Charles Davì

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Securitization Demystified

In Politicized Economy, Systemic Counterparty Confusion on October 30, 2008 at 1:02 am

What Is Securitization?

Securitization is a process that allows the cash flows of an asset to be isolated from the cash flows of that asset’s original owner. There are countless variations on this theme, and since our purpose here at derivative dribble is to foster clarity and simplicity, we will discuss only the main theme, and will avoid the Glen Gould variations.

Cui Bono?

We will explain how securitization works by first exploring the most basic motivation for isolating assets: access to cheaper financing. Assume B is a local bank that focuses primarily on taking deposits and earning money through very low risk investments of those deposits. Further, assume that B is a stable and solvent bank, but that it lacks the credit quality of some of the larger national banks and as such it has a higher cost of financing. This higher cost of financing means that it can’t lend at the same low rates as national banks. B’s local community is one in which home values are high and stable, and as a result the rate of default on mortgages is extremely low. As such, B would like to be able to compete in the local mortgage market, but is struggling to do so because its rates are higher than the national banks. What B would really like to do is borrow money for the limited purpose of issuing mortgages in its local community. That is, B wants to separate its credit quality from the credit quality of the mortgages it issues in its community. Securitization is the process that facilitates this isolation.

The Nuts And Bolts

The overall process is quite simple and reasonable, despite its portrayal in the popular press. We know that so long as B owns the mortgages, B’s creditors will still consider B’s credit as an institution when lending to it, even if that lending is for the limited purpose of issuing local mortgages. The solution to that problem is simple: B sells the mortgages off shortly after issuing them. But to whom? Well, common sense tells us that investors are not going to be too excited about buying mortgages piecemeal. So, B will wait until it has issued a pool of mortgages large enough to attract the attention of investors. Then, it will set up a special purpose vehicle (SPV) where that SPV’s special purpose is to buy the mortgages from B, using money from the investors, and issue notes to those same investors.

So, the SPV owns the mortgages since B is completely bought out by the cash from the investors. And the notes issued to the investors are basically bonds issued by the SPV with the mortgages as collateral. As a result, B is out of the picture from an investor’s perspective. In reality, B might still service the mortgages (i.e., sending bills to borrowers, maintaining address information on borrowers, etc.) but because the mortgages have been sold to the SPV, the notes issued by the trust have no credit risk exposure to B. So if B goes bust, the assets in the SPV are safe and will continue to pay.

So What Does That Accomplish?

B wanted to enter the local mortgage market but was struggling to do so because it couldn’t lend at the same rates as national banks. This was due to B’s inferior credit standing relative to large national banks. But the securitization process above allows B to isolate the credit quality of the mortgages it issues from its own credit quality as an institution. Thus, the rate paid on the notes issued by the SPV will be determined by examining the credit quality of the mortgages themselves, with no reference to B. Since the rate on the notes is determined only by the quality of the mortgages, the rate on any individual mortgage will be determined by the quality of that mortgage. As such, B will be able to issue mortgages to its local community at the market rate and profit from this by servicing the mortgages for a fee.

Derivatives/Synthetic Instruments Demystified

In Politicized Economy, Systemic Counterparty Confusion on October 27, 2008 at 4:44 pm

What Is A Derivative?

A derivative is a contract that derives its value by reference to “something else.” That something else can be pretty much anything that can be objectively observed and measured. For example, two parties, A and B, could get together and agree to take positions on the Dow Jones Industrial Average (DJIA). That’s an index that can be objectively observed and measured. A could agree to pay B the total percentage-wise return on that index from October 31, 2007 to October 31, 2008 multiplied by a notional amount, where that amount is to be paid on October 31, 2008. In exchange, B could agree to make quarterly payments of some percentage of the notional amount (the swap fee) over that same time frame. Let’s say the notional amount is $100 (a position that even Joe The Plumber can take on); the swap fee is 10% per annum; and the total return on the DJIA over that period is 15%. It doesn’t take Paul Erdős to realize that this leaves B in the money and A out of the money (A pays $15 and receives $10, so he loses $5).

But what if the DJIA didn’t gain 15%? What if it tanked 40% instead? In that case, we have to look to our agreement. Our agreement allocated the DJIA’s returns to B and fixed payments to A. It didn’t mention DJIA loss. The parties can agree to distribute gain and loss in the underlying reference (the DJIA) any way they like: that’s the beauty of enforceable contracts. Let’s say that under their agreement, B agreed to pay the negative returns in the DJIA multiplied by the notional amount.  If the market tanked 40%, then B would have made the fixed payments of 10% over the life of the agreement, plus another 40% at the end. That leaves him down $50. Bad year for B.

Follow The Money

So what is the net effect of that agreement? B always pays 10% to A, whether the DJIA goes up, down, or stays flat over the relevant time frame. If the DJIA goes up, A has to pay B the percentage-wise returns. If the DJIA goes down, B has to pay A the percentage-wise losses. So, A profits if the DJIA goes down, stays flat, or goes up less than 10% and B profits if the DJIA goes up more than 10%. So, A is short on the DJIA going up 10% and B is long on the DJIA going up 10%. This is accomplished without either of them taking actual ownership of any stocks in the DJIA. We say that A is synthetically shorting the DJIA and B is synthetically long on the DJIA. This type of agreement is called a total return swap (TRS). This TRS exposes A to the risk that the DJIA will appreciate by more than 10% over the life of the agreement and B to the risk that the DJIA will not appreciate by more than 10%.

What Is Risk?

There are a number of competing definitions depending on the context. My own personal view is that risk has two components: (i) the occurrence of an event and (ii) a magnitude associated with that event. This allows us to ask two questions: What is the probability of the event occurring? And if it occurs, what is the expected value of its associated magnitude? We say that P is exposed to a given risk if P expects to incur a gain/loss if the risk-event occurs. For example, in the TRS between A and B, A is exposed to the risk that the DJIA will appreciate by more than 10% over the life of agreement. That risk has two components: the event (the DJIA appreciating by more than 10%) and a magnitude associated with that event (the amount by which it exceeds 10%). In this case, the occurrence of the event and its associated magnitude are equivalent (any non-zero positive value for the magnitude implies that the event occurred) and so our two questions reduce to one question: what is the expected value of the DJIA at the end of the agreement? That obviously depends on who you ask. So, can we then infer that A expects the DJIA to gain less than 10% over the life of the agreement? No, we cannot. If A actually owns $100 worth of the DJIA, A is fully hedged and the agreement is equivalent to bona fide financing. That is, A has no exposure to the DJIA (short on the DJIA through the TRS and long through actually owning it) and makes money only through the swap fee. B’s position is the same whether A owns the underlying index or not: B is long on the DJIA, as if he actually owned it. That is, B has synthesized exposure to the DJIA. So, if A is fully hedged the TRS is equivalent to a financing agreement where A “loans” B $100 to buy $100 worth of the DJIA, and then A holds the assets for the life of agreement (like a collateralized loan). As such, B will never agree to pay a swap fee on a TRS that is higher than his cost of financing (since he can just go get a loan and buy the reference asset).

How Derivatives Create, Allocate, And “Transfer” Risk

It is commonly said that derivatives transfer risk. This is not technically true, but often appears to be the case.  Derivatives operate by creating risks that were not present before the parties entered into the derivative contract. For example, assume that A and B enter into an interest rate swap, where A agrees to pay B a fixed annual rate of 8% and B agrees to pay A a floating annual rate, say LIBOR, where each is multiplied by a notional amount of $100. Each party agrees to make quarterly payments. Assume that on the first payment date, LIBOR = 4%.  It follows that A owes B $2 and B owes A $1. So, after netting, A pays B $1.

Through the interest rate swap, A is exposed to the risk that LIBOR will fall below 8%. Similarly, B is exposed to the risk that LIBOR will increase above 8%. The derivative contract created these risks and assigned them to A and B respectively. So why do people say that derivatives transfer risk? Assume that A is a corporation and that before A entered into the swap, A issued $100 worth of bonds that pay investors LIBOR annually. By issuing these bonds, A became exposed to the risk that LIBOR would increase by any amount. Assume that the payment dates on the bonds are the same as those under the swap. A’s annual cash outflow under the swap is (.08 – LIBOR) x 100. It’s annual payments on the bonds are LIBOR x 100. So it’s total annual cash outflow under both the bonds and the swap is:

(.08 – LIBOR) x 100 +  LIBOR x 100 = .08 x 100 – LIBOR x 100  + LIBOR x 100 = 8%.

So, A has taken its floating rate LIBOR bonds and effectively transformed them into fixed rate bonds. We say that A has achieved this fixed rate synthetically.

At first glance, it appears as though A has transferred its LIBOR exposure to B through the swap.  This is not technically true. Before A entered into the swap, A was exposed to the risk that LIBOR would increase by any amount. After the swap, A is exposed to the risk that LIBOR will fall under 8%. So, even though A makes fixed payments, it is still exposed to risk: the risk that it will pay above its market rate of financing (LIBOR). For simplicity’s sake, assume that B was not exposed to any type of risk before the swap. After the swap, B is exposed to the risk that LIBOR will rise above 8%. This is not the same risk that A was exposed to before the swap (any increase in LIBOR) but it is a similar one (any increase in LIBOR above 8%).

So What Types Of Risk Can Be Allocated Using Derivatives?

Essentially any risk that has an objectively observable event and an objectively measureable associated magnitude can be assigned a financial component and allocated using a derivative contract. There are derivative markets for risks tied to weather, energy products, interest rates, currency, etc. Wherever there is a business or regulatory motivation, financial products will appear to meet the demand. What is important is to realize that all of these products can be analyzed in the same way: identify the risks, and then figure out how they are allocated. This is usally done by simply analyzing the cash flows of the derivative under different sets of assumptions (e.g., the DJIA goes up 15%).

Netting Demystified

In Systemic Counterparty Confusion on October 24, 2008 at 1:24 am

Netting Is For Everyone, Not Just Fancy Swap Traders

Unlike most terms used in the derivatives world, netting is a good one. It has an intuitive, albeit hokey, feel (unlike other rather sterile terms such as “synthetic collateralized debt obligation”). After all, economics is about human decisions and actions, and as such, it can stand to be a bit hokey. So what is netting? The concept stems from a very simple observation: if I owe you $5 and you owe me $10, you should just give me $5. We could have several debts between the two of us, (e.g., I owe you $2 from Wednesday, $3 from Thursday), but assume we add those up into one debt per person, resulting in one transactional leg (line connecting us) each. In this case, netting would save us a bit of trouble since we only exchange money once, instead of twice.

That Is So Obvious And Trivial That It Can’t Be Right

The observation above is indeed an example of the same principle (netting) that is applied to swaps. Our example however, only has 2 parties. The time saved from engaging in 1 transaction instead of 2 is minimal, especially when it’s a transaction for such a small amount of money. This is a result of the fact that when there are only 2 parties, let’s say you and me, there are only 2 legs to the transaction: the money coming out of me and the money coming out of you. The netting example above reduces that to 1 leg (you pay me). That’s called bilateral netting. Again, when there are only 2 parties, the application of netting is simple. But the number of legs increases dramatically as we increase the number of parties (for my fellow graph theorists, the number of legs is twice the number of edges in a complete graph with N nodes, where N is the number of parties). For example,  consider the obligations of 3 friends: A, B and C. A owes B $2; A owes C $3; B owes A $4; B owes C $5; C owes A $2; and finally C owes B $6.

We apply bilateral netting to each of the pairs. That leaves us with the following: A owes C $1; B owes A $2; and C owes B $1. We could just execute 3 transactions and call it a day. But we’re smarter than that. We notice that C is basically passing the $1 from A onto B. That is, his inflow is the same as his outflow, so he serves no purpose in our transaction. So, we cut him out of the picture:

Note that the last step we just took, cutting C out, was not bilateral netting. It was a different kind of netting. It required a different observation, but the principle is the same: only engage in necessary transactions. Finally, we apply bilateral netting to the transaction between A and B. So, in the end, that complex sea of relationships boiled down to B paying A $1.

Balsamic Reduction

Rather then execute a disastrously complicated web of transactions, swap dealers, and ordinary banks, use clearing houses to do exactly what we just did above, but on a gigantic scale. Obviously, this is done by an algorithm, and not by hand. Banks, and swap dealers, prefer to strip down the number of transactions so that they only part with their cash when absolutely necessary. There are all kinds of things that can go wrong while your money spins around the globe, and banks and swap dealers would prefer, quite reasonably, to minimize those risks.

An Engine Of Misunderstanding

As you can see from the transactions above, the total amount of outstanding debts is completely meaningless. That complex web of relationships between A, B, and C, reduced to 1 transaction worth $1. Yet, the media would have certainly reported a cataclysmic 2 + 3 + 4 + 5 + 2 + 6 = $22 in total debts.

Systemic Counterparty Confusion: Credit Default Swaps Demystified

In Politicized Economy, Systemic Counterparty Confusion on October 23, 2008 at 12:30 am

It Is A Tale Told By An Idiot

The press loves a spectacle. There’s a good reason for this: panic increases paranoia, which increases the desire for information, which increases their advertising revenues. Thus, the press has an incentive to exaggerate the importance of the events they report. As such, we shouldn’t be surprised to find the press amping up fears about the next threat to the “real economy.”

When written about in the popular press, terms such as “derivative” and “mortgage backed security” are almost always preceded by adjectives such as “arcane” and “complex.” They’re neither arcane nor complex. They’re common and straightforward. And the press shouldn’t assume that their readers are too dull to at least grasp how these instruments are structured and used. This is especially true of credit default swaps.

Much Ado About Nothing

So what is the big deal about these credit default swaps? Surely, there must be something terrifying and new about them that justifies all this media attention? Actually, there really isn’t. That said, all derivatives allow risk to be magnified (which I plan to discuss in a separate article). But risk magnification isn’t particular to credit default swaps. In fact, considering the sheer volume of spectacular defaults over the last year, the CDS market has done a damn good job of coping.  Despite wild speculation of impending calamity by the press, the end results have been a yawn . So how is that Reuters went from initially reporting a sensational $365 billion in losses to reporting (12 days later) only $5.2 billion in actual payments? There’s a very simple explanation:netting, and the fact that they just don’t understand it. The CDS market is a swap market, and as such, the big players in that market aren’t interested in taking positions where their capital is at risk. They are interested in making money by creating a market for swaps and pocketing the difference between the prices at which they buy and sell. They are classic middlemen and essentially run an auction house.

Deus Ex Machina

The agreements that document credit default swaps are complex, and in fairness to the press, these are not things we learn about in grammar school – for a more detailed treatment of these agreements, look here. Despite this, the basic mechanics of a credit default swap are easy to grasp. Let’s begin by introducing everyone: protection buyer (B) is one party and swap dealer (D) is the other. These two are called swap counterparties or just counterparties for short. Let’s first explain what they agree to under a credit default swap, and then afterward, we’ll examine why they would agree to it.

What Did You Just Agree To?

Under a typical CDS, the protection buyer, B, agrees to make regular payments (let’s say monthly) to the protection seller, D. The amount of the monthly payments, called the swap fee, will be a percentage of the notional amount of their agreement. The term notional amount is simply a label for an amount agreed upon by the parties, the significance of which will become clear as we move on. So what does B get in return for his generosity? That depends on the type of CDS, but for now we will assume that we are dealing with what is called physical delivery. Under physical delivery, if the reference entity defaults, D agrees to (i) accept delivery of certain bonds issued by the reference entity named in the CDS and (ii) pay the notional amount in cash to B. After a default, the agreement terminates and no one makes anymore payments. If default never occurs, the agreement terminates on some scheduled date. The reference entity could be any entity that has debt obligations.

Now let’s fill in some concrete facts to make things less abstract. Let’s assume the reference entity is ABC. And let’s assume that the notional amount is $100 million and that the swap fee is at a rate of 6% per annum, or $500,000 per month. Finally, assume that B and D executed their agreement on January 1, 2008 and that B made its first payment on that day.  When February 1, 2008 rolls along, B will make another $500,000 payment. This will go on and on for the life of the agreement, unless ABC triggers a default under the CDS. Again, the agreements are complex and there are a myriad of ways to trigger a default. We consider the most basic scenario in which a default occurs: ABC fails to make a payment on one of its bonds. If that happens, we switch into D’s obligations under the CDS. As mentioned above, D has to accept delivery of certain bonds issued by ABC (exactly which bonds are acceptable will be determined by the agreement) and in exchange D must pay B $100 million.

Why Would You Do Such A Thing?

To answer that, we must first observe that there are two possibilities for B’s state of affairs before ABC’s default: he either (i) owned ABC issued bonds or (ii) he did not. I know, very Zen. Let’s assume that B owned $100 million worth of ABC’s bonds. If ABC defaults, B gives D his bonds and receives his $100 million in principal (the notional amount). If ABC doesn’t default, B pays $500,000 per month over the life of the agreement and collects his $100 million in principal from the bonds when the bonds mature. So in either case, B gets his principal. As a result, he has fully hedged his principal. So, for anyone who owns the underlying bond, a CDS will allow them to protect the principal on that bond in exchange for sacrificing some of the yield on that bond.

Now let’s assume that B didn’t own the bond. If ABC defaults, B has to go out and buy $100 million par value of ABC bonds. Because ABC just defaulted, that’s going to cost a lot less than $100 million. Let’s say it costs B $50 million to buy ABC issued bonds with a par value of $100 million. B is going to deliver these bonds to D and receive $100 million. That leaves B with a profit of $50 million. Outstanding. But what if ABC doesn’t default? In that case, B has to pay out $500,000 per month for the life of the agreement and receives nothing. So, a CDS allows someone who doesn’t own the underlying bond to short the bond. This is called synthetically shorting the bond. Why? Because it sounds awesome.

So why would D enter into a CDS? Again, most of the big protection sellers buy and sell protection and pocket the difference. But, this doesn’t have to be the case. D could sell protection without entering into an offsetting transaction. In that case, he has synthetically gone long on the bond. That is, he has almost the same cash flows as someone who owns the bond.

The Not So Efficient Market (Theorem) Hypothesis

In Not So Efficient Market Hypothesis on October 10, 2008 at 12:26 am

Are Capital Markets Efficient?

Let’s examine the question using elementary game theory. That is, let’s assume that given any decision, each capital market participant acts in a way that maximizes his expected utility.

But How Would We Do That?

First we explore one example of incentive structures which leads to a sell off. Then we consider how the Efficient Market Hypothesis fits into the framework of economic knowledge and the notion of economic efficiency. Finally, we conclude that even if a capital market incorporates all available price-information, it is possible that the outcome is not an efficient allocation of capital.

The Sound And The Fury

Assume that Apocalypse Ann (A) and Tag Along Teds (T1, T2, …, Tn) are all traders that hold large positions in ABC stock. Assume that A is convinced that ABC is doomed because of recent conditions in the credit markets. She may or may not be correct in her prediction, but assume she honestly believes that ABC will be placed into receivership and liquidated, with little to no money left for equity holders.  Further, assume that each of T1, T2, …, Tn is aware of A’s belief. Personally, each thinks that A is out of her mind, that ABC is well positioned to ride the current credit crisis and that current equity valuations of ABC are rational. However, they know that given A’s belief, she will certainly liquidate her position.

Assume that each of T1, T2, …, Tn is a trader for a fund that has some rather jittery investors who are awaiting quarterly results and approaching a point in their investments where they have the right to withdraw their investment.  Assume that L is the maximum decrease in total value of any ABC position that any investor in any of the funds will accept for the quarter without withdrawing their investment; and assume that no trader wants its investors to withdraw.

Assume that based on historical data and current trading volumes, if the current price of ABC stock is P1, then the price after A liquidates a 100 share lot is expected to be P2 = Δ × P1, for some  0 < Δ ≤ 1. Let the number of shares held by A be k × 100; let S be the smallest number of ABC shares held by any one of  T1, T2, …, Tn; and let P be the current price of ABC’s stock.  For any Δ < 1, we can choose k such that L < S \times P \times (1 - \Delta ^{k} ) . That is, the expected decrease in the smallest position of ABC’s stock held by any of T1, T2, …, Tn as a result of A liquidating her position is greater than the maximum decrease in total value that any investor will accept without withdrawing their investment. Therefore, each of T1, T2, …, Tn will try to sell their positions before A does so, further deteriorating the price of ABC stock. Moreover, each has an incentive to be the first to sell.

Interesting, But That Looks Like A Very Specific Scenario

While catered to fit our current economic context, the root of the problem comes from the interactions between two sets of facts: the group of investors (the Teds) with a contingent investment horizon that could shorten dramatically upon the occurrence of a particular event (if the price of ABC tanks, the Teds’ investment horizons collapse to the present because the investors will want their money back); and the fact that the occurrence of that event is in the control of another party that benefits (or at least believes they will benefit) from its occurrence.

In the example, Ann acts as an individual. In theory and reality, Ann could be an individual or a group of individuals. Ann could be a group of short sellers. Ann could be a large bank that was forced to liquidate its assets. It doesn’t matter. So long as Ann will certainly liquidate a sufficiently large enough position, the Teds will as well.

But Doesn’t The EMH Imply That ABC’s Price Would Go Back Up?

EMH proponents would argue that in the case of such a mass liquidation, white knights will run in and bid the price up again if the underlying equity were truly “worth it.” This must be true on some level, since the number of sales must always equal the number of purchases. However, prices move. And “sell offs” cause prices to fall. This fact cuts to the nature of prices and is beyond the scope of this essay. We simply note that the fire sale dynamic creates its own little race to the bottom: each Ted has an incentive to lower their asking prices given the possibility that another Ted will go even lower.  Thus, the Teds are playing a game where expected utility decreases the longer it takes for them to close a sale. This entire fiasco is a result of the incorporation of relevant price information. That is, the fact that Ann will liquidate is relevant price information, and is therefore incorporated into the Teds’ decision to liquidate.

Straighten Out Your Mind’s Eye

We need to get our epistemology straight before we examine the consequences of what I’ve just outlined. First, the Efficient Market Hypothesis (EMH) is just that, a hypothesis. While there are 3 different flavors, the general idea is that all available information is quickly incorporated into the price of a stock in the world’s most developed stock markets. This hypothesis was then tested with empirical research. Whatever your opinion on how well the research actually tested that hypothesis, just assume for our purposes that the research conducted to date did test the hypothesis, and failed to prove it false.

Even if we assume that the EMH is supported by empirical evidence, its name is still a misnomer. While it does assume that information is observed and then quickly incorporated into the price of a stock, that process does not fit nicely into any well accepted notion of efficiency. For the EMH does not treat information as a good to be efficiently allocated. It boldly assumes that information is automatically available and incorporated to the maximum extent: to the point where no one could create an opportunity for arbitrage through the use of any information. This assumption is in and of itself puzzling and undermines the notion that information has value, which it clearly does. So, I prefer to think of pricing, which includes the incorporation of available price-information, as anterior to efficiency. That is, if assets are accurately priced, then resources will be allocated efficiently among those assets. This allows us to separate the EMH itself (the informational aspect) from its implications (efficiency). So, the EMH implies that the equity prices of companies trading in the most advanced capital markets will accurately reflect all available information, and that therefore capital will be distributed efficiently within those markets.

So How Is That Inefficient?

Good Question. As discussed earlier, the main purpose of assuming the EMH is true is to convince us that the markets distribute capital efficiently. (The observation and incorporation of information is itself interesting and important, but the goal is to allocate goods based on that information). While there are competing definitions of efficiency, the general gist is that a market is said to distribute capital efficiently if there’s no better way to distribute capital than the distribution created by the market: there might be other distributions that are just as good, but no distribution is better. “Good” and “better” are clearly imprecise terms, and we should have some definition of utility that we seek to maximize in the capital markets. However, the outcome of the Ann and Ted scenario is sub optimal under any reasonable definition of utility.

The purpose of the capital markets is to distribute capital to companies. The EMH takes as one of its corollaries that this distribution is efficient. However, as demonstrated above, the separation of control over an event and contingent investment horizons keyed to that event can lead to changes in equity prices that have nothing to do with the financial health of the underlying company. The result is that a company that becomes subject to such a situation will have a higher of cost raising capital through equity.

Q.E.D.

Assume that the state of affairs before the ABC sell off was efficient. We assume that when all other variables are fixed, there is only one efficient cost of equity capital for any company. Therefore, all variables other than the sell off being fixed, because ABC’s cost of equity capital has deviated from an efficient level, the state of affairs after the sell off must be inefficient.  So, something else must have changed if the state of affairs after the sell off is to be efficient. In theory, this is entirely possible. In reality, however, given that panic sales usually go to cash or cash equivalents, it is not likely. Thus, theory agrees with common sense: even if the EMH is true, panic sales are still possible and lead to inefficeint results. That is, whether or not the timely observation and incorporation of relevant price-information is a necessary condition for efficient allocation of capital, it is not a sufficient condition.

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