How Much of a Good Trade Is Too Much? A Bond Arbitrager Is Shaken and Stirred in Tokyo

Victor Haghani discusses an attractive opportunity identified by Salomon Brothers’ fixed income arbitrage traders in 1988. But how much capital did the trade put at risk and how much of the trade should Salomon do?

I joined Salomon Brothers in 1984 after completing an undergraduate degree at the London School of Economics. Moving to New York, I worked for Bob Kopprasch and Marty Leibowitz in the Bond Portfolio Analysis Group doing quantitative fixed income research. After a year-and-a-half, I was asked to join the fixed income arbitrage desk run by John Meriwether.

I was surprised and honored by the invitation to change jobs. I was the youngest member on the desk, 24 years old, and became immersed in trading. The idea was to put on trades that had convergence properties. We called it “arbitrage,” but the path to convergence might be risky.

Victor explains convergence trades.

My former colleague at Salomon Brothers, the author Michael Lewis, explains convergence trades by asking his reader to imagine a world where red and blue dollars exist in addition to traditional green ones. The new funny-colored dollars can’t be spent for five years. They should have the same value because they have the same properties, “but for all sorts of reasons -- a mania for blue, a nasty article about red -- the blue dollar becomes more expensive than the red dollar.”

I’ll add some numbers to Michael’s example, so I can make some points about how an individual and a Wall Street trading desk might take advantage of this price discrepancy. Suppose blue dollars sell for $0.945 and red ones for $0.90. An individual who owns 20 blue dollars could sell them and buy 21 red dollars, ensuring 5% greater buying power (21/20 - 1 = 5%) in five years’ time when red dollars and blue dollars can be used to buy goods and services.

But a Wall Street trading desk isn’t going to be content earning a cumulative five percent over five years. It might instead take advantage of the price difference between red and blue dollars in the following way. It would borrow, say, 200 million blue dollars, promising to pay back the lender those blue dollars at some later date. It would then sell the blue dollars and with the proceeds buy 210 million red dollars. Now the trading desk has a liability of 200 million blue dollars and an asset of 210 million red dollars. Given the prices above, the value of liability and asset equal each other, $189 million (200 million blue dollars * 0.945 equals 210 million red dollars * 0.90). But in five years, when red and blue dollars are spendable, their value must converge to $1, and the trading desk will have made $10 million.

But the path to convergence might be volatile, and that volatility is difficult to estimate as it arises primarily from demand and supply imbalances rather than changes in intrinsic worth. Given that the prices of red and blue dollars are out-of-whack now, they could become even more out-of-whack in the future. If so, and the value of blue dollars increases relative to red dollars, the trading desk will experience a mark-to-market loss. That loss will have to be reported if the trading desk is part of a publicly listed company.

And going deeper into the mechanics of borrowing blue dollars, the lender probably required collateral to secure the loan. The trading desk might well have posted the red dollars it bought. If the value of the blue-dollar-denominated loan increases relative to the value of red-dollar-collateral, the trading desk will have to post more collateral to secure the loan. Otherwise, the lender might seize the collateral and terminate the loan at a time the trade has lost money. Finally, if the trading desk is part of a regulated entity, it will have capital requirements associated with the positions. Meanwhile, the trading desk hopes the prices of red and blue dollars don’t take a full five years to converge so it can earn its return sooner and avoid these risks and expenses.

We traded a lot of different instruments: bond options, interest rates swaps, swap options, and interest rate caps and floors. We even created new products such as yield curve agreements, something insurance companies liked, and we hedged it on our desk. In 1988, the relative-value fixed-income trading we specialized in was becoming a bigger and bigger part of Salomon Brothers, not only in New York, but also in our London and Tokyo offices.

John Meriwether became global head of fixed income arbitrage trading and he encouraged cross-fertilization of ideas among the New York, London, and Tokyo arb desks. He had members of the Tokyo and London desks come to New York where we shared information and trade ideas. There was so much going on in Tokyo at the time that John wanted someone on the New York desk to go to Tokyo and spend six months or so over there.

Well, it turned out that not only was I the youngest person on the New York desk, I was also the only one who wasn’t married. So, all eyes turned to me and John said, “Vic, would you like to go to Tokyo?” I had never been to Asia, so it was going to be all new to me. I was in a relationship with the woman who was to become my wife, but we transitioned to long-range mode and I went to Tokyo.

When I got on the flight to Tokyo, I saw John Gutfreund, Salomon’s chairman and CEO, sitting in first class. He recognized me and said, “What are you doing?” Answering his question literally, I clumsily told him I was going to Tokyo -- luckily for me he took it as me being awkward rather than sassy. After he found out why I was going to Tokyo, he asked, “Oh, you know what? Can you read this book and tell me what you think about it when we get to Tokyo?” And he handed me a book on chaos theory. That gave me something to do on the 14-hour overnight trip.

When the plane got to Tokyo, I assumed Gutfreund, being in first class and having gotten off the plane first and having a head start through passport control, would be long gone. Maybe I would discuss the book with him in the office, or maybe he’d forget all about me and the book. But Gutfreund was waiting for me in baggage claim and gave me a ride into Tokyo. We had a good chat about the book on the one-hour trip. After we got to his hotel, he had his driver drop me off at mine. Spending so much time with Salomon’s CEO was a sign to me of how crazy things were going to be on the visit.

I got to the office and met everybody. It was a pretty small office. The head of the Tokyo arb desk was Shigeru Myojin. Really bright guy, funny and full of personality. Everybody called him Sugar, except for the Japanese people who worked for him. They almost bowed down to him when they talked to him. They would incline their heads a little bit and start any conversation with “Myojin-san.” It was quite formal, yet he was hilarious and cared deeply about everyone who worked for him.

Being parachuted onto the Tokyo arb desk, I didn’t know what to expect. I just wanted to get the trust of the people to be able to talk to them about what they were doing. On a typical day, I’d come to work and check in on what happened on the New York arb desk the day before. Then we would talk about what was going on in Japan, and I would see Tokyo’s positions and we would talk about valuations, opportunities, and risks. They would explain the market to me and then we’d go out for a big and delicious lunch-feast. In the evening, Sugar had some of the younger people on the arb desk take me out. We’d go out eating and drinking and sightseeing.

On the weekends, Sugar organized tours to onsens, hot spring spas. We’d climb hills and mountains to different shrines where we would pay priests to say prayers for our trades. It was amusing to hear the priests chanting in Japanese and then suddenly catching “Salomon Brothers fixed income arbitrage desk” in English.

My kids think one story from this time hilarious. The first week I was there I was exhausted from jet lag, working, and going out at night. The Japanese markets close at lunchtime for an hour and a half and everybody goes out and nothing happens during that time. I was so tired one day I just needed to rest so I said “Guys, I’m just going back to my hotel. I’ve got some stuff I have to do there.” They knew I was going to take a nap. I walked the ten minutes to my hotel, fell on the bed, and went right to sleep; clothes on, suit, tie, and everything.

All of a sudden, I wake up and feel a tremor. I’m on the 40-something floor of the ANA Hotel and the building is swaying. I say to myself “Oh, my God. This is the Tokyo earthquake scenario. This is terrible.” A few seconds later, the phone rings and it’s a Japanese woman asking in English “Mr. Haghani-san, are you okay?” I say I’m fine and she says, “Don’t worry, don’t worry. But don’t leave your room. Stay there, but don’t do anything.” So now I’m more worried.

The phone rings again five minutes later and the same lady says “Mr. Haghani-san, everything okay? You’re there? We’re expecting more tremors, but don’t worry. Everything’s going to be okay.” I say “all right” and she says “What I want you to do is don’t leave your room, go to your bathroom and fill up your bathtub. Fill up your bathtub with water right now please. This is important. Also, are you wearing your clothes? Please make sure you are fully dressed. Put your shoes on and make sure you’re fully dressed.” Even more worried now, I think “wow,” and she hangs up the phone.

I’m thinking about how strange this is. I’m already dressed, so I just put my shoes on. I’m wondering why she wants me fully dressed with my shoes on and think maybe I’ll have to run down the stairs to evacuate the hotel. But why fill up the bathtub? Maybe the water supply is going to stop and we need water to drink? Nothing makes sense in my sleep-deprived state of confusion.

Anyway, ten minutes later the phone rings again and it’s the same woman. She says “Mr. Haghani-san, is everything okay? I don’t want you to worry, but is your bathtub filled?” I say “Yes, the bathtub is filled.” “Are your clothes on?” “Yes, my clothes are on.” “Are your shoes on?” “Yes, my shoes are on.” She says, “Okay, we’re expecting more tremors. We want you to get into the bathtub with your clothes on right now.” I’m freaked out. You got to be kidding me!

I’m about to head to the bathtub when I hear some laughter in the background and realize I’m on speaker phone. This whole thing is the guys at the office trying to prank me. So, I say, “Oh, you’re calling from the Salomon arb desk, aren’t you?” At first, she said “no,” and then after a long pause … “yes” and then laughter, from her and many others in the background. I went back to the office and they were still laughing, but disappointed I hadn’t drenched my suit and shoes. Anyway, I got to be really friendly with everybody.

It was really interesting to see how different things were culturally and to start to understand, just a little bit, the Japanese perspective on life. But the desk dealt with bonds and futures and swaps, the same instruments I knew, so I could readily understand the financial side of things. The trade that the Tokyo desk loved doing at the time took advantage of the fact that Japanese Government Bond (JGB) futures were really cheap relative to the actual bonds on which they were based, and which were deliverable into the contracts. We could take advantage of this disparity, using Salomon Brothers’ relationships with clients who would lend us 10-year JGBs from their portfolios. The desk went long the 10-year futures contracts and sold short the cheapest-to-deliver bond into the contract.

Victor explains the JGB against futures trade:

A futures contract is a promise to buy or sell a specified thing at a specified price at a specified date in the future. The classic example is a farmer promising to sell, and a baker promising to buy, bushels of wheat. The farmer gives up the chance that the price of wheat could be higher in the future and avoids the risk that the price of wheat could be lower. The baker gives up the chance that the price of wheat could be lower in the future and avoids the risk that the price of wheat could be higher.

In the case of bond futures, “the specified thing” is a little loose. A bond futures contract allows the seller to deliver any one of several bonds. The characteristics of these bonds are similar: they are all obligations of the same issuer, in the case here the Japanese government; and the bonds have maturities in a specific date range. But inevitably, these bonds will have slightly different prices. A seller will therefore deliver the cheapest of eligible bonds to the buyer on the date of sale.

“JGB futures were cheap” means that the futures price was less than price of the bond today (the spot price) minus the cost of borrowing the bond to the expiration of the futures contract. We could borrow the cheapest-to-deliver bond and sell it, and simultaneously enter into a futures contract where we promised to buy an eligible bond. At the futures’ expiration date, we would fulfill our obligation to buy the delivered bond. If the bond delivered to us was the same as the bond we borrowed, we would simply deliver that bond to the lender. If we received a different bond, then we would sell that bond, buy the bond that we were short, and deliver that second bond to the lender. The long-futures-short-cheapest-to-deliver trade could be thought of as being short a deliverability option, which the traders had to assess and value.

This simple explanation masks several complicating factors: interest earned on bond sale proceeds, the cost of borrowing the bond, the cost of posting collateral to the lender, the cost of posting collateral to the futures exchange, and the cost of working capital and regulatory capital to support the trade.

But we hoped that before the futures date the futures price would rise relative to the spot price of the bond we borrowed. If so, we could earn our profit sooner, by unwinding our positions. On the other hand, the futures price could decline relative to the spot price of the bond we borrowed. If so, we’d experience a mark-to-market loss, but hopefully, if held to the expiration date of the futures contract, all would turn out roses.

The Tokyo arb desk was building up this trade and probably had $1 billion on. Its profitability was between a quarter to a half a percent every three months. So, on an annual basis, the trade was making 1%-2% or $10-$20 million on the cheapness of JGB futures. And then they started to short other bonds that weren’t the cheapest to deliver, or in some cases even deliverable at all into the contract, but which were expensive relative to the cheapest-to-deliver bond. These chained trades, as they were referred to, were generating an additional $40-$80 million of profitability a year, but with more risk, too.

Now on the other side of the office, about 30 yards away from the arb desk, were traders doing interest rate and cross-currency swaps. A lot of their business stemmed from Japanese bond investors wanting to diversify from JGBs and Japanese corporate issuers. These investors admired large, well-known, almost iconic, US brands and corporations like IBM and GE, and would buy their bonds if the bonds were yen-denominated. In fact, Japanese investors would accept a lower yield on certain US corporate debt than they would on JGBs.

But these US corporations didn’t have a need to raise funds in yen and didn’t want interest and repayment obligations denominated in yen. Wall Street financial engineering came to the rescue, allowing Japanese investors to get exposure to the US issuers they wanted, and those US issuers to get the cheap funding they wanted. To do this, Salomon’s swap desk entered into cross-currency swaps with these US issuers so they could issue yen-denominated bonds, yet have USD cashflows. At issuance, the US corporate would exchange yen bond proceeds for USD from Salomon. Later, the US corporate would pay USD to Salomon in exchange for the yen required for bond coupons and principal repayment.

Because Japanese investor demand for some US issuers was so strong relative to American investor demand, US issuers could get a great deal by issuing in yen and swapping into dollars. If 10-year JGBs yielded 4%, a US issuer with a good brand name might be able to issue a yen bond at 3.5% and swap into USD at an interest cost of, say, 0.5% less than what the US issuer would have had to pay to issue a USD bond.

When Salomon’s Tokyo swap desk did these trades, it would usually try to find another bank to do an offsetting cross-currency swap. If the desk could find a counterparty willing to pay 3.6% yen, the desk would lock in a 10-basis-point spread over what it was paying the US issuer. And the desk wouldn’t be using Salomon’s balance sheet to make this profit. This was very nice.

But other times, the swap desk would hedge its yen payments by buying JGB futures. The swap desk’s yen obligation to the US issuer was like being short a yen-denominated bond: the swap required periodic yen coupon payments and then a final yen principal payment. What the swap desk did was similar to what the arb desk did when it shorted the cheapest deliverable bond and bought JGB futures. But while the arb desk was shorting a JGB paying, say, 4%, the swap desk was short cashflows that replicated a 3.5% coupon bond. Right off the bat, the transaction with the swap was 50 basis points more profitable than shorting the bond! The swap also saved a borrowing fee to the bond lender, and wouldn’t show up on Salomon’s balance sheet. We figured that, all-in, the swap added another 100 basis points to the profitability of shorting JGBs against JGB futures.

At first glance, it was a very attractive trade, but at the same time swaps were illiquid. There wasn’t an active two-way market in swaps at this time; they traded by appointment. Swaps would be created whenever somebody issued a yen bond and wanted to get back to dollar borrowing. We thought that it was possible for swap rates to decline to 100 basis points below JGBs, from their current level of 50 basis points below. If they did, conditions would perhaps be more attractive for new deals, but the swap desk would have a large mark-to-market loss on its existing book of trades. That loss would show up in Salomon Brothers’ quarterly earnings, which our investors wouldn’t like very much, and which Salomon’s CEO also wouldn’t like!

We thought swap rates were going to rise, not fall, as more and more US corporations issued yen-denominated bonds. We thought Japanese investor appetite for US corporate bonds would eventually be sated and both US corporate bond yields in yen and swaps rates would rise closer to, or even rise above, the JGB rate. If the swap rate rose from 50 basis points below JGBs to the JGB rate, the swap desk could enter into off-setting swaps and lock in a profit. Yet, while we thought that eventually swap rates would rise to the level of JGBs, we recognized that there could be bumps along the way. What if for some reason US corporates became even more attractive to Japanese investors relative to JGBs and swap rates declined relative to JGBs?

A side issue was whether the transactions should remain on the swap desk or be taken over by the arb desk. Sugar’s reasoning to take over the trades was that his desk was already doing this trade against JGBs, and it fit in well with what he was already doing. His team was very close to the JGB market so when futures contracts expired every three months, his team could better handle the roll forward into new contracts. His team had a better risk-taking culture, whereas the swap desk was primarily serving clients. If it’s serving clients, but also keeping high expected profit trades that it’s doing for itself, that might not be very good if clients became aware of it. Although the swaps staying within Salomon, just on a different desk, wouldn’t completely fix the optics.

Eventually, the arrangement was made that the swap desk would still do the trades with clients, but pass the yen position to the arb desk with a 10-basis-point profit. The swap desk was happy because they were making a risk-free profit as long as they could originate these trades.

The big question the Tokyo arb desk faced now was “how much of the swap versus JGB futures and JGBs versus JGB futures trade should we do?” Or, how much of a good thing was the right amount for Salomon Brothers? Yes, the expected profit to the firm was higher if we did $6 billion, rather than $3 billion, but if expected profit was the sole decision metric, why not do $100 billion of it? We needed a way of thinking about the sizing of the trade that wasn't just about maximizing expected profit. We needed a framework that integrated risk into the sizing decision directly. And, of course, we needed to understand the nature and amount of risk involved in the trades.

There was clearly some size that would be too risky, likely well below the maximum level set by the size of the Japanese market and Salomon’s capital base. How should we determine what that was? We could look at the average daily or weekly volatility of the trade, but we knew that was a very poor indicator of the tail risk of the trade. We felt that if the trades reached $10 billion or even $15 billion, Salomon could withstand the roughly $300 million after-tax mark-to-market loss the trade would experience from an adverse move of 50 basis points in the spread between swaps and JGBs. Salomon’s capital base at the time was around $3 billion, so yes, survivable for the firm -- but perhaps not by us in our jobs.

But if the trade could go against us by 50 basis points, why not 100 basis points, causing twice the loss, and a loss that would matter for Salomon’s stability? In retrospect, there’s not a really satisfying answer to that question—if something is mispriced, what stops it from being more mispriced? When it comes to relative value trades, it’s hard to know, because when something is super attractive, it shouldn’t be there, it shouldn’t exist. When something shouldn’t exist, trying to think about its risk is difficult. Once something is already somewhere it shouldn’t be, why can’t it go anywhere else it also shouldn’t be? There’s no bound anymore. Once you’ve recognized that it’s outside its rational boundaries, then anything is possible. It’s very difficult to analyze the risk. Moreover, it’s very difficult to analyze the risk of leveraged trades where potential losses are, in principle, unlimited.

We knew that Credit Suisse and other banks active in Japan were trying to get US companies to issue yen bonds. That made us feel more confident because that issuance should push swap rates higher. But what if for some reason Credit Suisse had to sell its swap positions? Those positions were pretty illiquid, and in the short term at least, “Swap-ageddon” would ensue!

We spent a lot of time thinking about the size of the flows and the capital available to put these trades on if the flows got bigger. We had a lot of information about who was doing what and how much, and we thought we had a pretty good idea of what supply and demand looked like over a range of worsening spreads between swaps and JGBs. But, in the end, there was still a lot of uncertainty in our estimates. In retrospect, there were a number of risk mitigations we could have executed. One of the smartest things we could have done was raise a “Japan fixed income fund” that would have both outside capital and Salomon capital. The fund could have invested in the swap-vs-futures trade, with Salomon taking a slice of the profits, but none of any losses outside capital realized on the trade.

Also, it was pretty clear that the JGB-vs-futures trade was lower risk than the swap-vs-futures trade, and more thought should have gone into determining the right mix of those two trades. Finally, it would have been worth the effort to try to find counterparties willing to insure losses beyond a certain amount on the swap-vs-futures trade, to limit losses to say a 50-basis point widening. It’s at least conceivable that Warren Buffett’s Berkshire Hathaway or Hank Greenberg’s AIG may have been willing to write such insurance, feeling that if they ever had to make good on it, they’d be taking over a very attractive transaction.

As things turned out, the question of maximum size became moot for the Tokyo arb desk, because swap rates steadily rose from 50 basis points below JGBs to pretty close to JGBs over a couple of years, and the desk’s positions never had the opportunity to grow to a size which posed great risk to the firm. I think the swap and JGB versus JGB futures trades in aggregate got up to about $4 billion in notional value and Salomon made $400-$600 million of profit, maybe a little more. The Tokyo arb desk continued to make money on JGBs against JGB futures, but eventually that too quieted down and although it was still an attractive trade, it wasn’t the great trade it used to be.

It’s interesting to think about the risk and return characteristics of leveraged relative-value trades compared to long-only trades, like owning an unleveraged portfolio of fifteen individual equities. With the stock portfolio, it’s difficult to estimate its expected return, but less difficult to forecast its volatility. Sure, a portfolio of equities exhibits a fat-tailed return distribution, but the big outlier events are not as large as the outcomes we have seen with relative-value trades. And of course, a long-only unleveraged portfolio has a well-defined maximum downside—the portfolio goes to zero.

By contrast, with leveraged relative-value trades it’s relatively easy to estimate the expected gain, assuming you don’t get blown out of the trade due to mark-to-market losses, but more difficult to define, and assign a probability to, how bad things might get prior to convergence. That’s the trade-off you have: the more you can tie down the expected return as of some date, the less sure you can be as to value fluctuation over the time it takes to get to that date. Trades like the yen interest rate swap-vs-futures trade are great, but they need more capital than people generally think.

That’s how people can get into trouble with these relative value trades. They’re very attractive over the horizon needed for them to converge (e.g., ten-years for the swap-vs-futures trade), but it’s hard to figure out how much capital you need behind them to hold onto them over their course. The Japanese have an apt saying: “even monkeys fall from trees.”

Anyway, we didn’t fall, this time, and my whole experience in Japan was a highlight of my life. I’ve remained friends with Sugar to this day. He’s one-of-a-kind: warm, intelligent and with a contagious sense of humor. There are enough memorable and entertaining stories from when I was in Japan to fill a book, but this story will have to do for now.

Victor Haghani had a near 20-year career in fixed income arbitrage, becoming a managing director at Salomon Brothers and a founding partner at Long-Term Capital Management. In 2011, he founded Elm Partners, a wealth management firm which manages client portfolios using broadly diversified ETFs in separately managed accounts, with an approach that is rules-based, dynamic, and low-cost.

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