Why Large Financial Institutions Buy Long-Term Put Options from Companies

Why Large Financial Institutions Buy Long-Term Put Options from Companies

Vladimir Atanasov Department of Finance

Penn State University

609 Business Administration Building University Park, PA 16802

vaa3@psu.edu

Stanley B. Gyoshev Finance Department Drexel University 55-209 Academic Building

Philadelphia, PA 19104 (215) 895-1742 stan@drexel.edu

Current Draft: March, 2001

Why Large Financial Institutions Buy Long-Term Put Options from Companies

Abstract

This study explores the strategic interaction between large institutional investors and firms that issue put options written on their own stock. The firms experience large positive abnormal annual returns after they sell put options. The vast majority of issued put options expire without being exercised, and the buyers of these options, which are predominantly investment banks, lose money.

We propose a model that gives a rationale why an uniformed party, an investment

bank will trade in put options with an informed party, the issuing firm, although the

expected profits from this trade are negative. The model shows how trading with an

informed party can be profitable because the bank can acquire valuable information and

afterwards earn abnormal returns on trades in other securities of the same firm. Finally,

we outline several predictions from the model, and propose empirical tests to establish

our proposition that an investment bank can legally acquire private information and trade

profitably on it.

I. Introduction

The seminal work of Akerlof (1970) showed how asymmetric information might lead to the collapse of a market because uninformed participants are not willing to incur losses while trading with informed parties. Asymmetric information and the associated with it “winner’s curse” and adverse selection lead to inefficient market outcomes like larger bid-ask spreads and IPO underpricing because, in general, the uninformed parties have to receive an outside payment before they trade with informed parties.

Our work focuses on the interaction between investment banks and corporations when corporations sell to banks long-term put options written on the stock of the

corporation. The analysis of this setting documents a rare examp le where an uninformed party, an investment bank willingly accepts to trade with an informed party, a

corporation, although the trade has a negative expected profit for the investment bank

. The reason for this, at first glance irrational behavior, is that the investment bank can infer from the behavior of the corporation valuable information about the distribution of stock prices, and trade on this information on the stock market. In other words, by accepting an expected loss trade with an informed party the investment bank invests in a lawful acquisition of inside information, and then earns abnormal return on this

investment.

Our model is similar to the screening models used in the insurance, banking and industrial organization literature where an uninformed firm proposes different contracts

1 Other large institutional investors may also participate in the put option sale. For brevity we will denote all these investors by the term “investment bank”.

to various types of informed customers, and by choosing the optimal contracts manages to separate the customers based on their type

. In our case, the investment bank offers to buy long-term put options from corporations that have recently announced stock

repurchases. By setting optimally the premium of the options, the bank learns which corporations have positive and which corporations have negative private information about their future prospects. Later, based on this information the investment bank can take long positions in publicly traded put options written on the stock of the companies with bad prospects, or take short positions in put options and long positions in call options written on the stocks of companies with good prospects.

In order to implement this scheme, the investment bank has to use a surprisingly simple strategy. The only thing that the investment banks needs to do is to offer a put option premium to the issuing corporations that is equal to the fair premium computed using public information. As a consequence, only companies that have positive private information about the distribution of their stock price in the future will accept to sell put options. The companies with bad prospects will refuse participating in the trade because it has negative expected value for them. This assures the existence and uniqueness of the separating equilibrium. Note that through this screening scheme the investment bank has acquired private information in a perfectly legal way.

Gibson and Singh (2000) propose a theoretical model that also analyses the use of put options by firms. In their model corporations that need to raise new capital use put options to signal their quality and reduce their financing costs by fetching a better price for their newly offered securities. The model is not applicable to firms that repurchase

2 See for example the pioneering works of Rotschild and Stiglitz (1976) and Wilson (1977)

stocks because they are not in need of new capital. In addition, in the model of Gibson and Singh (2000), as in any signaling model, the informed party moves first. There is plenty of anecdotal evidence that the investment banks are usually the first to contact the firms with ongoing stock buybacks, and promote the put options scheme that will

“enhance” the stock repurchase.

The outline of the paper is as follows. Section II describes the institutional details of the log-term put options sold by companies. The theoretical model is outlined in Section III. Section IV describes the predictions of the model and proposes ways to test them. Section V concludes.

II. Institutional details of the sale of put options by firms

The remarkable spread in the use of derivatives, combined with well-known cases of large losses associated with their use, has tremendously increased the interest in derivatives usage by firms. Derivatives can be used to hedge or to speculate. Hedging attempts to lessen or avoid unexpected revenue loss or gain from activities not related to the core firm operations by making counterbalancing investments. In contrast,

speculation is the divesture of financial derivatives or real assets that increases the

variability of the firm cash flows or earnings. Selling put options on firm’s own stock is a good example of speculation. When a firm has good financial performance there is an additional positive cash flow from the collected option premiums. When a firm experiences weak financial performance, there is an additional negative cash flow

because its stock price is likely to fall and the put options sold by the firm are going to be

exercised.

Because of the possibility of losing a substantial amount of money, the managers will sell put options only if they have strong expectations that their firms are going to have a good performance during the life of the options. This notion is supported by Gyoshev and Tsetsekos (2000). The authors find in a sample of 45 firms that have sold put options an average of 14.1% risk-adjusted abnormal return in the year following the announcement of the put sale in the 10-Q or 10-K statements. They also report that most of the put options expire out of the money. This evidence of good firm performance after the put option sale implies that the buyers of the put options, which are mainly

investment banks and other large financial institutions, lost money on these trades.

It is interesting to note that the investment banks actively solicit firms to buy put options from them. In the Investment Dealers' Digest from December 5, 1994, Paul Mazzilli, a principal in equity capital markets at Morgan Stanley & Co., is cited to say that "A large portion of the companies that do [share repurchase] programs with us have been introduced to it, and use the strategy from time to time." Tyler Dickson, a VP in equity capital markets at Salomon Brothers is cited to say that: "This year, put warrants have come of age," and also that: "Companies are much more familiar with them as an enhancing vehicle to share repurchases." He added that Salomon has purchased put warrants from three Fortune 500 companies in the last two weeks alone.

The put option sale is not publicly known at the time when it was done. The

earliest time it may become public information is after the release of the next 10-Q or 10-

K statement, but a large subset of the firms investigated by Gyoshev and Tsetsekos

(2000) report the put option trades a lot later. On average the time from the date of the

trade to the time the public learned about it is more than four months. Moreover, SEC

states that if the put option sale affects the financial situation of the firm in a non-material way, there is no legal requirement to disclose it. This implies that potentially some firms have chosen not to disclose their put option trades at all.

III. Theoretical model

III.A. Outline of the game between the investment bank and the firms

Players

Consider one risk neutral investment bank denoted by I, and two types of firms that have recently initiated market stock repurchase programs

. Type A firms have a positive signal about their future prospects, while type B firms have a negative or neutral signal about their future prospects

.

Timeline

The order of moves is as follows. At time t = 0, Nature picks firm type A or B. At time t = 1, the Investment bank, I offers each of the firms to buy from them at a pre- specified premium put options written on the firms’ stock. At time t = 2, based on their

3 The assumption that the firms are facing a single investment bank for that deal is reasonable for two reasons. First, there is usually a long-term relationship between the investment bank and the firm. It is costly for both of them to build a new relationship. Second, as evident in Gyoshev and Tsetsekos (2000), the option contracts are privately negotiated with non-standard features like long maturity and European style exercise. These types of optio ns are not traded on organized exchanges.

4 The results of this paper can be easily extended for a continuum of firm types. For expositional simplicity we focus only on two firm types.

type and the size of the premium, the firms agree or disagree to sell put options to the investment bank. Last, at time t = 3, the Investment bank infers firm type from the actions of the firms at time t = 2, and trades on this legally acquired private information.

The extensive form of the game between the investment bank I and the two types of firms A and B is shown in Figure 1.

Information

At time t = 0, the investment bank has no private information about the future stock price of the firms. In other words, the investment bank cannot distinguish firm type.

At time t = 0, type A firms have private information that their stock price will go up. In general, type A firms are more optimistic than the other market participants, including the investment bank, about their future performance. Or, the firms know that they are less risky than the market expects given the available public information. Type B firms, on the other hand, have a private signal that their future price will go down or that they are more risky than the market expectations. At time t = 2, if the bank has proposed the optimal premium offer and has ensured the existence of a separating equilibrium, the bank infers firm type and learns which firms will have a stock increase (or are less risky) and which will not.

Payoffs

The payoffs for the firms from participating in the game are denoted by P

for firm A, and P

for firm B, where the following is true:

( )

[ ^{emium Value Type A} ]

P

= max 0 , Pr −

| = (1)

( )

[ ^{emium Value Type B} ]

P

= max 0 , Pr −

| = (2)

Both firms will get 0 if they don’t agree to sell put options to the investment bank.

Therefore, the firms will agree to the terms of the investment bank only if the premium they will get is larger than the value of the put option computed given their private information.

The payoff for the bank is denoted by P

, where the following is true:

( )

[ ^{emium E Value} ] ^{E ( V separating equilibriu m )}

P

= min 0 , Pr −

+

| _ (3)

The first term of the investment bank payoff is the negative of the payoffs for the firms, because the sale of put options is a zero sum game. The nature of the second term underlines the main contribution of this paper. This is the value of information that the bank can infer about firm type if there is a unique separating equilibrium in the game. If there is a pooling equilibrium in the game, the bank cannot infer firm type. The second term then is equal to 0, and the model reduces to the classical adverse selection model of Akerlof (1970), where the bank as an uninformed party will be facing negative expected profits from participating in the trade. The monetary gains V

from acquiring private information can potentially be very large. If the bank knows what firms have a positive signal about their future prospects, the bank can purchase call options on these firms’

stock, sell put options, or buy their stock that is currently undervalued. In Section III.C., we illustrate the potential value of private information V

with two numerical examples.

III.B. Resulting equilibrium

The investment bank will engage in the put option sale only if it assures the

existence and uniqueness of a separating equilibrium, where firms of type A accept the

conditions of the sale, and firms of type B reject the contract. If the separating

equilibrium exists and it is unique, then the bank acquires private information about firm types and the second term, V

in (3) is positive. If the derivatives or stock markets of the firms are liquid enough, the value of V

will dominate over the negative adverse selection term, and the bank will earn positive profits from the transaction. Below we construct a feasible strategy for the investment bank that ensures a unique separating equilibrium.

Let’s assume that the following condition about firm type is true for any price > 0:

( ) ∫ ( ) ∫ ( )

∫ ^>

^>

price

A

price dprice f price dprice f price dprice f

0 0

0

(4)

Where f

(price) and f

(price) are the probability distribution functions (p.d.f) of the prices of firms type A and firms type B, and f

(price) is the unconditional p.d.f. of the price of the average firm, given that the public cannot distinguish firm types. The interpretation of this assumption is that the firms of type A are with better than average prospects and it is more likely for them to have higher stock prices in the future than firms of type B. The type of the firm is private information. The rest of the market has an unconditional cumulative distribution of the future stock price of the average firm that in a stochastic sense is dominated by the distribution of the firm type A, and dominates the distribution of firm type B.

Consider the following strategy for I at time t = 1:

Propose to every firm that has a highly liquid market in derivatives to buy European-style out-of-the money put options with a long maturity for a put premium that is equal to:

∫ ⁻

=

Strike price f

price dprice

premium Put

0

) (

* ) (

_ (5)

The interpretation of equation (5) is that investment bank offers a fair price for the put options given the public information that all market participants have about the future distribution of stock prices.

Necessary conditions for a separating equilibrium

We have to show that the above proposed strategy of the bank leads to a unique separating equilibrium. In order for a separating equilibrium to exist and be unique, the following sets of individual rationality and incentive compatibility constraints have to be satisfied for both firm types:

IR(A): P

≥ 0 IR(B): P

≥ 0

IC(A): P

≥ The payoff for a type A firm if it pretends to be a type B firm IC(B): P

≥ The payoff for a type B firm if it pretends to be a type A firm

Given the stochastic dominance condition (4), it turns out that:

A) The individual rationality constraint for firm type A coincides with the incentive compatibility constraint for firm type A, and both reduce to the following inequality:

∫ ⁻

≥

Strike price f

price dprice

premium Put

0

) (

* ) (

_ (6)

This condition directly follows from the description of I’s strategy (5), and condition (4).

B) The individual rationality constraint for firm type B coincides with the incentive

compatibility constraint for firm type B, and both reduce to the following inequality:

∫ ⁻

<

Strike price f

price dprice premium

Put

0

) (

* ) (

_ (7)

Similar to A) this condition directly follows from the description of I’s strategy (5), and condition (4).

The strategy of the bank to propose a take it or leave it offer to buy put options for a premium equal to the expression in (5) assures that only firms of typ e A will agree to sell options to the bank. Firms of type A have positive private information about their future performance. The true value of the put options computed using their private information is lower than the premium proposed by the bank. Therefore, firms of type A will accept the proposal by the bank and earn positive profits. On the other hand, firms of type B have private information that their performance will be less than average. The value of the put option computed using their private information will be higher than the premium proposed by the bank and all firms of type B will not accept the terms of the investment bank. As a consequence, the separating equilibrium of the game exists and it is unique. When the bank sees that a firm accepts its terms, the bank can immediately update its beliefs that this firm is a firm of type A, and later use this information to earn profits trading in other options of the same firm.

III.C. Numerical Examples

In this sub-section we present two numerical examples that illustrate how the

investment bank can earn informational rents after losing money trading in put options

with the issuing firms.

Example 1. The difference between firm types is based on future stock returns

This example uses a binomial option-pricing model to show the value of

information about future price changes of the stocks of the two firms. Suppose there are only two future states of nature, a good and a bad state. Let type A firms have a payoff of 120 in the good state and a payo ff of 60 in the bad state. Type B firms have a payoff of 100 in the good state and a payoff of 40 in the bad state. If we assume for simplicity that there is an equal number of firms of both types, then the expected payoff of a firm of unknown type is 110 in the good state and 50 in the bad state. Let the stock price of the average firm to be 80, and the rate on T-bills (the risk- free security) to be 5%.

Now, the investment bank offers to each firm to buy put options with a strike of 65. The payoff of this put option given the public information is 0 is the good state and 15 in the bad state. The put option price computed using only public information is then

$6.19

. Both firms know their type and therefore they know for sure the true value of the put optio n for them. The value of the put for firm type A is $2.86, while the value of the put for firm type B is $6.35. As a result, only firms of type A will agree to sell put options and the bank will lose on this trade 3.49 per option. After the losing trade, the bank learns what firms are type A, and what firms are type B. After acquiring this private information that the rest of the market does not have, the bank buys a call option with a strike of 100,

5 See Lo and Wang (1995) for a sophisticated option pricing model that incorporates information about future returns.

6 See, for example, page 662 of Bodie, Kane, and Marcus (1999) for an exposition how to price options using the binomial pricing model

written on the stock of a type A firm. The true value of this call option is $7.62, while the bank can buy it from an uninformed investor for only $5.40 (the fair price given public information). The bank makes a profit of $2.22 per option. In order to make positive profits from the whole transaction, the bank needs to make sure that it buys at least 1.57 times more call options from the market than the number of put options that it bought from the issuing firms. For example if the bank proposes to buy 100 put option contracts (10,000 options) from one firms, and the firm agrees. Then, the bank can buy 200 call option contracts from the market, and make a total profit of:

20,000*2.22-10,000*3.49 = $9500

The bank can continue buying additional call options until the rest of the market participants detect the abnormal trading, and update their information about firm type. At this point the call option price will rise to its fair value of $7.62, and the informational rents for the bank will disappear.

Example 2. The difference between firm types is based on the volatility of returns

This example will illustrate how the investment bank can earn profits if it learns

valuable information about the volatility of stock returns of a firm. Suppose that there are

two types of firms. Firms of type A that have a standard deviation of returns σ

= 0.2,

while for firms of type B, σ

= 0.6. If there are an equal number of firms of type A and

type B, then E(σ) = 0.4. Assume that the current stock price of both firm types is $50, and

the risk-free rate is 5%.

The investment bank offers every firm to buy put options written on the firm’s stock with a maturity of one year and a strike price of $45. The price of these put options, given the publicly available information and using the Black and Scholes (1973) formula is $4.30. The firms know their type and they can compute the true value of this option.

The true value of the option of firms of type A is $1.12, while for firms of type B it is

$7.70. If the bank offers a price of $4.30 to all firms, only firm of type A will agree to sell. The bank loses $3.18 per option. Let the bank buy 100 contracts from one firm, and incur a total loss of $31,800. Now, the bank knows that this firm is of type A, and has the low volatility of 0.2. The rest of the market thinks that this firm on average has a

volatility of 0.4. The bank then sells 500 3- month put contracts with the same strike price of $45 at the market price of $1.614, while the true price of the puts is $0.276. The bank makes a profit on the sale of these short-term puts of 50,000*(1.614-0.276) = $66,900.

The net gain from the transaction is then 66,900 – 31,800 = $35,100.

IV. Empirical predictions of the model

The theoretical model presented in Section III produces several predictions, which are outlined below. The identity of traders on capital markets in the USA is not publicly available information. Therefore, it is impossible to document the actual trades of the investment banks after they have bough put options from the firms. We have to focus on indirect predictions about informed trading around the date of the put option sale.

Prediction 1. Firms that have sold put options have more liquid option trading markets.

Black (1975) and Easley, O’Hara, and Srinivas (1998) suggest that informed traders prefer to profit on their informatio n by trading in options as opposed to stocks, because derivatives allow for higher leverage. On the other hand, transaction costs like the bid-ask spread are on average several times larger when trading in options compared to trading in stocks. Informed traders then will prefer to trade in firms with more liquid derivative markets. In such firms an informed party can make more money before the other participants in the market detect her activities. Therefore, in order to assure that the informational rent earned by the bank are high enough, the bank will propose to buy options only from firms that have a highly liquid derivative market, with a large daily trading volume and a significant amount of uninformed trading.

This prediction of the model can be tested by comparing the liquidity of the

derivative markets for a sample firms that have recently sold put options and a sample of

control firms that are with a similar size, are from the same industry, and have recently

initiated market stock buy-backs.

Prediction 2. There is an abnormal volume of trading in the option market around the date of the put option sale.

If the investment bank acquires private information about firm type, it will proceed and buy a large number of call options or sell a large number of put options. A test of the model will then involve documenting the change in trading volume in various types of options after the date of the put option sale. Cao, Chen, and Griffin (2000) implement a similar approach to detect informed trading before take-over announcements. In ongoing work we intend to apply their methodology to provide empirical evidence on Prediction 2 of our model.

Prediction 3. The Option market of firms that have sold put options leads the stock market in terms of information.

Another indirect way to detect informed trading is to look at the relationship of option and stock prices. If informed investors prefer to trade on the option market, the option prices will reveal information before the stock prices. As a result option prices will lead stock prices. There are various time-series test that can be utilized to document this relationship. A recent paper by Pirinski (2000) uses an extension of a VAR model to test whether option prices changes can predict stock prices changes before earnings

announcements. A similar approach can be taken here to establish that there is an

increase in informed trading in firms that have recently sold put options.

Prediction 4. The time from the sale of put options to its disclosure to the public will be inversely related to the size of the expected losses of the investment bank from the trade and to the liquidity of the firm stock and publicly traded options.

This prediction relies on the anecdotal evidence that firms cooperate with the investment bank in the trade and on the fact that SEC does not require immediate disclosure of derivative transactions by firms. The bank will be willing to incur more losses when buying put options from the managers if it can assure that there will be enough time to recover those losses through informed trading. This implies that if firm managers want to maximize the proceeds from the sale, they will have to agree to postpone the public disclosure of the trade. Also, similar to Prediction 1, the bank can make larger profits faster in firms with more liquid securities. In such firms, it is not necessary for the managers to postpone the disclosure of the put option transaction.

V. Conclusion

This study provides an explanation why an investment bank may agree to

purchase from a company long-term put options written on the stock of the company. The issuer is more informed about the payoff of the put options. Therefore, the investment bank has ex ante negative expected profits from this trade. Our model demonstrates that the investment bank is behaving in a perfectly rational manner, because the information gained from this loss making activity can be used to make larger profits in trading with other uninformed parties.

The idea that an uninformed player may engage in negative profit interactions in

order to gain valuable information from its informed counter-parties has been largely

ignored by the extensive literature modeling asymmetric information. Nevertheless, this notion potentially has many applications beyond the analyzed by this study case where an investment bank offers firms to buy put options written on their stock. For example, marketing companies incur costs to offer free subscriptions for various specialized

magazines to a large pool of consumers. From the selections chosen by the consumers the marketing companies learn valuable information about consumer types. This information is used afterwards for promotional purposes. Also, banks with large credit card portfolios sell high interest rate credit cards to extremely risky clients, although they expect to lose on these sales. Banks engage in these transactions in order to test the completeness of their risk evaluation models. After improving their models, the banks are able to price risk better and avoid heavy losses due to model error.

One direction in which the model can be extended is as follows. If the distribution of firm quality (or risk) is continuous instead of binomial, it may be optimal for I to offer each firm a premium for the put options that is smaller than the fair premium computed using public information. If the premium is lower than the fair premium, only the firms with the best prospects will accept to sell put options. Thus, when I decreases the

premium, it reduces the set of firms that will accept to trade and simultaneously increases the average quality of the accepting firms. The optimal premium the bank has to balance these two effects and maximize the expected profits of the bank

. The solution for the optimal premium that the investment bank should propose given a certain distribution of firm values is left for future work.

7 This maximization problem is similar to the problem of choosing the opt imal bids in an auction – a lower bid decreases the probability of winning but increases the profits if it wins.

References

Akerlov, George, 1970, The market for lemons: Quality uncertainty and the market mechanism, Quarterly Journal of Economics, 89, 488-500

Black, Fisher, 1975, Fact and fantasy in use of options, Financial Analyst Journal, 31, 36-41 and 61-72

Black, Fisher, and Myron Scholes, 1973, The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637-659

Bodie, Zvi, Alex Kane, and Alan Marcus, 1999, Investments, 4

Edition, Irvin/McGraw Hill,

Cao, Charles, Zhiwu Chen, and John Griffin, 2000, The informational content of option volume prior to takeovers, Working paper

Easley, David, Maureen O’Hara, and P.S. Srinivas, 1998, Option volume and stock prices: Evidence on where informed traders trade, Journal of Finance, 53, 431- 466

Gibson, Scott, and Raj Singh, 2000, Using put warrants to reduce corporate financing costs, Working paper, University of Minnesota

Gyoshev, Stanley B. and George P. Tsetsekos, 2000, Enhancing share repurchase programs: Use of firm’s own stock as an underlying asset in issuing put derivatives, Drexel University Working Paper Series

Lo, Andrew, and Jiang Wang, 1995, Implementing option pricing models when asset returns are predictable, Journal of Finance, 50, 87-129

Pirinski, Christo, 2000, Do equity options lead underlying stocks?, Working paper

Rotschild, M., J.E. Stiglitz, 1976, Equilibrium in competitive insurance markets: An essay in the economics of imperfect information, Quarterly Journal of Economics, 80, 629-649

Wilson, C., 1977, A model of insurance markets with incomplete information, Journal of

Economic Theory, 16, 167-207

Figure 1. Extensive Form of the Game Played by the Investment Bank and the Firms Repurchasing Stocks

The description of the information, players and payoffs is in Section II. From inequality (4) and equation (5) follows that PA1>0, and PB1<0. This ensures that firms of type B will always disagree, while firms of type A will always agree to sell put options to the investment bank. Because this separating equilibrium is unique, the bank acquires private information about firm type, and then the payoffs for the bank that matter PI1, PI7 are both greater than 0

.

0. Nature picks type A or B

1. IB offers to buy Puts

2. Firms decide to agree or not

3. Bank decides whether to trade on Information

A B

Agree Disagree Agree Disagree

(P

1, P

1) (P

2, P

1) (P

3, 0) (0, 0) (P

5, P

1) (P

6, P

1) (P

7, 0) (0, 0) 4. Payoffs

Trade Not Trade Trade Not Trade Trade Not Trade Trade Not Trade