5

Hedging and Yield Enhancing Strategic Stakes

This chapter and the next one examine the management of strategic stakes. A strategic stake, also called a “concentrated stock position”, is a substantial equity position in a stock, usually taken with a long-term view. Strategic equity transactions can be implemented to enhance the acquisition, hedge, yield enhancement and disposal of a stake. In this chapter I will focus on the hedging and yield enhancement of strategic stakes. I will assume that the reader is already familiar with equity options, otherwise, I strongly recommend the reader to carefully read Chapter 1.

5.1 HEDGING A STRATEGIC STAKE

An investor owning a strategic stake is exposed to a decrease in its value. The simplest way to mitigate an exposure to the downside of a stock price is to sell the stake. However, an investor is often unable or unwilling to sell the stake. For example, an investor may have a strong commercial relationship with the company or may believe that the stock has attractive future prospects, or may want to avoid a substantial tax bill. This section covers the main strategies to protect a strategic stake.

Common Background Information

Let's assume that on 1 June 20X1, ABC Corporation (ABC) owned 40 million shares of XYZ. On that date XYZ stock was trading at EUR 10.00, and thus, the stake was worth EUR 400 million. ABC was worried about a potential large fall in XYZ's stock price. Figure 5.1 highlights the value of the stake as a function of XYZ's stock price. ABC was looking to protect the value of the stake in 12 months’ time but it was not willing to sell its stake unless the stock price experienced a substantial rise.

5.1.1 Hedging with a Put Option

The simplest way to hedge ABC's position, without selling the stake, was to buy a put option on XYZ. The purchase of a put option could provide ABC protection against downward stock price movements below the put's strike price. During the life of the put, ABC continued to participate in any stock appreciation. The put option compensated ABC for any fall in XYZ's stock price below the strike price. The maximum potential loss for ABC was the premium paid.

The two main parameters that ABC had to determine were the put expiration date and its strike price. ABC chose a 12-month expiry date (i.e., 1 June 20X2) because it wanted to hedge the value of the stake in 12 months’ time. The selection of the strike price very much depended on ABC's risk aversion, its view on the stock price and the premium amount it was willing to pay for the hedge. ABC received from Gigabank quotes of 12-month European puts on XYZ stock for different strikes, as shown in the following table. Remember that the premium of an option is usually quoted as a percentage of its notional amount.

Put strike	Implied volatility	Premium
100%	24.4%	8.5%
90%	28.0%	5.5%
80%	33.2%	3.9%
70%	39.8%	2.9%
60%	47.5%	2.3%

Other option terms that ABC needed to define included:

• The type of option – European or American. A European option can only be exercised at expiration. An American option can be exercised at any time during the life of the option. ABC chose a European type of option because it was interested in hedging the value of the stake only at expiry.
• The type of settlement – cash or physical. ABC was not looking to sell the shares at expiry, and as a result, chose cash settlement only.

ABC decided to buy the 90% strike put. The 100% put was too expensive. Also, ABC was not willing to be exposed to a loss larger than 16%. Taking into account its 5.5% premium, the 90% put implied a maximum loss of 15.5% (= 100% – 90% + 5.5%), occurring if the shares traded at 90% at expiry. The main terms of the put option were the following:

Cash-settled Put Option – Main Terms
Buyer	ABC Corp.
Seller	Gigabank
Option type	Put
Trade date	1-June-20X1
Expiration date	1-June-20X2
Option style	European
Shares	XYZ
Number of options	40 million (one share per option)
Strike price	EUR 9.00 (90% of the spot price)
Spot price	EUR 10.00
Premium	5.5% of the notional amount, or EUR 22 million (i.e., EUR 0.55 per share)
Premium payment date	3-June-20X1
Notional amount	Number of options × Spot price EUR 400 million
Settlement price	The closing price of the shares on the valuation date
Settlement method	Cash settlement
Cash settlement amount	The maximum of: (i) Number of options × (Strike price – Settlement price), and (ii) Zero
Cash settlement payment date	4-June-20X2

ABC paid a 5.5% premium on 3 June 20X1. The notional amount was EUR 400 million (= 40 million × 10.00), equal to the product of (i) the number of options and (ii) the spot price. Therefore, the premium was EUR 22 million (= 5.5% × 400 million), or EUR 0.55 per share (= 5.5% × 10.00).

At expiry, there were two scenarios:

• If XYZ's stock price was greater than or equal to the put strike price, the option would expire worthless.
• If XYZ's stock price was lower than the put strike price, ABC would receive from Gigabank a cash amount equal to the number of options × (strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 7.00, ABC would receive EUR 80 million [= 40 million × (9.00 – 7.00)].

Figure 5.2 depicts ABC's payoff under the put as a function of XYZ's stock price at expiry, taking into account the settlement amount and the EUR 22 million upfront premium and ignoring timing differences. Therefore, the payoff was calculated as: EUR 40 million × Max(strike price – settlement price, 0) – EUR 22 million.

Advantages and Weaknesses of the Strategy

The advantages of the strategy were the following:

• At expiration, ABC had full downside protection below the put strike price.
• ABC retained ownership of the stake, maintaining the voting rights and receiving the dividends.
• ABC participated in full in a potential appreciation of the stake.

The weaknesses of the strategy were the following:

• ABC paid an upfront premium.
• ABC was exposed to the difference between the stock price prevailing at inception and the put strike price.
• In order to delta-hedge its position, the seller of the option (i.e., Gigabank) needed to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.1.2 Hedging with a Put Spread

Let us assume that ABC was interested in buying the 90% put, but found the 5.5% premium too expensive. Let us assume further that ABC had the view that XYZ stock price would not be falling substantially. As a result, ABC considered buying the 90% put and selling a lower strike put, both with a 12-month expiry. The purchase (sale) of a put while simultaneously selling (buying) another put on the same underlying is called a put spread. After studying different alternatives, ABC entered into a 90%/70% put spread strategy, by buying a 90% put and selling a 70% put.

A 90%/70% put spread meant that the stake was protected once it had fallen by 10% (i.e., fallen through the 90% strike) and would continue to be protected thereafter as long as XYZ's stock price did not decline by more than 30% (i.e., fall through the 70% strike).

The following table summarizes the terms of the put spread (the rest of the terms were identical to the 90% put terms specified in the previous subsection):

Cash-settled Put Spread – Main Terms
Upper strike price	EUR 9.00 (i.e., 90% of the initial price)
Lower strike price	EUR 7.00 (i.e., 70% of the initial price)
Upper strike put buyer	ABC Corp.
Lower strike put buyer	Gigabank
Premium	3.0% of the notional amount, or EUR 12 million (i.e., EUR 0.3 per share)

ABC paid a 3% premium on 3 June 20X1. The notional amount was EUR 400 million (= 40 million × 10.00), equal to the product of (i) the number of options and (ii) the spot price. Therefore, the premium was EUR 12 million (= 3% × 400 million), or EUR 0.3 per share (= 3% × 10.00).

At expiry there were three scenarios:

• If XYZ's stock price was greater than, or equal to, the EUR 9.00 upper strike price, both puts would expire worthless.
• If XYZ's stock price was lower than the EUR 9.00 upper strike price and greater than the EUR 7.00 lower strike price, ABC would receive from Gigabank a cash amount equal to the number of options × (upper strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 8.00, ABC would receive EUR 40 million [= 40 million × (9.00 – 8.00)].
• If XYZ's stock price was lower than, or equal to, the EUR 7.00 lower strike price, ABC would receive EUR 80 million [= 40 million × (9.00 – 7.00)] from Gigabank.

Figure 5.3 depicts ABC's payoff under the put spread as a function of XYZ's stock price at expiry, taking into account the settlement amount and the EUR 12 million upfront premium and ignoring timing differences. The payoff was calculated as: EUR 40 million × [Max(upper strike price – settlement price, 0) – Max(lower strike price – settlement price, 0)] – EUR 12 million.

A put spread can take advantage of a steep skew. When the skew is large, the implied volatility of the lower strike put is notably larger than the implied volatility of the upper strike put. As a result, the lower strike put is sold at an attractive premium relative to that of the upper strike.

Advantages and Weaknesses of the Strategy

The advantages of the strategy were the following:

• At expiration, ABC had downside protection below the upper strike price.
• ABC retained ownership of the stake, maintaining the voting rights and receiving the dividends.
• ABC participated in full in an appreciation of the stake.
• The premium paid was significantly lower than the premium to be paid under the single put hedging strategy.

The weaknesses of the strategy were the following:

• ABC paid an upfront premium.
• ABC was exposed to the difference between the stock price prevailing at inception and the upper strike price.
• ABC's downside protection was limited below the lower strike price.
• In order to delta-hedge its position, the seller of the upper strike put option (i.e., Gigabank) needed to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.1.3 Hedging with a Collar

When protecting a stake with a put, a popular way of reducing the cost of the hedging strategy is to sell an out-of-the-money call. When the purchase of a put option is combined with the simultaneous sale of a call option, the strategy is known as a collar. The premium received by the sale of the call partially, or totally, reduces the premium to be paid for the put. Should an investor want a specific put, it is possible to find a call with a certain strike price such that the proceeds from the call sale finance completely the purchase of the put. A collar that does not require any overall premium payment (or receipt) is called a zero-cost collar.

Let us assume that ABC was interested in buying the 90% put but did not want to pay any premium for the downside protection. ABC then sold a call 108% to completely offset the cost of the put. With this zero-cost collar strategy, ABC protected for zero cost its downside exposure below 90% of the then prevailing stock price at the expense of capping any gains should the stock price rise by more than 8%. The following table summarizes the terms of the zero-cost collar (the rest of the terms were identical to the 90% put terms specified earlier):

Cash-settled Zero-cost Collar – Main Terms
Put strike price	EUR 9.00 (i.e., 90% of the initial price)
Put buyer	ABC Corp.
Put cash settlement amount	The maximum of: (i) Number of options × (Put strike price – Settlement price), and (ii) Zero
Call strike price	EUR 10.80 (i.e., 108% of the initial price)
Call buyer	Gigabank
Call cash settlement amount	The maximum of: (i) Number of options × (Settlement price – Call strike price), and (ii) Zero
Overall premium	None

At expiry there were three scenarios:

• If XYZ's stock price was greater than the EUR 10.80 call strike price, ABC would pay to Gigabank a cash amount equal to the number of options × (settlement price – call strike price). For example, if XYZ's stock price at expiry was EUR 12.00, ABC would pay to Gigabank EUR 48 million [= 40 million × (12.00 – 10.80)]. The put would expire worthless.
• If XYZ's stock price was lower than, or equal to, the EUR 10.80 call strike price and greater than, or equal to, the EUR 9.00 put strike price, both options would expire worthless.
• If XYZ's stock price was lower than the EUR 9.00 put strike price, ABC would receive from Gigabank a cash amount equal to the number of options × (put strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 7.00, ABC would receive EUR 80 million [= 40 million × (9.00 – 7.00)].

Figure 5.4 depicts ABC's payoff under the zero-cost collar as a function of XYZ's stock price at expiry. The payoff was calculated as: EUR 40 million × [Max(put strike price – settlement price, 0) – Max(settlement price – call strike price, 0)]. The graph shows that by establishing the zero-cost collar, a minimum value and a maximum value were created around ABC's equity position until the expiry of the options. The minimum value was EUR 360 million (= 40 million × 9.00) and the maximum value was EUR 432 million (= 40 million × 10.80).

Advantages and Weaknesses of the Strategy

The advantages of the collar strategy were the following:

• At expiration, ABC had full downside protection below the EUR 9.00 put strike price.
• ABC retained ownership of the stake, maintaining the voting rights and receiving the dividends.
• ABC participated up to a certain level (EUR 10.80) in an appreciation of the stake.
• The premium paid was significantly lower (zero in our case) than the premium to be paid under either the single put or the put spread hedging strategies.

The weaknesses of the strategy were the following:

• ABC did not participate in XYZ's stock price appreciation above the EUR 10.80 call strike price.
• ABC was exposed to the difference between the EUR 10.00 stock price prevailing at inception and the EUR 9.00 put strike price.
• In order to delta-hedge its position, the seller of the option (i.e., Gigabank) needed to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.1.4 Hedging with a Put Spread Collar

The main problem with the zero-cost collar strategy is that it limits notably the participation in the upside of the stock. In our previous example, ABC sold a 108% call, not allowing it to participate beyond an 8% appreciation of the stock. One solution to increase the strike of the call is to combine a put spread with a call, in a zero-cost strategy. This strategy is called a zero-cost put spread collar strategy. Under this strategy, the premium received by the sale of the call totally offsets the premium to be paid for the put spread.

Let us assume that ABC was interested in buying the 90% put without paying a premium, but found the zero-cost collar strategy unattractive. Instead, ABC entered into a zero-cost put spread collar strategy in which ABC bought a 90% put, sold a 70% put and sold a 118% call. With this strategy, ABC protected for zero cost its downside exposure below 90%, and up to 70%, of the then prevailing stock price at the expense of capping any gains should the stock price rise by more than 18%. The following table summarizes the terms of the zero-cost put spread collar (the rest of the terms were identical to the 90% put terms specified in an earlier subsection):

Cash-settled Zero-cost Put Spread Collar – Main Terms
Upper put strike price	EUR 9.00 (i.e., 90% of the initial price)
Upper put buyer	ABC Corp.
Upper put cash settlement amount	The maximum of: (i) Number of options × (Upper put strike price – Settlement price), and (ii) Zero
Lower put strike price	EUR 7.00 (i.e., 70% of the initial price)
Lower put buyer	Gigabank
Lower put cash settlement amount	The maximum of: (i) Number of options × (Lower put strike price – Settlement price), and (ii) Zero
Call strike price	EUR 11.80 (i.e., 118% of the initial price)
Call buyer	Gigabank
Call cash settlement amount	The maximum of: (i) Number of options × (Settlement price – Call strike price), and (ii) Zero
Overall premium	None

At expiry there were four scenarios:

• If XYZ's stock price was greater than the EUR 11.80 call strike price, ABC would pay to Gigabank a cash amount equal to the number of options × (settlement price – call strike price). For example, if XYZ's stock price at expiry was EUR 14.00, ABC would pay to Gigabank EUR 88 million [= 40 million × (14.00 – 11.80)]. The two puts would expire worthless.
• If XYZ's stock price was lower than, or equal to, the EUR 10.80 call strike price and greater than, or equal to, the EUR 9.00 upper put strike price, the three options would expire worthless.
• If XYZ's stock price was lower than the EUR 9.00 put strike price and greater than or equal to the EUR 7.00 lower strike price, ABC would receive from Gigabank a cash amount equal to the number of options × (upper put strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 7.50, ABC would receive EUR 60 million [= 40 million × (9.00 – 7.50)]. Both the call and the lower strike put would expire worthless.
• If XYZ's stock price was lower than the EUR 7.00 lower strike price, ABC would receive EUR 80 million [= 40 million × (9.00 – 7.00)] from Gigabank as net compensation from the two puts. The call would expire worthless.

Figure 5.5 depicts ABC's payoff under the zero-cost put spread collar as a function of XYZ's stock price at expiry. The payoff was calculated as: EUR 40 million × [Max(upper put strike price – settlement price, 0) – Max(lower put strike price – settlement price, 0) – Max(settlement price – call strike price, 0)].

5.1.5 Hedging with a Fly Put Spread

Let us assume that ABC was interested in buying the 90% put and that it had the view that it was quite unlikely that XYZ's stock would fall below 70%. ABC considered that the 90%/70% put spread was providing an unnecessary protection below the 70% level. As an alternative, ABC entered into a fly put spread. A fly put spread, or butterfly put spread, extends the put spread concept further by limiting the protection obtained. In our case, a fly put spread strategy could be built as follows:

• ABC buys a 90% put (the upper strike put), on 40 million shares.
• ABC sells a 70% put (the middle strike put), on 80 million shares.
• ABC buys a 50% put (the lower strike put), on 40 million shares.

This strategy can also be designed as the combination of two put spreads:

• ABC buys a 90%/70% put spread, on 40 million shares.
• ABC sells a 70%/50% put spread, on 40 million shares.

ABC paid a 2.1% premium, or EUR 8.4 million (= 400 million × 2.1%), to enter into the fly put spread strategy. With this strategy, ABC protected for a modest premium its downside exposure below 90%, and up to 70% (of the then prevailing stock price) at the expense of gradually losing its protection were the stock to fall below 70%. Below 50%, ABC would have lost all its protection.

At expiry there were four scenarios:

• If XYZ's stock price was greater than, or equal to, the EUR 9.00 upper put strike price, the three options would expire worthless.
• If XYZ's stock price was lower than the EUR 9.00 upper put strike price and greater than, or equal to, the EUR 7.00 middle put strike price, ABC would receive from Gigabank a cash amount equal to the number of options × (upper put strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 7.50, ABC would receive EUR 60 million [= 40 million × (9.00 – 7.50)]. Both the middle strike put and the lower strike put would expire worthless.
• If XYZ's stock price was lower than the EUR 7.00 middle put strike price and greater than, or equal to, the EUR 5.00 lower put strike price, ABC would receive from Gigabank a cash amount equal to the number of options × (upper put strike price – settlement price) – 2 × number of options × (middle put strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 6.00, ABC would receive EUR 40 million [= 40 million × (9.00 – 6.00) – 80 million × (7.00 – 6.00)]. The lower strike put would expire worthless.
• If XYZ's stock price was lower than, or equal to, the EUR 5.00 lower put strike price the overall settlement amount would be zero.

Figure 5.6 depicts ABC's payoff under the fly put spread as a function of XYZ's stock price at expiry, taking into account the settlement amount and the upfront premium, and ignoring timing differences. The payoff was calculated as: EUR 40 million × [Max(upper put strike price – settlement price, 0) – 2 × Max(middle put strike price – settlement price, 0) + Max(lower put strike price – settlement price, 0)] – EUR 8.4 million.

Advantages and Weaknesses of the Strategy

The advantages of the strategy were the following:

• At expiration, ABC had full downside protection between the EUR 9.00 upper put strike price and the EUR 7.00 middle put strike price.
• ABC retained ownership of the stake, maintaining the voting rights and receiving the dividends.
• ABC participated in full in an appreciation of the stake.
• The premium paid was significantly lower than the premium to be paid under the single put or the put spread hedging strategies.

The weaknesses of the strategy were the following:

• ABC paid an upfront premium.
• ABC was exposed to the difference between the EUR 10.00 stock price prevailing at inception and the EUR 9.00 upper put strike price.
• ABC's downside protection faded below the EUR 7.00 middle put strike price, being completely lost below the EUR 5.00 lower put strike price.
• In order to delta-hedge its position, the seller of the option, i.e., Gigabank, needed to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.1.6 Hedging with a Knock-out Put

A knock-out put takes the fly put spread or the put spread strategies to an extreme. If the share price closes below the knock-out barrier at expiry, the put expires worthless. In contrast, a put spread delivers a capped payout, the difference between the two put strike prices.

Let us assume that ABC entered into a knock-out put with a 90% strike price and a 70% knock-out barrier. ABC paid a 1.9% premium, or EUR 7.6 million (= 400 million × 1.9%), to buy the knock-out put. With this strategy, ABC protected for a modest premium its downside exposure below 90%, and up to 70% (of the then prevailing stock price) at the expense of losing its protection were the stock price to fall below 70% at expiry.

At expiry there were three scenarios:

• If XYZ's stock price was greater than, or equal to, the EUR 9.00 put strike price, the knock-out put option would expire worthless.
• If XYZ's stock price was lower than the EUR 9.00 strike price and greater than, or equal to, the EUR 7.00 knock-out barrier, ABC would receive from Gigabank a cash amount equal to the number of options × (put strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 7.50, ABC would receive EUR 60 million [= 40 million × (9.00 – 7.50)].
• If XYZ's stock price was lower than the EUR 7.00 knock-out barrier, the put option would expire worthless.

Figure 5.7 depicts ABC's payoff under the knock-out put as a function of XYZ's stock price at expiry, taking into account the settlement amount and the EUR 7.6 million upfront premium, and ignoring timing differences. The payoff was calculated as either: (i) if the settlement price was above or at the knock-out barrier, the payoff was EUR 40 million × [Max(strike price – settlement price, 0)] – EUR 7.6 million, or (ii) otherwise, the payoff was minus EUR 7.6 million.

Advantages and Weaknesses of the Strategy

The advantages of the strategy were the following:

• At expiration, ABC had full downside protection between the EUR 9.00 strike price and the EUR 7.00 knock-out barrier.
• ABC retained ownership of the stake, maintaining the voting rights and receiving the dividends.
• ABC participated in full in an appreciation of the stake.
• The premium paid was significantly lower than that of a single put and the put spread hedging strategies.

The weaknesses of the strategy were the following:

• ABC paid an upfront premium.
• ABC was exposed to the difference between the EUR 10.00 stock price prevailing at inception and the EUR 9.00 strike price.
• ABC's downside protection disappeared below the EUR 7.00 knock-out barrier.
• In order to delta-hedge its position, the seller of the option, i.e., Gigabank, needed to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.1.7 Summary of Main Hedging Strategies

The strategies just covered are the most common hedging strategies. Each company has overriding objectives and challenges, and correctly identifying those forms an integral element to the success of a hedging strategy. In Figure 5.8, I have tried to select the optimal hedging strategy, as a function of ABC's expectations regarding XYZ's stock price in 12 months. It can be seen that the probability distribution of XYZ's stock price is not symmetrical due to the volatility skew (i.e., implied volatilities for puts being notably greater than volatilities for calls).

5.1.8 Hedging with Ladder Puts

A ladder option is an option that locks in gains once the underlying reaches predetermined price levels or “rungs”. A ladder put locks in a minimum payout if the underlying falls below a rung before expiry. This feature may be valuable for entities that want to buy a put to limit losses when the stake share price declines, but want to avoid the frustration of seeing the share price recover later. An important advantage of ladder puts versus a standard put is that the former provides better mark-to-market protection against an early market decline because some of its payout may get locked in at intrinsic value before expiry.

Let us assume that ABC bought a ladder put on 40 million XYZ shares, with a 90% strike (EUR 9.00) and a 12-month expiry. The ladder had two rungs, one at 85% (EUR 8.50) and another at 80% (EUR 8.00). ABC paid 7.5%, or EUR 30 million (= 400 million × 7.5%), for the ladder put. The payoff of the ladder put, ignoring its premium, would be at least the payoff of a standard put.

• If XYZ stock price reached 85% (EUR 8.50) at any time during the life of the put, the settlement amount would be locked in to be at least EUR 20 million [= 40 million × (9.00 – 8.50)].
• If XYZ stock price reached 80% (EUR 8.00) at any time during the life of the put, the settlement amount would be locked in to be at least EUR 40 million [= 40 million × (9.00 – 8.00)].

Figure 5.9 shows the ladder put payoff as a function of XYZ's stock price at expiry, taking into account the settlement amount and the EUR 30 million upfront premium, and ignoring timing differences. The settlement amount was calculated as EUR 40 million × Max(put strike – settlement price, 0), with a minimum of EUR 20 million (or EUR 40 million) if the 85% (or the 80%) rung was reached during the life of the option.

Advantages and Weaknesses of the Strategy

The advantages of the ladder put strategy were the following:

• At expiration, ABC had full downside protection below the EUR 9.00 put strike price.
• ABC locked in gains each time a rung was reached.
• ABC retained ownership of the stake, maintaining the voting rights and receiving the dividends.
• ABC participated in full in an appreciation of the stake.

The weaknesses of the strategy were the following:

• ABC paid an upfront premium.
• The premium paid was significantly larger than that of a standard put.
• ABC was exposed to the difference between the EUR 10.00 stock price prevailing at inception and the EUR 9.00 strike price.
• In order to delta-hedge its position, the seller of the option, i.e., Gigabank, needed to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.1.9 Hedging with Variable Premium and Variable Expiry Timer Puts

During periods in which the implied volatility of the stock to be hedged is unusually high, a more structured hedging strategy might make sense: a hedge with timer puts. There are two types of timer puts: (i) timer puts with variable premium and (ii) timer puts with variable expiry.

As an example, let us assume that the stock market in general is experiencing an unprecedented level of implied volatilities. As a result, 12-month 90% puts on XYZ are priced using a 50% implied volatility (a volatility much larger than XYZ's 30% 12-month average historical volatility), resulting in a EUR 35 million premium. Let us assume further that ABC believed that the realized volatility of such an option would be much lower than the implied volatility the market was pricing. Instead of acquiring the standard put option, ABC decided to purchase a timer put.

Timer Puts with Variable Premium

A timer put with variable premium is similar to a standard put except that the premium paid upfront is adjusted at expiry to take into account the realized volatility of the underlying stock during the life of the option.

Let us assume that ABC bought from Gigabank a 12-month, 90% strike timer put with variable premium. ABC paid a EUR 35 million premium at inception to Gigabank due to a pricing using a 50% implied volatility. This premium would be adjusted at expiry, to take into account the realized volatility of XYZ's stock during the 12-month life of the put. The terms of the timer put were identical to those of the 12-month, 90% strike, standard put covered earlier in this chapter, except that two new terms called “rebate” and “realized volatility” were added to the terms and conditions of the put. The “rebate” term was defined as follows:

• Rebate: Two currency business days after the exercise date, the “rebate payer” shall pay to the “rebate receiver” the “rebate amount”, as shown in the following table (the rebate amount will be linearly interpolated using the two closest realized volatility levels):

For example, if the realized volatility during the 12-month life of the option was 30%, ABC would receive a EUR 14 million rebate. Taking into account the initial EUR 35 million premium and ignoring the time value of money, ABC would have paid a EUR 21 million (= 35 million – 14 million) total premium for the put option. Using a different example, if the realized volatility was 60%, ABC would pay a EUR 7 million rebate. Taking into account the initial EUR 35 million premium and ignoring the time value of money, ABC would have paid a EUR 42 million (= 35 million + 7 million) total premium for the put option. Therefore, ABC was exposed to the realized volatility of XYZ's stock.

Realized Volatility Calculation

The formula to calculate the realized volatility is defined at inception of the trade. The realized volatility σR is the annualized standard deviation of a stock's returns during a period, expressed in percentage. A common formula is the following:

where:

Timer Puts with Variable Expiry

A less popular strategy when hedging a strategic stake is to buy a timer put with variable expiry. The terms of a timer put are identical to those of a standard put except that the timer put's expiration date is unknown on the trade date. The realized volatility of the underlying is used to determine the expiry of the option, as opposed to this being set at trade inception for a standard option.

Let us assume that ABC bought from Gigabank a timer put with variable expiry. ABC paid a EUR 22 million premium at inception to Gigabank. This premium would not be adjusted at expiry. Instead, the expiry date was unknown at inception, being set once a realized 30% volatility of XYZ's stock was “consumed”. The terms of the timer put were identical to those of the 12-month, 90% strike, standard put covered earlier in this chapter, except that two new terms called “expiration date” and “realized volatility” would be added to the terms and conditions of the put. These terms were defined as follows:

• Expiration date: The first trading date that the realized volatility is greater than, or equal to, 30%.
• Realized volatility (the terms Pi and Pi–1 were defined earlier for the timer puts with variable premium):

where:

ABC expected the 12-month realized volatility to be 30%. If ABC was right, the option would expire in 12 months. If XYZ showed a more volatile pattern since the trade date, the life of the option would be shorter than 12 months. Conversely, if it showed a less volatile pattern, the life of the option would be longer than 12 months.

In my view a timer put with variable premium makes more sense than a timer put with variable expiry, as ABC knows at inception that it will be protected during the next 12 months. Nevertheless, a timer put with variable expiry should not be completely discarded as a useful hedging strategy, especially if ABC wants to spend a certain limited premium. If the realized volatility is consumed much quicker than expected, for example during 9 months, probably it is because XYZ's stock price has fallen sharply. At the 9-month expiry, ABC can decide what to do next: whether to sell the stake, enter into a 3-month forward or buy a new 3-month put.

5.1.10 Hedging with Pay-later Puts

A pay-later put is a put option that is paid for only if the stock price declines. Thus, there is no upfront premium and the buyer pays for the protection only as the protection is needed. At inception the buyer of the option gets a standard put option for free. However, the buyer pays immediately a fixed amount once the underlying stock price falls below predetermined price levels or “rungs”. This feature may be valuable for entities that want to buy a put to limit losses, but that want to avoid the frustration of paying for a protection that was not needed during the life of the option. However, it is possible that all the rungs are breached and the protection turns out to be more expensive than a standard put. It is also possible that all the rungs are breached during the life, making the buyer pay a substantial premium, and that at the end the protection was not needed because the stock price ended up above the strike price.

As an example, let us assume that ABC was interested in buying a 90% European put with 1-year expiry on 40 million shares of XYZ to consolidate the recent strong performance of XYZ stock. Remember from an earlier example that a standard put was worth a EUR 22 million premium (i.e., 5.5%). Because the stock market was strong, ABC thought that it was quite likely that the protection would turn out to be useless. However, ABC was convinced that if XYZ stock price reversed it would reverse sharply. As a result, ABC bought a pay-later put with three rungs, at the 95%, 90% and 85% levels. The breach of any of these three rungs would oblige ABC to pay a EUR 12 million premium (i.e., 3%) immediately. Regarding the cost of the protection, four scenarios were possible:

• If no rungs were breached during the life of the option, the cost would be zero. This cost would look very favorable relative to the EUR 22 million premium of the standard put.
• If only the 95% rung was breached during the life of the option, the cost would be EUR 12 million. This cost would look notably favorable relative to the EUR 22 million premium of the standard put.
• If only the 95% and 90% rungs were breached during the life of the option, the cost would be EUR 24 million. This cost would look similar to the EUR 22 million premium of the standard put.
• If all the rungs were breached during the life of the option, the cost would be EUR 36 million. This cost would look notably unfavorable relative to the EUR 22 million premium of the standard put.

As an example, let us assume three scenarios of future performance of XYZ's stock price (see Figure 5.10):

• Under the first scenario, XYZ's stock price continued its rally. ABC did not pay any premium for the put because no rungs were breached during the life of the option. As a result, ABC got a 90% put for free.
• Under the second scenario, XYZ's stock price suffered a temporary correction, ending above its initial level. ABC paid a EUR 24 million premium because two rungs were breached during the life of the option. The protection was not needed at the end.
• Under the third scenario, XYZ's stock price suffered a sharp correction, ending well below its initial level. ABC paid a EUR 36 million premium because all three rungs were breached during the life of the option. The protection was needed. However, ABC would have paid a notably lower premium (EUR 22 million) by buying a standard put option.

Ignoring the premium, the payoff of the pay-later option at expiry was identical to that of a standard put option. Therefore, at expiry, there were two scenarios:

• If XYZ's stock price was greater than or equal to the 90% put strike price, the option would expire worthless.
• If XYZ's stock price was lower than the 90% put strike price, ABC would receive from Gigabank a cash amount equal to the number of options × (strike price – settlement price). For example, if XYZ's stock price at expiry was EUR 7.00, ABC would receive EUR 80 million [= 40 million × (9.00 – 7.00)].

Advantages and Weaknesses of the Strategy

The advantages of the pay-later strategy were the following:

• At expiration, ABC had full downside protection below the put strike price.
• In a bullish or moderately bearish performance of XYZ's stock price, the pay-later premium was notably lower than that of a standard put.
• ABC retained ownership of the stake, maintaining the voting rights and receiving the dividends.
• ABC participated in full in an appreciation of the stake.

The weaknesses of the pay-later strategy were the following:

• In a temporary or more permanent bearish performance of XYZ's stock price, the pay-later premium was notably greater than that of a standard put.
• ABC was exposed to the difference between the stock price prevailing at inception and the put strike price.
• In order to delta-hedge its position, the seller of the option needed to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.2 YIELD ENHANCEMENT OF A STRATEGIC STAKE

In this section I will briefly cover different strategies to generate additional income on a strategic stake.

5.2.1 Lending the Stock

An investor can obtain an additional income by lending the strategic stake without taking any major additional risk. By lending the stock, the investor receives a fee, called the borrowing fee. As seen in Chapter 1, the stock can be lent on an open basis or on a guaranteed basis. A stock lent on an open basis can be terminated early by any of the two parties at any time, while a stock lent on a guaranteed basis cannot be terminated early before maturity.

The lending fee is quoted on an annual basis and calculated on a daily basis. For very liquid stocks, the lending fee can be small (e.g., 10 bps). However, there are situations in which the lending fee can be substantial (e.g., 5%), like the following:

• There is a stock-for-stock hostile tender offer. Arbitrageurs with a view that the offer will succeed would be selling the stock of the acquirer and buying the stock of the buyer. To sell the stock of the acquirer, the arbitrageurs would need to borrow the stock.
• The stock fundamentals are very weak, attracting hedge funds willing to short a stock. However, there is no stock lending market in that stock.
• An investment bank is trying to offer a derivatives hedge position to a client on a stock, but there is no stock lending market in that stock.

5.2.2 Selling Part of the Upside with a Call

A popular way to increase the yield on a strategic stake is to sell a call on the stake, a strategy called “covered call writing”. The investor would receive a premium for providing the call buyer with the right to acquire the underlying shares at the call strike price. By receiving a premium, the investor is being compensated for the possibility of selling the stock at a determined price in the future.

Let us assume that ABC owns 40 million shares of XYZ stock, which is currently trading at EUR 10.00 per share. Therefore, the stake is worth EUR 400 million. ABC wants to generate additional income and is willing to sell the stake if the stock appreciates by 15% in 12 months’ time. ABC sells a 12-month European call with a strike price of EUR 11.50. ABC receives a 4%, or EUR 16 million (= 400 million × 4%), upfront premium. The following table describes the main terms of the call option:

Cash-settled Call Option – Main Terms
Buyer	Gigabank
Seller	ABC Corp.
Option type	Call
Trade date	1-June-20X1
Expiration date	1-June-20X2
Option style	European
Shares	XYZ
Number of options	40 million (one share per option)
Strike price	EUR 11.50 (115% of the spot price)
Spot price	EUR 10.00
Premium	4% of the notional amount, or EUR 16 million (i.e., EUR 0.40 per share)
Premium payment date	3-June-20X1
Notional amount	Number of options × Spot price EUR 400 million
Settlement price	The closing price of the shares on the valuation date
Settlement method	Cash or physical settlement, to be elected by the option seller (ABC Corp.) five business days prior to the expiration date
Cash settlement amount	The maximum of: (i) Number of options × (Settlement price – Strike price), and (ii) Zero
Cash settlement payment date	4-June-20X2

One interesting feature of the call option was that it could be cash settled or physically settled, at ABC's election. This feature provided ABC flexibility to not have to sell the stake if the call was exercised by Gigabank. For example, if the option was slightly in-the-money at expiry, ABC would prefer to choose cash settlement, paying the modest settlement amount and keeping the stake. However, if the option was very deep-in-the-money and, thus, the settlement amount very large, ABC would prefer to choose physical settlement, delivering the shares.

At expiry, there were two scenarios:

• If XYZ's stock price was greater than the EUR 11.50 call strike price, ABC would choose between cash and physical settlement. In case of physical settlement, ABC would deliver to Gigabank 40 million shares of XYZ in exchange for EUR 460 million (= 40 million × 11.50) – the strike amount. In case of cash settlement, ABC would pay to Gigabank a cash amount equal to the number of options × (settlement price – strike price). For example, if XYZ's stock price at expiry was EUR 13.00, ABC would pay to Gigabank EUR 60 million [= 40 million × (13.00 – 11.50)].
• If XYZ's stock price was lower than, or equal to, the EUR 11.50 call strike price, the option would expire worthless. If XYZ stock increased in price moderately, below the EUR 11.50 strike price, ABC would have the best scenario. ABC would benefit from the price appreciation and the received premium.

Figure 5.11 depicts ABC's payoff under the call as a function of XYZ's stock price at expiry, taking into account the settlement amount and the EUR 16 million upfront premium and ignoring timing differences. Therefore, the payoff was calculated as: EUR 16 million – EUR 40 million × Max(settlement price – strike price, 0).

Advantages and Weaknesses of the Strategy

The advantages of the strategy are the following:

• Investor receives an upfront premium.
• Investor benefits from a stock price appreciation up to the call strike price.
• Investor retains ownership of the stake, maintaining the voting rights and receiving the dividends.

The weaknesses of the strategy are the following:

• Investor does not participate in the stock price appreciation above the call strike price.
• Investor does not get any downside protection. However, the upfront premium can be viewed as a cushion against a drop in the stake's value.
• To meet the option settlement, the investor should not sell the stake during the life of the call, unless he/she terminates the call early, which can be costly.
• In order to delta-hedge its position, the buyer of the call option needs to borrow the stock in order to maintain a short position in the underlying stock over the term of the transaction.

5.2.3 Monetization of Dividend Optionality

Sometimes, when distributing a dividend, a listed company gives shareholders the right to choose between receiving cash (a cash dividend) and receiving stock (a scrip dividend). Sometimes the number of shares underlying the scrip dividend is calculated incorporating a discount to the then prevailing share price. This discount is included to incentivize the election of the scrip dividend alternative. If the election period is large enough, the election right may contain an embedded value that can be monetized.

As an example, let us assume that on 1 September 20X1, ABC owns 40 million shares (the “number of shares”) of XYZ. Let us assume that XYZ would be distributing a dividend on 16 December 20X1. XYZ would give, until 4 December 20X1, the right to its shareholders to choose between a cash dividend and a scrip dividend.

• In case a cash dividend is chosen, XYZ would pay a gross dividend per share of EUR 0.20 (the “gross dividend”), net of a 15% withholding tax (the “withholding tax”), on 16 December 20X1.
• In case of a scrip dividend, the number of shares to be received per share would be calculated by dividing (i) 0.20 by (ii) the conversion price. The conversion price would be calculated by multiplying (i) 90% (i.e., a 10% discount) by (ii) the average opening price of XYZ stock during the striking period (the “reference price”). The striking period would be the period from, and including, 14 September 20X1 to, and including, 11 October 20X1.

Because ABC always elects to receive a cash dividend, it is willing to sell the option embedded in the dividend election. For example, ABC would be selling a call on XYZ stock on 1 September 20X1 to Gigabank with the following terms:

Physically-settled Call Option – Main Terms
Buyer	Gigabank
Seller	ABC Corp.
Option type	Call
Trade date	1-September-20X1
Expiration date	4-December-20X1
Option style	European
Shares	XYZ
Number of options	To be described below (one share per option)
Strike price	To be described below
Premium	To be described below
Premium payment date	13-October-20X1
Settlement method	Physical settlement
Settlement date	16-December-20X1

The definition of the number of options, the strike price and the premium describes the process described next. On 11 October 20X1, the reference price would be calculated as the average opening price of XYZ stock during the striking period. Let us assume that the reference price was 11.00. The conversion price would then be calculated as 90% of the reference price:

The number of shares to be received by ABC as a dividend, were it to elect a scrip dividend, would be calculated as follows:

The number of options of the call would be the number of dividend shares, thus, 686,869 options.

The strike price of the call would be the conversion price, therefore, EUR 9.90.

Gigabank was willing to pay the intrinsic value of the call. Therefore, the premium was calculated as:

Regarding the call option, there would be two scenarios at expiry (4-December-20X1):

• If XYZ's stock price was greater than the EUR 9.90 call strike price, Gigabank would exercise the call. ABC would deliver to Gigabank 686,869 shares of XYZ in exchange for EUR 6.8 million (= 686,869 × 9.90) – the strike amount.
• If XYZ's stock price was lower than, or equal to, the EUR 9.90 call strike price, the option would expire worthless.

Next I am going to explain the mechanics of the transaction by analyzing the different steps of the transaction, combining the flows of the dividend election right and the call.

Steps at inception (1 September 20X1):

• ABC sells the call to Gigabank. The strike price, the number of options and the premium are unknown on trade date.

Steps on the reference price fixing date (11 October 20X1):

• The scrip dividend terms are fixed.
• The call strike price, the number of options and the premium are fixed. Gigabank pays the premium on 13 October 20X1.

Steps on expiration date (4 December 20X1) (two different scenarios could occur):

As a result, in any scenario, ABC would be receiving EUR 6.8 million and EUR 755,556 (i.e., the call premium). Therefore, ABC would be better off by implementing this strategy than by choosing a cash-only dividend. However, bear in mind that ABC may be levied corporate taxes on the premium received.

5.2.4 Reduction of Dividend Withholding Taxes with a Stock Lending Strategy

Frequently, investors are levied a withholding tax when receiving a dividend from the issuer of the strategic stake. In general, investors would be subject to one of the following situations:

• The investor is not levied any withholding tax.
• The investor is levied a withholding tax and is able to recover it at a later stage.
• The investor is levied a withholding tax and is able to use it against a tax base.
• The investor is levied a withholding tax and is unable to recover it.

The last situation is typical of foreign investors domiciled in tax haven jurisdictions. Let us assume that ABC owned 40 million of XYZ shares and that when a dividend is distributed to these shares ABC is levied a 15% withholding tax and is unable to recover it. Let us assume further that in three weeks, XYZ would be distributing a EUR 0.20 gross dividend per share. Thus, the gross dividend to be distributed to the 40 million XYZ shares would be EUR 8,000,000 (= 40 million × 0.20). Taking into account the 15% withholding tax, ABC would be receiving EUR 6,800,000 [= 8 million × (1 – 15%)].

Let us assume that Gigabank had a domestic presence in XYZ's jurisdiction and was able to receive a dividend on XYZ shares without being levied any taxes. A potential strategy for ABC would be to temporarily “transfer ownership” of the shares to Gigabank, and have the bank receive the dividend tax-free. Commonly, the temporary transfer of ownership is done in one of two ways:

• To enter into a stock lending transaction.
• To enter into a converse transaction.

Stock Lending Strategy

The implementation of a stock lending transaction is the simplest way to reduce the tax effects on dividends. However, some banks may be reluctant to enter into this type of trade with the only purpose of exploiting a tax arbitrage situation because the tax authorities may question the tax treatment of the transaction. Let us assume that Gigabank and ABC entered into a stock lending transaction with the following steps:

• Two weeks before the ex-dividend date, ABC lent its 40 million XYZ shares to Gigabank. Ownership was transferred to Gigabank. Because, on the dividend record date, Gigabank was the owner of the shares, it was entitled to receive the upcoming dividend.
• On dividend payment date Gigabank received the EUR 8 million dividend, free of any taxes.
• Also on dividend payment date Gigabank paid ABC a manufactured dividend of EUR 7.3 million.
• Two weeks after dividend payment date, Gigabank returned the stock and paid a EUR 100,000 fee.

As a result, ABC received a total of EUR 7.4 million (= 7.3 million + 0.1 mn) under the transaction. This amount represented 600,000 more than the EUR 6.8 million net dividend ABC would have received if it had not entered into the transaction. However, this transaction would probably require ABC and Gigabank to disclose the transfer of ownership (the 40 million shares could represent a substantial percentage of XYZ's share capital), potentially alerting the tax authorities about the existence of a tax arbitrage transaction.

5.2.5 Reduction of Dividend Withholding Taxes with a Converse Strategy

A converse strategy is a bit more robust than the previous stock lending transaction. Remember that a converse is the combination of a long (short) position in a European call and a simultaneous short (long) position in a European put, with the same terms. Let us assume that besides the assumptions mentioned in the stock lending transaction, XYZ's stock was trading at EUR 10.00. The converse transaction was implemented as follows:

• Two weeks before the ex-dividend date, ABC sold 40 million XYZ shares to Gigabank. ABC received EUR 400 million (= 40 million × 10.00). Ownership was then transferred to Gigabank. Because, on the dividend record date, Gigabank was the owner of the shares, it was entitled to receive the upcoming dividend. Simultaneously, ABC and Gigabank entered into a zero-cost converse. Under the converse, ABC purchased a European call and sold a European put. The strike of both options was 10.185. The expiration date of the options was two weeks after the dividend payment date.
• On dividend payment date Gigabank received the EUR 8 million dividend, free of any taxes.
• At expiry, i.e., two weeks after dividend payment date, either ABC exercised the call or Gigabank exercised the put. As a result, ABC bought back the 40 million XYZ shares, receiving EUR 407.4 million (= 40 million × 10.185).

Thus, ABC received a total of EUR 7.4 million (= 407.4 million – 400 million) under the transaction. This amount represented 600,000 more than the EUR 6.8 million net dividend it would have received if it had not entered into the transaction. Although this transaction would probably require ABC and Gigabank to disclose the transfer of ownership (remember that the 40 million shares could represent a significant percentage of XYZ's share capital), it was under an initial sale and a later purchase being potentially friendlier than a pure stock lending trade. A weakness of this converse trade was the large credit risk exposure that Gigabank had to ABC because of the EUR 400 million initial payment. However, this exposure was collateralized by the XYZ shares. A way to avoid this credit exposure was to have ABC post the EUR 400 million received at inception as cash collateral to the converse transaction.