Question

An investment management firm CA is concerned about the risk level of a client’s equity portfolio. In June 2020, the client has 60% of this portfolio invested in two equity positions: ABC and EFG stocks. CA’s research provides the following views on the two stocks.

• ABC’s share price is very likely to go down in the next 3 months;
• EFG does not have immediate substantial downside risk but its upside potential is likely to be limited.

Although the client refuses to sell her shares in either company, she has agreed to use option strategies to manage these concentrated equity positions over the next 3 months. The options available to construct the positions are shown in the table below.

Stock	Shares	Stock Price in June	European Options	Option Premium
ABC	325,000	$24.20	September 23.00 put	$0.80
			September 27.50 call	$0.65
EFG	280,000	$33.00	September 31.50 put	$0.85
			September 34.00 call	$1.20

1. Choose between covered call and protective put strategies to manage the risk exposure of ABC based on CA’s research. Then calculate the maximum profit and loss and the breakeven price.

2. Choose between covered call and protective put strategies to manage the risk exposure of EFG based on CA’s research. Then calculate the maximum profit and loss and the breakeven price.

CA also wishes to increase the beta for one of its portfolios under management from 0.95 to 1.20 for a 3-month period. The portfolio has a market value of $175,000,000. The investment firm plans to use a futures contract priced at $105,790 in order to adjust the portfolio beta. The futures contract has a beta of 0.98.

3. Calculate the number of futures contracts that should be bought or sold to achieve an increase in the portfolio beta.

4. At the end of three months, the overall equity market is up 5.5%. The stock portfolio under management is up 5.1%. The futures contract is priced at $111,500. Calculate the value of the hedged stock portfolio ending value and the effective beta of the portfolio.

5. Explain whether the above three strategies based on option and futures incur any credit risk.

Answer 1

1) To hedge ABC Shares' position which has a substantial downside risk, using protective put strategy is better than covered call as the protective put will provide gains almost equal to the loss in the shares.

Protective Put : Buying September 23.00 put options for 325000 shares at $0.80 premium per share will ensure that the minimum amount for the share is (Strike - premium) = $23- $0.80 = $22.20 per share. So, maximum loss in this strategy is $0.80 per share. Breakeven price = $22.20 as above

Covered Call : Selling September 27.50 call option for $0.65 will only give rise to a maximum possible realised price of $27.50+$0.65 = $28.15 and a fixed profit of $0.65 per share only when the price goes down.So, maximum profit in this strategy is $0.65 per share. Breakeven price = $28.15 as above

2)

To hedge EFG Shares' position which has limited upside potential, using covered call strategy is better than protective put as the covered call will provide some gains.

Protective Put : Buying September 31.50 put options for 280000 shares at $0.85 premium per share will ensure that the minimum amount for the share is (Strike - premium) = $31.50- $0.85 = $30.65 share. So, maximum loss in this strategy is $0.85 per share. Breakeven price = $30.65 as above

Covered Call : Selling September $34 call option for $1.20 will only give rise to a maximum possible realised price of $34+$1.20 = $35.20 and a fixed profit of $1.20 per share only when the price goes down.So, maximum profit in this strategy is $1.20 per share. Breakeven price = $35.20 as above

c) To increase the Beta of the portfolio ,one has to purchase Index futures

No of Index futures bought = (1.20-0.95)/0.98 * $175000000/$105790 = 421.995 or 422 contracts

So, to increase the beta from 0.95 to 1.20 , 422 future contracts must be bought

d) Value of Stocks = $175000000*1.051 = $183,925,000

Gain in Futures contracts = 422* (111500-105790)= $2409620

Value of the hedged stock portfolio ending value = $183925000+2409620 = $186,334,620

Effective return = 186334620/175000000 -1 = 0.06477 or 6.477%

So, Effective Beta = 6.477%/5.5% = 1.177 (assuming risk free rate to be 0%)