a dy- namic hedging strategy in order to preserve the gains. He is won- dering how he can hedge his portfolio of stocks and options. His portfolio is currently worth INR 3 billion. Of this, INR 200 million is invested in stocks. The stock portfolio is highly correlated with the Nifty index, with a correlation of 0.88. On September 1, the Nifty index is at 4,800 and index call options and put options are available with an exercise price in the range of INR 4,700 to INR 5,000 with expiry on October 29. The prices of these options are as shown in Table 1. There is also an October index futures with a futures price of INR 4,637 expiring on October 29. The volatility of the Nifty index is estimated as 24%, and the risk-free rate is 8%. Bharat Fund also received money from foreign investors for USD 1 million, and these investors are paid a dividend of 10% every three months, with the next payment due on December 31. Since the amount is to be paid in U.S. dollars, Akhil would like to hedge the exchange rate risk by buying U.S. dollar options. The exercise price of December options is INR 46.85, and the options are selling for INR 1.28. The volatility of the USD-INR exchange rate is 18%. Akhil is worried about a possible downside risk and wants to hedge the value of the portfolio. Table 1 Discussion Questions Exercise Price (INR) Call Price (INR) Put Price (INR) 4,600 267 247 4. 4,700 217 286 1. Explain the risks associated with the use of options for hedg- ing 2. Explain how Akhil can delta-hedge the portfolio. 3. How can Akhil make the portfolio gamma-neutral? How can Akhil make the portfolio vega-neutral? 5. How can Akhil make the portfolio gamma-neutral as well as vega-neutral? 6. How can Akhil create a put option synthetically in order to hedge the portfolio? 7. How can Akhil make the U.S. dollar option gamma-neutral and vega-neutral? 4,800 173 358 4,900 135 400 5,000 105 474
