Derivatives and the Repo Market • Options • Interest Rate Swaps • Credit Default Swaps (CDS) • Repo Market

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• Derivatives: Options • Call Option: The right, but not the obligation, to buy an asset at a specified exercise (or, strike) price on or before a specified date. • Put Option: The right, but not the obligation, to sell an asset at a specified exercise (or, strike) price on or before a specified date. • Exercise or Strike Price: Price set for calling (buying) or putting (selling) an asset. • Premium: The purchase price of an option. • In the money: An option where exercise would be profitable • Out of the money: An option where exercise would not be profitable • American Option: The buyer of an option has the right to buy (call) or sell (put) the underlying asset on or before the expiration date. • European Option: The buyer of an option has the right to buy (call) or sell (put) the underlying asset only on the expiration date. • Expiration Date: Normally the third Friday of the month in the United States. • Writer of Option: The seller of the option (e.g., write a call means to sell a call option to someone) • Stock Option Contract: normally (U.S. exchanges) the right to buy or sell 100 shares 2

Notation S = the value of the asset at the expiration date X = the exercise (strike) price C = the premium (or, price) of the call option P = the premium (or, price) of the put option

Payoffs and Profit of Call Options: Payoff = S – X if S > X; otherwise 0 Profit = S – X – C if S > X; otherwise -C

Payoffs and Profit of Put Options: Payoff = X – S if X > S; otherwise 0 Profit = X – S - P if X > S; otherwise -P

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Simple Numerical Examples of Call and Put Options (1) Call Option Current price of stock $50 Exercise (strike) price (X) = $55 Price at expiration (S) = $60 Premium (C) = $2 Payoff = S – X = $60 - $55 = $5 Profit = S – X – C = $60 - $55 - $2 = $3

(2) Put Option Current price of stock $50 Exercise (strike) price (X) = $45 Price at expiration (S) = $40 Premium (P) = $2 Payoff = X - S = $45 - $40 = $5 Profit = X - S– P = $45 - $40 - $2 = $3

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Graphical Representation of the Profit on the Call Option

Profit/Loss

+3 0

50

55

60

S

-2

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Profit on the Call Option vs. Purchase and Sale of Stock

Profit/Loss

+10

+3 0

50

55

60

S

-2

Why buy the call? Why not just purchase the stock then sell it when the price goes up?

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Rate of Return from buying 100 shares of the stock at a price of $50 then selling all at a price of $60 Investment = $50 x 100 = $5,000 Payoff = $60 x 100 = $6,000 Profit = $10 x 100 = $1,000 = $6,000 - $5,000 Rate of Return =

$1,000 = .20 = 20% $5,000

Rate of Return from buying a call option contract (100 shares) with a premium of $2 per share Investment = $2 x 100 = $200 Payoff = $5 x 100 = $500 = ($60 - $55) x 100 Profit = $3 x 100 = $300 = ($60 - $55 - $2) x 100 Rate of Return =

$300 = 1.50 = 150% $200

Suppose you had used all of your $5,000 to buy call options Investment = $2 x 2,500 = $5,000 Payoff = $5 x 2,500 = $12,500 Profit = $3 x 2,500 = $7,500 Rate of Return =

$7,500 = 1.50 = 150% $5,000

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Graphical Representation of the Profit on the Put Option Exercise price (X) = $45; Price at expiration (S) = $40; Premium (P) = $2 Profit/Loss

+3 0

40

45

S

-2

What about the writer (seller) of the call option and put option?

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Profit from a Writing a “Naked” Call Option Exercise (strike) price (X) = $55; Price at expiration (S) = $60; Premium (C) = $2 Profit/Loss

+2 0

55

60

S

-3

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Profit from a Writing a “Covered” Call Option Current Price = 50; Exercise (strike) price (X) = $55; Price at expiration (S) = $60; Premium (C) = $2 First, purchase the stock…

Profit/Loss

0

50

60

S

10

Second, write the call… Profit/Loss

+2 0

55

60

S

-3

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Profit on the ‘covered’ call… Profit/Loss

Buying the stock

Buying stock and writing a call option

+7 +2 0

48

50

55

60

S

2-50= -48

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Profit for the Writer of the Put Option Exercise price (X) = $45; Price at expiration (S) = $40; Premium (C) = $2 Profit/Loss

+2 0

40

45

S

-3

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Interest Rate Swaps Two ‘traditional’ types of swaps: currency and interest rate Swaps, as the name implies, are simply contracts to ‘swap’ payments/income between two parties. Simple intuitive example of a currency swap: Suppose you work in the U.S. receiving $1,000 per month. You have a friend working in Japan receiving 2,000 yen per month. Further, suppose you plan on making a trip to Japan and your friend plans on making a trip to the U.S. Instead of going to the bank to exchange currencies, you and your friend could enter into an agreement to ‘swap’ your paychecks for the month. Thus, you get 2,000 yen and sign over your $1,000 paycheck to your friend. This would be an example of a currency swap. Firms (financial and nonfinancial) can do this as well. A firm receiving payments in dollars would like to have yen instead. Another firm receiving payments in yen would like to have dollars. If the firms could find each other, they could simply agree to swap the payment streams. In order to find each other, the firms might have to use a ‘matchmaker’ ---- in reality, they use a bank or investment bank to arrange the deal. If the bank or investment bank cannot find a counterparty for a firm, then the may choose to enter into the swap agreement themselves. Simple intuitive example of an interest rate swap: Suppose you work on commission. Sometimes your paycheck is large because you’ve had a good month while other times it’s small. You have a friend that gets a constant salary. Now, it might be the case that you’re in a position that you would like a steadier monthly paycheck. Also, you’re friend might be in a position that s/he would like to take a little more risk in hopes of getting some larger paychecks. Again, you and your friend (this time one that receives the paycheck in the same currency as you) might enter into an agreement to ‘swap’ your paychecks. We can see that this agreement satisfies your desire for greater stability and your friend’s desire for greater risk. Thus, both financial desires have been met without either of you having to give up your jobs. An interest rate swap works similarly. One firm might be receiving interest payments that have a floating rate. Thus, the interest payment will change when the reference interest rate (e.g., LIBOR) changes. Another firm might be receiving interest payments on a fixed interest rate. Rather than each try to sell the underlying assets, they could enter into an agreement to simply swap the received interest payments.

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Example 1. A portfolio manager has $100 million in long-term bonds paying an average fixed interest rate of 7% (thus, $7 million per year in interest income). The manger believes that interest rates will soon go up. Thus, the manager would like to swap the fixed rate for a floating rate. The manager calls a swap dealer (e.g., bank) to see if this is possible. The swap dealer agrees to swap the cash flow of the 7% fixed rate (i.e., $7 million per year) for a floating rate based on LIBOR (London InterBank Offere Rate, this is the most common reference rate though it could be anything). So, our portfolio manager agrees to pay the swap dealer $7 million per year in exchange for $100 million x LIBOR (whatever LIBOR turns out to be, this will fluctuate or float just like the manager wanted). Portfolio Manager’s NET cash flow = (LIBOR – 7%)x $100 million Notice what happens under various assumptions about LIBOR

LIBOR = 6.5%

LIBOR=7%

LIBOR=7.5%

Income from the Bonds

$7,000,000

$7,000,000

$7,000,000

Net Cash flow from Swap

-$500,000

Total

$6,500,000

0 $7,000,000

+$500,000 $7,500,000

The manager and dealer have entered into an agreement to swap interest payments. The manager will ‘pay’ the dealer the $7 million each year of the agreement and the dealer will pay the manager an amount that depends upon the LIBOR. If, for example, the LIBOR is 7.5% (thus, interest rates did go up like the manager thought), then the dealer will pay the manager $7,500,000. Actually, they will most like just pay each other the amount of the Net Cash Flow (thus, writing one check instead of them both having to write a check). Notice, the first line is now what the dealer gets --- a fixed income stream. The third line is what the manager gets --- an income stream that fluctuates depending upon current interest rates. The values on the third line are equal to LIBOR x $100 million. The second line gives us the difference between the two streams of cash flows. The main point here, though, is that the manager had changed his fixed interest rate holding into a floating rate holding without having to actually sell the huge amount of bonds (incurring transactions costs) – especially when you consider that his views about future interests rate change again.

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What does the swap dealer do? Well, the swap dealer could in fact enter into the above contract on its own account. More likely though, the swap dealer will act as an intermediary (‘matchmaker’ if you like) between the above manager who wants to change fixed rate for floating rate, and someone who wants to do the opposite. Of course, the swap dealer does this for a reason. Example 2. Company A has issued a 10% fixed rate bond, but wants to convert the payments into a floating-rate debt. Company B has issued a floating-rate bond tied to LIBOR, but wishes to convert it into a fixed-rate bond. A swap dealer can stand in the middle of company A and B to meet their needs. Company A has issued 10% fixed-rate bond but enters a swap to pay the dealer LIBOR and receive 9.95%. Thus, the net payment for Company A is Net Payment for A = 10% + (LIBOR – 9.95%) = LIBOR + .05% Company B has issued a floating-rate bond tied to LIBOR but enters a swap to pay the dealer 10.05% in return for LIBOR. Thus, the net payment for Company B is Net Payment for B = LIBOR + (10.05% - LIBOR) = 10.05% Company A now has a floating rate payment (like it wanted) and B has a fixed rate payment (like it wanted). What about the dealer? Net Cash from A = LIBOR – 9.95% Net Cash from B = 10.05% - LIBOR Net from A and B = (LIBOR – 9.95%) + (10.05% - LIBOR) = 10.05% - 9.95% = .1% The .1% that the dealer earns is called the bid-ask spread. Suppose the amount in question is $100 million. The dealer makes .1% of this amount, or $100,000 (not bad for just arranging the swap).

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Credit Default Swaps (CDS) A credit default swap is an insurance policy. For example, suppose that Bank of America (BofA) buys a $10 million bond issued by General Motors (GM). BofA may choose, for many reasons (one being a reduction in its capital requirement), to purchase insurance in case GM defaults on the bond – or some ‘credit event’ occurs (e.g., GM’s bonds are downgraded by a credit rating agency). Thus, BofA goes to AIG to purchase a CDS. The price of the insurance is stated as a CDS spread. For example, suppose BofA agrees to a 200 basis point spread (hence, 2%). BofA will make annually $200,000 (= $10,000,000 x 5%) to AIG. These payments are just like insurance premiums. $200,000 premiums Bank of America

AIG Insurance

$10 million Cash

$10 million Bond

General Motors

Now, suppose the dreaded ‘credit event’ occurs. Further, suppose that the bond is now worth only $4 million. AIG will make BofA ‘whole’ in the sense of paying them $6 million. What would you say if AIG was selling CDS’s only on GM, Ford, and Chrysler? This would be a strange thing to do. It could be very likely that a downturn in the auto industry could hurt all three companies at the same time. Thus, as with any insurance, the provider will want to ‘diversify’ into other types of loans – hoping that the correlation of defaults will not be positive. Thus, if one company defaults another will not. This implies that the strategy should be to ‘pool’ a lot of these CDS’s. The only problem is that in doing so, they become subject to systemic risk in that sense that all loans might get into trouble at the same time. An insurance company doesn’t expect all holders of its insurance to get into a car wreck at the same time. However, with financial markets, it is certainly possible (though, admittedly not likely) that all will get into trouble at the same time.

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One last feature of the CDS is important. There’s nothing to prevent another party from entering into CDS. For example, a hedge fund could believe that GM will in fact default on the bond (or, loan) that BofA holds. The Hedge fund could also purchase a CDS from AIG. $200,000 premiums Bank of America

AIG Insurance

$10 million Cash

$10 million Bond

General Motors

Insurance

$200,000 premium

Hedge Fund

Notice, the hedge fund does not actually own a GM bond. That is, it hasn’t made a loan to GM. The hedge fund only believes that GM will default, and it wants to profit if it does. Now, of course, the hedge fund is speculating on the GM bond. However, one could make a case that the hedge fund is playing an important role in this market. Before, there was just BofA and AIG attempting to decide on the appropriate price (i.e., the CDS spread, in our case 500 basis points or 5%; note 100 basis points = 1%) of the CDS. Now, we have the hedge fund come along with their own information and beliefs about the quality of the underlying asset (the GM bond). We have assumed that the CDS spread remained the same. However, it could be that the CDS spread rose to say 600 basis points (or, 6%). Thus, all parties are attempting to find the right price for the CDS based upon the quality of the GM bond.

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REPO Market REPO stands for repurchase agreement. We use the example from Gary Gorton’s paper. Fidelity, a money management firm, has $500 million that it wishes to hold until needed to purchase securities. However, there is no insured bank deposit for this large of an amount. On the other hand, Bear Sterns (an investment bank) wants to borrow $500 million on a short-term basis. Thus, the two agree that Fidelity will deposit the $500 million with Bear Sterns in exchange for $500 worth of securities that Bear Sterns owns. These securities could be something like U.S. Treasuries (a very safe asset) or something like a highly rate Mortgage Backed Security (MBS), or Collateralized Debt Obligation (CDO). The MBS and CDO are similar in the sense that they are bundles of loans – it’s just that the type of loans that have been bundled (i.e., securitized) are different. Bear Sterns might be earning a 6% interest rate on the security, and may agree to pay Fidelity 3% interest on the deposit. The ‘trick’ for the repo is that Bear Sterns also agrees to ‘repurchase’ the securities from Fidelity with the additional interest. Opening Leg (day of agreement) “sells” $500 million of securities Bear Stearns

Fidelity “Deposits” or “loans” $500 million cash

Closing Leg (day agreement ends)

Buys $500 million of securities + 3% ($15 million) Bear Stearns

Fidelity Sell the Securities back

In the above case, the “haircut” was zero. That is, Fidelity deposited just what the securities were worth that day.

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In Gorton’s example, he asks what happens with a 20% haircut? In this case, the opening leg looks like the following: Opening Leg (day of agreement) “sells” $500 million of securities Bear Stearns

Fidelity “Deposits” or “loans” $400 million cash

Thus, in order to protect itself from a sudden fall in the value of the collateral (i.e., the securities), Fidelity only deposits $400 million in cash. Thus, the value of the securities could fall by 20% ($100 million) and Fidelity would still get its money back. The important point for Gorton is that the haircut represents a kind of withdraw from Bear Sterns. This would be similar to a situation in which all the customers of a certain bank decided to withdraw 20% of their bank deposits (checking, saving). The bank would need to find another funding source or reduce its assets. Remember, ASSETS = DEBT + EQUITY. The Debt (or, Liability) side has decreased and therefore must either be replaced by another debt or with an increase in equity (e.g., issue new shares). If neither of these occurs, then assets must decrease. According to Gorton, these haircuts were withdraws from investment banks. The investment banks, like Bear Stearns, were forced to sell assets quickly (the ‘fire sales’) – they needed cash to meet expenditures. However, if they all begin to sell assets, then the value of the assets will decline sharply. The $500 million security might only be sold for $450 million. An important point that Gorton makes is that the investment banks sold the bonds that they thought would not fall in price much (AAA rated corporate bonds). However, since everyone was scrambling for cash, the price of the bonds did fall. The interest rate on these very safe bonds shot above the interest rate on risky bonds (see p. 15 of Gorton) --- the interest rate spread moved in a way that wasn’t anticipated. Now, we can also see the further implication that what the investment bank is left with are bonds of lower quality.

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