Violating the ‘Law of One Price’ in the Financial Crisis

Bonds

mic Listen to the podcast:

Wharton finance professors David Musto and Krista Schwarz explain why there was an unusually big price gap between Treasury bonds and notes during the financial crisis.

During the financial crisis, a strange thing occurred: The price of 30-year, off-the-run Treasury bonds were extremely discounted compared to Treasury securities originally issued with shorter maturities, but now had the same cash flows and remaining duration. In normal times, two securities with the same expected payments would typically command the same price. But in the crisis, the bonds became way too cheap. What caused this big price differential? And what lessons does it hold for capital markets in the future?

That is the focus of the research paper, “Notes on Bonds: Illiquidity Feedback During the Financial Crisis,” by Wharton finance professors David Musto and Krista Schwarz, along with Greg Nini of Drexel University. Musto and Schwarz recently spoke to Knowledge@Wharton about their research and its implications to the capital markets, regulators and financial industry players. (Listen to the podcast at the top of the page.)

An edited transcript of the conversation follows.

Knowledge@Wharton: This year is the 10th anniversary of the peak of the financial crisis. So it seems fitting to talk about the related research you’ve done. In your paper you note that the crisis moved many pricing relationships far out of line. And it’s generally understood to be due to liquidity issues. But your research dug deeper into the relationship between liquidity and asset prices during the crisis. Can you tell us more about your study?

David Musto: This study grew out of the course that Krista and I both teach, called Capital Markets. We cover various aspects of the capital markets including the bond market and the basic arbitrage relationships between bond prices. By arbitrage relationships what I mean is price relationships that should be just so, or else people can engage in arbitrage when they get out of line.

In this class there’s an example that I have given over the years, of prices that have to be exactly in line with each other in a particular way. And you’d show them to illustrate what people in finance call the “law of one price.” You have two different ways of buying the same future cash flows. They should command the same price. When the financial crisis hit … they simply were not in line. In fact, they were way out of line.… We thought, ‘that is really peculiar. Let’s pursue that. Let’s see if we can nail down what’s going on here.’

Krista Schwarz: Often, the assumption is that you have a frictionless, perfectly efficient market. A reason we found this [research topic] particularly interesting was that the Treasury market, which is the market in which there was this pricing deviation, where this relative price divergence occurred, is a market that is known for being among the most liquid and the least subject to price deviations or frictions.

To see a very large relative price difference in this market — where you have securities that can perfectly replicate the cash flows of other securities in the same market and all have the same credit risk — this is just a very clear violation of what economists refer to as the “law of one price” whereby two portfolios that have the same guaranteed, or certain cash flows, should be priced identically. And what we found was that these two portfolios were priced more than $5 per $100 par value differently.

“This is just a very clear violation of what economists refer to as the ‘law of one price.'”–Krista Schwarz

Knowledge@Wharton: What Treasury securities did you look at specifically? And how did you go about collecting that data?

Musto: The distinction that we found was between securities that were issued with 30 years to maturity, issued back in the 1980s, and securities issued 20 years later that had 10 years to maturity when they were issued (30-year bonds and 10-year notes). So they were issued 20 years later with 20 fewer years to maturity. In fact they had the same maturity date. That’s what allowed us to line them up exactly. And there’s a little more twist to it, but basically that’s what allowed us to line these things up exactly.

What we found was those that were issued way back in the 1980s were the ones that were really cheap. And consistently, if you look from one bond to the next it really didn’t matter which one you looked at, each of them during the crazy crisis times, was really cheap — 5% below its exact match that you created out of the securities that were issued 20 years later. So you have a connection there. The old ones were cheap, even though they had the same length of time to maturity. And that’s what started us thinking about what could be different [since] they looked exactly the same.

Well, one big difference that immediately came up was the question of liquidity. When you look at those 30-year bonds … initially they’d be purchased by investors who trade a lot. But over the years, they’re going to percolate into the long-term portfolios of, let’s say, insurance companies, pension funds that just hold onto these things. They just bury them deep in there and they’re just held there until they mature. And so the security kind of goes to sleep and there’s not much trading, even though it’s, as I say, exactly the same as this other security that’s issued much later and hasn’t had that happen to it yet.

Knowledge@Wharton: Were you surprised by the findings?

Schwarz: The very fact that this anomaly was there and was present in the Treasury market and was so large [was surprising]. I should emphasize that the price differential did not occur overnight and then the next day it came back; this is something that lasted for months.

In normal times, you would have arbitrageurs buying the relatively cheap securities, selling the relatively expensive security. The way that we were combining these securities … actually perfectly matched the cash flows. We used these other securities in the Treasury market called STRIPS whereby we could really have these perfectly replicating portfolios. In normal times, an arbitrager would buy the cheap thing, sell the expensive thing and that would cause these pricing relationships to come back in line with one another. And the fact that that didn’t happen for such a long period of time, I think that was perhaps one of the most surprising things.

Market liquidity can be interpreted in lots of different ways. And I think that was what was underlying a lot of what occurred in the 2007 to 2010 period. But exactly what the mechanism was through which that manifested itself in these price differences, that was what intrigued us [enough] to really pick it apart.

“When the financial crisis hit, … [prices of assets with the same future cash flows] were way out of line.”–David Musto

Musto: One thing we looked at immediately was … the repo market. What I mean by repo is repurchase agreements. Repurchase agreements are fundamental to trading in the bond market. If you want to buy something, you finance your purchase by borrowing in the repo market. If you want to short sell something, which you’re going to do in an arbitrage like this, you’re going to short sell the expensive thing and buy the cheap thing. To short sell you use the repo market actually in the other direction. You’re not borrowing cash, you’re actually borrowing the security. When people see an arbitrage like this they might think that it looks profitable. Once you try to do those repos you will see the repos are so expensive that there goes your profit.

We actually went and got data from the repo market so that we could look directly. Let’s see, how expensive was it to put on this trade? Is it in fact wiping out profitability? And the answer was no. I guess that was sort of a surprise. We’re kind of used to the idea that once you actually dig down and look at actually putting on the trade you see that there’s this friction that turns out to wipe out the whole thing. No, it was a bit of a friction, but not the order of magnitude of the mispricing. So you weren’t going to explain it by saying it looks like a juicy trade but you couldn’t have actually done it. You could have done it.

Knowledge@Wharton: Can you get into the causes of the mispricing in more detail?

Musto: The contrast between the cheap thing and the expensive thing, it would almost have to be [caused by the level of] liquidity. By elimination, there’s nothing else. So then the question is, who is trading in a way that is essentially creating this big premium price for more liquid securities at this time?

Schwarz: What we were looking for was the characteristic that identified the type of investor that would be more likely to buy the relatively expensive security as it got more expensive, and/or sell the relatively cheap one. Because clearly that’s the type of activity that would have to be occurring in order for this anomaly, for the price differential, to widen further for so long and then to persist afterward.

We found a set of data that showed all Treasury transactions that were signed and we could see security-specific, whether they were purchases or sales and in what quantities. We examined that to discover whether there were certain characteristics of investors either on the side of the trade that were ‘arbitraging it’ or on the other side of the trade, arguably worsening it.

The data set that we had was actually quite a large data set. It’s for all U.S. registered insurers. It shows all of their transactions over our sample period. We found that the types of insurers that tended to exploit this price differential more, and perhaps profiting from it, were those that actually were well-capitalized, those that were not as highly levered, and importantly, those who were able to hold onto a position for a long period of time or have a long investment horizon.

We’re looking at a mispricing in the fixed income market. In the Treasury market you sort of assume that the cash flows are guaranteed because the government is not going to default. They’re going to pay their debts. And so you could think, this might be an arbitrage if I can hold it until maturity for the next X number of years until the securities pay back their cash flows. But it might not be if I have to unwind it in the next year or two. And so there is that risk.

“The types of insurers that tended to exploit this price differential more … were those that actually were well-capitalized.” –Krista Schwarz

Our findings were very consistent with the idea that the investors who would be more likely to hold on for a long period of time and see this thing through to maturity and be guaranteed that relative price differential that they had locked in when they bought cheap and sold at an expensive price, those are the ones actually doing it. The ones on the other side of the trade were those who were … more highly subject to liquidity redemptions — insurers that tended to be annuity focused and those that were more highly levered.

Indeed, the first title of the paper was ‘Liquidity at All Costs in the Great Recession,’ or something along those lines. I kind of liked that intuition because let’s say you are in a position as an insurer where you need to get liquidity or you need to raise cash immediately. You’re willing to sell your security at any cost to do that, or you’re willing to buy a security that’s particularly liquid at any price. You’re willing to pay any premium because you want to hold a security that if you need to you can turn that thing around quickly.

Musto: This leads to why we have the title we have now. The way I look at this is, you have two securities, they’re actually the same in some sense, but now the people who want liquidity more are buying security A. People who need liquidity less are buying security B. And then security B becomes less liquid as a result. And because it’s less liquid you now have a bigger contrast in their liquidity and that exacerbates the fact, this tendency for the people who want liquidity to buy security A and those who don’t want it to buy security B. So then it’s a feedback loop.

That’s why we used the word feedback in the title — this feedback loop that’s making the liquid one more and more liquid, the less liquid one, less and less liquid. The contrast is growing. And this hunger for liquidity is among certain insurers in the case we’re looking at — but it’s not just insurers. Insurers just happen to be the [group whose] data we could get and they’re a good example. But there’s all sorts of other Treasury traders who had an appetite for liquidity. So it gets exacerbated in the crisis, this feedback loop worsens and then you get this huge contrast.

You have a huge contrast in liquidity and that’s going to affect the price. On top of that you have this huge price being paid for liquidity. That difference in liquidity is going to command a big price. Now you find yourself all the way up to this 6% difference. Maybe six doesn’t sound so big, but in the Treasury market that’s just enormous. I don’t even know if there’s a precedent for that.

Knowledge@Wharton: Has this price gap normalized since the financial crisis? Or are we operating in the new normal?

Schwarz: I recently put together an updated measure of the pricing error that we study in our paper. And while there is still some very small price differential, … it’s really largely come back. That said, the price differential had persisted through 2012 at the very least, to quite a noticeable extent.

I was surprised … that it had come together as much as it had because since the crisis, I have increasingly heard dealers and market participants discussing and bemoaning the reduction in liquidity in the Treasury market in light of a lot of the post-crisis regulation that had been introduced. Part of that is regulation that affects the Treasury cash market directly, and part of it is regulation that affects it through the repo market. And so if you have a funding market being, perhaps, held back from operating the way it would normally, then the securities that are used as collateral in that funding market are affected as well.

“You have a huge contrast in liquidity and that’s going to affect the price.”–David Musto

… We start out with this theory that says a long-horizon investor is willing to buy a security that has a higher liquidity discount because they’re amortizing that over a longer holding horizon, over a long number of years, which a short-horizon investor is not willing to do. We see that it’s not just that initial willingness to buy or sell the security that matters, but the very fact that you have the investor holding onto it for a period of time takes it out of commission and makes it more difficult for a counter-party who is looking for it to find that security. And you see that manifest itself in the position of the market maker who is going to quote you a price to buy or sell this security. They’re looking at how risky is it that I might be able to put my hands on that security or not? And that’s what the price I quote you is going to depend on.

Musto: Let me give the listeners one thing to Google, … which is the phrase supplemental liquidity ratio. That’s a very obscure inside baseball, bank regulatory term. But in fact it’s what everyone is talking about in the big money center banks. Basically, this is a capital test that the big banks have to satisfy now which is not risk weighted. That means that activities such as building a big Treasury repo book that used to not require that much capital, now do. And because they do that, it has made various market participants less interested in carrying a big repo book. That’s giving you what Krista was talking about.

Knowledge@Wharton: What would be some practical implications of your research to folks like the Fed, institutional investors, traders, and market makers?

Schwarz: One very practical implication is that market liquidity alone can have a large effect on prices. From a policy perspective, if you can identify that that’s what’s going on at the moment, there are activities that policy makers can take to improve market conditions specifically for the securities that are suffering. That was something that the Federal Reserve did in the crisis by lending out certain securities that were particularly pinched and particularly in demand.

The other practical implications are that by taking some kind of action or by cutting through that feedback loop, it’s possible to perhaps shift to not-so-bad an equilibrium. If you have disruptions occurring due to market liquidity, this can cause other disruptions that are more fundamental in nature, which might turn some firms insolvent if that persists for a long period of time or if it becomes large enough.

If you can somehow prevent the liquidity situation from becoming as severe, then that may lessen the likelihood of those other extreme events … from occurring.… David mentioned the supplementary leverage ratio, and there are several other ratios from Basel and the Dodd Frank Act that have made financial intermediation more difficult and more expensive for banks and dealers. It’s good to just recognize what the relative pricing implications, what the liquidity effects, could be.

There is some recent research that shows that market liquidity is correlated with funding liquidity in times of stress. This is something that may indicate that today … the Treasury market isn’t suffering so much, but perhaps it’s in a more fragile state whereby if we were in a bit of a downturn things might move adversely more quickly. Perhaps we’re in a more fragile state of the world with the Treasury market.

Citing Knowledge@Wharton

Close


For Personal use:

Please use the following citations to quote for personal use:

MLA

"Violating the ‘Law of One Price’ in the Financial Crisis." Knowledge@Wharton. The Wharton School, University of Pennsylvania, 23 August, 2018. Web. 20 November, 2018 <http://knowledge.wharton.upenn.edu/article/david-musto-krista-schwarz-liquidity-asset-prices-financial-crisis/>

APA

Violating the ‘Law of One Price’ in the Financial Crisis. Knowledge@Wharton (2018, August 23). Retrieved from http://knowledge.wharton.upenn.edu/article/david-musto-krista-schwarz-liquidity-asset-prices-financial-crisis/

Chicago

"Violating the ‘Law of One Price’ in the Financial Crisis" Knowledge@Wharton, August 23, 2018,
accessed November 20, 2018. http://knowledge.wharton.upenn.edu/article/david-musto-krista-schwarz-liquidity-asset-prices-financial-crisis/


For Educational/Business use:

Please contact us for repurposing articles, podcasts, or videos using our content licensing contact form.