Question

You are an Investment Advisor with a Wealth Management firm. One of your clients has approached you for investing Rs. 10 Lacs for one year. He is a conservative investor and would like to protect his principal. He is considering buying a stock that is currently trading at Rs 800/- but is worried about the downside risk. The yield on one-year government bonds is 8% pa. Call options with strike prices of Rs. 800 and Rs 830 are trading at Rs. 109.60 and Rs 96 respectively. The stock price at the expiration of the call options may possibly lie in the range of Rs 600/- to Rs. 1200/-.

Suggest an appropriate trading strategy using bonds, calls, and /or stock, with the objective of protecting the principal amount for the investor

Lot Size of Stock = 1250

Answer 1

The strategy can be a combination of Purchasing the stock , selling call options and investing remaining money in risk free government bonds

Let us create a riskfree portfolio which is created by taking long position in X stocks and short position in 1 call option (with strike 800)

Let us assume a binomial model where the stock price may be either Rs.600 or Rs.1200

The riskless portfolio's value will be X*600 -0 if the stock price becomes Rs.600 (call option will be worthless)

The riskless portfolio's value will be X*1200 -400 if the stock price becomes Rs.1200 (call option will have a value of Rs.400)

So, X*600-0= X*1200-400

X =0.66667

So, for every 0.66667 stock, one call option needs to be shorted to create a riskless portfolio

So, for 1250 stocks, no of call options shorted = 1250/0.66667 = 1875

Now , the strategy is as given below

Today, purchase 1250 stocks for Rs.800 each for Rs.10 lakhs

Sell 1875 call options with strike 800 to get Rs. 1875*109.60 = Rs.205500

Invest the amount in govt bonds to get 205500*1.08 =Rs.221940 at maturity

Now, if stock price is more than 800 at maturity

1875 Call option will be exercised, so, the investor can sell 1250 stocks and purchase the rest 625 at market price and deliver at Rs.800. in the worst case, if Stock price at maturity = 1200.

Value of portfolio = 1250*1200 - 1875*400+221940 = Rs.971940 i.e.. a loss of Rs. 28060 overall or Rs.22.45 per stock.

Now, if stock price is less than 800 at maturity

Call option will not be exercised, so, the investor will have St*1250+ 221940 at maturity where St is the stock price at maturity

In the worst case, St=600

In that case , value of portfolio = 600*1250+221940 = Rs.971940 i.e.. a loss of Rs. 28060 overall or Rs.22.45 per stock.

So, in all scenarios, the maximum loss for the investor will not exceed Rs. 28060 overall or Rs.22.45 per stock.