Category / Capital Structure Arbitrage

If it doesn’t work as a hedge fund strategy, try making policy with it March 7, 2014 at 12:24 pm

Capital structure ‘arbitrage’ is largely discredited as a hedge fund strategy for the rather good reason that a lot of people lost a lot of money on it. An arbitrage, remember, is supposed to involve a risk-free profit. But using the Merton model or its variants to ‘arbitrage’ between different parts of the same companies’ capital structure didn’t work very well — or, at least, it worked well until it didn’t. One of the problems (aside from various liquidity premiums embedded in prices) is that the first generation of these models assumed that the value of a firm’s assets follow a random walk with fixed volatility: which they don’t. In fact it has been known for over two decades that the PDs backed out from Merton models are far too high, something that KMV try to fix with some success at the cost of what might kindly be termed ‘pragmatic adjustments’. Now there may well be capital structure arbitrage models which don’t have these first generation problems and don’t involve arbitrary adjustments, but they are not well known (not least because if you had one that worked, you would want to use it to trade rather than to burnish your academic credibility).

There is an exercise by the US Government Accountability Office to determine how much lower big bank borrowing costs are due to expectations of government bailouts. Stefan Nagel suggests on Bloomberg that there is a risk that, by using a simple Merton-type model, the GAO will “underestimate both the banks’ proper borrowing costs and the implicit subsidy they receive from taxpayers”. True, there is. But there is also the risk that they will overestimate it, not least because as we noted above, models like this are flawed, and they tend to overestimate PDs. I absolutely think that taxpayers deserve to know what the implicit subsidy they are providing to big banks is worth – but by the same token, I think they deserve to know the model risk in those estimates. Scaremongering to suggest that the estimate will necessarily be too low is not helpful here.

The Co-op suggests – co-operative interest? May 10, 2013 at 9:00 pm

Listening to the sad news about the Co-op bank today on the radio, it occurred to me to wonder if with-profits banking might work for them. Let me explain.

  • Some banks, the Co-op included, need more equity. Indeed, if Brown-Vitter get their way, all big banks will need a lot more equity.
  • No one wants to buy new equity.
  • And debt holders want interest.
  • An old fashioned insurance solution* to this problem was the ‘with profits’ policy whereby instead of getting a coupon, investors still have a senior claim on return of principal, but interest is paid in equity.
  • So why not offer, or even require, that interest paying bank accounts pay a certain fraction of interest in equity, at least until the bank reaches ‘very well capitalised’ (whatever that means)?
  • You would of course need an easy cheap way for deposit holders to sell these equity stakes, but that’s OK; for sufficiently low levels of leverage, bank equity would have a rather stable price (like a utility stock), and so this should not be beyond the wit of bankers.
  • The dilution for existing shareholders would of course be vicious. Sorry, I can’t see a way around that.

*OK, this isn’t quite what with profits insurance policies do. But it is close enough for these purposes.

Capital is funding January 25, 2012 at 7:07 am

FT alphaville has a nice riff on the whole systemic risk of margin calls thing, discussing in particular the risk of variation margin calls in the ECB’s LTRO. They quote some Nomura research which makes a number of good points, but one dodgy one. The major thrust first:

The cost of the haircuts and existing funding costs on leveraged banks balance sheets means that the cost of funding from the ECB is not 1%.

True. You fund only 71% of the asset (assuming the collateral is a >5y corporate loan, which gets a 29% haircut at the ECB) at the ECB rate. The rest has to be borrowed unsecured*.

The error comes when the discussion turns to capital:

In this case against a €100 asset there would be a €29 haircut and €5 capital charge giving €34 to fund through other sources.

Nope. The capital charge is funding too. If you have a €5 capital charge on a €100 asset, then 5% of it is equity funded and the rest is debt funded. Thus if the ECB haircut is 29%, you get 71% from the ECB and 5% from your equity investors leaving 24% to raise in the unsecured market.

Now, often people keep ROE separate from ‘cost of funds’, as this separate is typically convenient for reporting; but both equity and debt capital are funding. Thus in this separation the ‘cost of funds’ should be the cost of the debt needed to fund the asset, i.e. interest on €95, not on €100.

*The Alphaville article says ‘Unsecured funding is closed (to all but the bestest of the best), ergo the bank scrapes together assets to pledge for cash somewhere, running the gauntlet of the collateral crunch.’ That isn’t quite it as you don’t fund the haircut of a collateralized asset (the 29%) with more collaterized borrowing. You fund it unsecured, because you have to – you have used 100% of the asset you have to raise 79% of its value. All assets need funding, and there aren’t spare ones lying around to use as collateral as – roughly – anything you can use as collateral is being used to fund itself. This just follows from balance sheets, err, balancing.

Bank capital structure in the year of FVAOL November 6, 2011 at 12:52 pm

I am sure you could make a case for pronouncing that ‘fvail’…

Dealbreaker points out a nice trick here. Note that:

  • Basel III is demanding banks increase the amount of equity they have (as opposed to total capital);
  • Some banks, like BofA, have seen large increases in their credit spread;
  • If you buy back your own debt at the market price, you can monetise that fair value gain.
  • So what has BofA done? Buy back subordinated debt and preferreds, and issue both equity and senior debt. It’s cute:

    Note first of all that you profit by “volatility in credit spread movements” by buying back the things with the longest duration: perpetual preferred and trust preferreds, which are trading at double-digit percentage discounts to where they were issued. You replace them with a thing that in some loose theoretical way looks similar from a duration and capital structure perspective: a mix of about half common stock (400mm shares = about $3bn on a good day) and half senior notes. It’s a regulatory capital improvement. And you’ll be paying out less cash going forward, since the senior debt should be cheaper than the preferred and, um, about those common dividends. Sure your common shareholders will be diluted, but not so much on an EPS basis, and they’ll be so thrilled with the juiced earnings this quarter that they won’t be too worried about the dilution.

    Update. I fixed a typo; thanks to Dennis for pointing that out.

ROE, capital, and false conclusions September 30, 2011 at 5:22 pm

This post is an attempt to figure out what ROEs, returns on capital, and capital structure really tells us about the risk of banks. It is partly a response to Martin Wolf’s FT blog post What do the banks’ target returns on equity tell us? but also more generally a comment on the whole banks can have more equity and it won’t cost much meme.

First, we should define some terms. By ROE or return on equity, I mean the return on equity based on the current market price. So if I buy a share for a dollar, and my total return (price appreciation plus dividend yield) in a year is seven cents, I have a 7% ROE.

Return on regulatory capital is slightly different. This is because capital is not the market price of a firm’s equity; rather it is* shareholders funds. This includes money raised from issuing equity, retained earnings, and a few other (typically smaller) items. Thus the return on capital is based on the price of equity at issue, plus whatever earnings have been retained, and a few other bits and bobs. Firms typically cannot issue meaningful amounts of new equity at the current price, as new equity dilutes existing shareholders. It also usually irritates them. Therefore it is usually easier to increase capital by retaining earnings rather than by issueing new stock.

The naive ‘banks can easily have more capital’ crowd typically argue thus:

  • The Miller Modigliani theorem says that capital structure does not matter; if you have more equity, you are safer, hence your debt trades tighter, hence the extra cost of the equity is made up for in having cheaper funding;
  • Remember that more equity makes banks safer?
  • Get more of it.

The problem with this is that the Miller Modigliani theorem is false. Amongst other things, it assumes no taxes; it assumes that investors are risk neutral; and it assumes that risk is perfectly known by all investors. None of these things are true, and thus those who trade capital structure based on MM alone are known as ‘bankrupts’. For me, the biggest issues in MM are the linked ones of no risk premiums and perfectly known risk. Of course if I know the distribution of a firm’s earnings precisely then I can price the stock. It is the very fact that I don’t that makes equity investment difficult: it means that investors demand a variable but high premium for taking equity risk. Because an equity issuer has to pay this extra premium whereas a debt issuer doesn’t (or at least doesn’t have to pay as much of a one, assuming we are not in high yield territory), equity cannot be substituted for debt without cost.

Note that the existence of risk premiums means that you cannot assert that just because a bank’s target ROE is 15%, it is highly risky. Wolf makes this mistake, saying that mid teens ROEs demonstrate that ‘these desired returns must represent the result of extreme risk-taking’. Of course, he may be right, but one cannot conclude that from the evidence available.

What happens if you raise capital requirements above current levels? Clearly a bank has two choices:

  1. Raise more capital; or
  2. Reduce risk (as measured by capital requirements).

The first of these is typically done by retaining earnings, unless the new capital required is large, due to the aforementioned pissing-off-the-stockholders feature of issueing new equity.

It is the second I want to focus on, though. What would we do to reduce risk? Well, clearly, we need to cut those businesses with a low return on regulatory capital. And that, sadly, means commercial lending. Both retail banking (because it has relatively low regulatory capital requirements for the risk) and investment banking (because it, historically at least, has high returns) look better under return on reg cap than commercial banking. So that’s where you cut. And you cut savagely as your whole portfolio generates regulatory capital, so to meaningfully affect it, you have to make a dramatic change to the speed of origination of new business.

This is why I think that meaningful changes to banking regulation are best done in good times, not bad ones. In a boom, a decrease in the supply of credit is probably a good thing. It is certainly less bad than it is in a recession.

Note, by the way, that both increasing capital and reducing risk have the effect of reducing ROE. The first because either there will be more shares for the same earnings or because increasing retained earnings will be reflected in a higher stock price; the second because reducing risk will typically reduce earnings. The effect is not linear and not easily modelled though, especially capital tends to be sticky. For a large bank, raising another hundred million dollars of capital will often not budge the stock price at all, but a couple of billion will move it substantially.

At the end of the day, economics should be about what works. Yes, we want a more stable financial system. But we also want economic growth. Whether increasing bank capital requirements should or should not lead to decreased lending in your model or mine does not ultimately matter. What matters is whether it in fact does, and what the macroeconomic consequences of that are. It would be truly irresponsible to attempt banking reform in the depths of a recession without at least being alert to the possibility of adverse consequences, and moving quickly to address them if they occur.

*For simplicity here I have ignored deductions and a few other wrinkles which mean that common equity tier 1 is not quite the same as shareholder’s funds.

Covering up the capital structure March 10, 2011 at 8:50 am

FT alphaville earlier in the week pointed out the continuation of a trend we discussed earlier, the increase in the use of covered bonds. Indeed, according to UBS, some Spanish banks in particular are close to their limit for issueing covereds. In other words, all the mortgages that can be used to support covereds, have been.

Now the problem with covered bonds is that they reduce the assets available to senior unsecured creditors in the event of default. If you combine higher covered issuance, then, with the (in my view reasonable) Irish burden sharing, whereby senior unsecured creditors will be on the hook to share some of the costs of a bailout, then the picture for bank senior debt is pretty bleak.

The hard part here is managing the balance between moral hazard and pragmatism. A credit spread is a return for risk, so there should actually be risk. And I don’t just mean liquidity risk. Bank bond holders should actually have capital at risk from default or restructuring (or bail in/resolution) losses. But if we dramatically change both the chances of those losses happening and the size of the loss when it does happen, then bank debt gets a lot more expensive. At a time when bank supervisors want banks to issue more long term debt (see, if you must, the Basel 3 liquidity rules), that might not be the best outcome.

Seniority destruction through resolution and covering November 14, 2010 at 6:06 am

The Bond Vigilantes point out that in the new post-Basel III world, bank capital structure may well get a lot simpler:

deposits, covered bonds, senior notes, CoCo’s and equity

The covered bonds will be needed to meet funding requirements, but of course this process removes assets which would otherwise be available to meet senior creditors. As the vigilantes point out, if bank resolution regimes make senior creditors share the pain, then this will have the effect of making bank senior debt a good deal less attractive:

If you imagine a situation (shouldn’t be too hard) where a bank gets into difficulty, its CoCo’s are triggered but still falls into bankruptcy. The equity will be wiped out leaving a senior debt holder not only at the bottom of the pile in a liquidation, but also with a claim over fewer assets than they historically would have had, since most of the mortgages would have been pledged to the covered bond pools.

How much for that Coco in the window? December 24, 2009 at 7:34 am

An interesting observation from Financial Crookery about the Lloyds Cocos:

the 15% ECNs were indicated at 122/123 on minimal volumes, compared to 110/112 for the previous 13% series. Absent the EU-mandated 2 year coupon pass for the 13% security for “burden sharing”, the 13% notes would have been trading around 132/133, so credit markets value the trigger risk at around 10 points higher than the additional 2% coupon. Is this enough? How should the ECNs be valued?

In exchange for protection from regulatory cashflow interference and the coupon hike, investors add a “wander to loss” risk to the pre-existing “jump to default” risk. These two volatile processes are correlated, and can be modelled to value the ECN. It is essentially a 15% bond which knocks-out if either (i) Lloyd’s book value falls around 45% during the 10 years, returning the value of the (correlated but more volatile) stock price at that time or (ii) Lloyds jumps to default in the normal credit way.

I am conscious of the jaundiced reader’s likely view of model-based pricing. Nevertheless my own valuation of the ECN using this framework was in the 115-120 range(1). The cost of the “wander to loss” risk is higher than credit markets are estimating. The current ECN quote is not particularly cheap on this reckoning, particularly as the ECN would usually trade at some discount to theoretical value. In short, I think the stampede to exchange may have been misguided.

The model used could be questioned – in particular using a 2 factor random walk with correlation strikes me as a rather simplistic way of modelling the joint equity/book process, especially for a credit like Lloyds with a lot of different kinds of subordinated debt – but it is still a pretty reasonable start.

The only question remaining is why the market values the Co-Co’s so generously. The answer may be surprisingly straightforward: a hunger for yield, maintenance of current income and resolute belief in the sovereign put.

I suspect the high coupon is also attractive to those playing tax games. High interest income certainly used to be necessary in some tax ‘structuring’ (aka defrauding the ordinary tax payer).

Furthermore, some capital structure arbitrage players, assuming there are any left, would be hedging the note with purchased protection on Lloyds sub debt. That would be a classic short credit gamma long carry position. And we know how well those sometimes work out…

The continuing equity/credit disconnect April 4, 2009 at 8:57 am

I have written several times before about the equity credit disconnect of the last few years and its implication for capital structure arbitrage models. Recently, the disconnect has reappeared, as this chart of the day from Bloomberg illustrates:

Bondholders losing faith

If there are any CSA funds left after the earlier dislocation, this would theoretically be a great time to go short equity long credit. The trouble is we now know that these dislocation can last for considerable periods, and reversion to anything close to the theoretical relationship is not guaranteed. Does this sound the death knell for capital structure models?

The equity credit dislocation June 30, 2008 at 6:41 pm

I have observed before that the equity markets have not yet reacted as fully as the debt markets to the crisis – and increasingly it looks likely that they will fall further rather than that the debt markets will rise to join them. Goldman is of that mind, and has recently observed that downside vol is cheap so now is an excellent time to buy puts. Bloomberg reports that Goldman:

recommended Dow Jones Euro Stoxx 50 Index puts that expire in December and have a strike price of 3,000, or 11 percent less than the measure’s closing level today.

“High inflation/low growth is an increasing downside tail risk …If that risk crystallizes, we think it means material rather than modest downside.”

The Euro Stoxx 50 plunged 24 percent to 3,354.20 in 2008 and closed at the lowest since November 2005 last week. The December 3,000 puts on the index fell 6.7 percent to 83.50 euros today. They cost as much as 189.30 euros in March.

Equity/Credit: Who’s Right? February 21, 2008 at 8:30 am

Naked Capitalism has a thought provoking article on the current disconnection between the equity markets and the credit markets, which in turn refers to FT articles by John Authers and John Dizard. Authers describes the issue:

If you believe the credit market, things have worsened sharply in the past few weeks. With spreads widening significantly, recession is a certainty in the US and Europe.

If you believe the equity market, there are grounds for optimism. Stocks are still above the low they hit in January, before the Federal Reserve made its emergency rate cut – betting that this huge monetary stimulus would ensure that any recession is shallow.


But in the past few weeks, as credit spreads have widened, the shares of those companies the credit market sees as most risky have rallied, and outperformed the rest of the market. Equity investors are making a bet that the credit market has got it wrong.

The credit market may be at levels that cannot be justified by the fundamental outlook for defaults: its investors have difficulty raising liquidity; many need to clean their balance sheets; there are unprecedented worries over various structured credit products, many of which did not exist during the last downturn in the credit cycle; and the problems of the monoline bond insurers create further uncertainty.

One has to sympathise with this last: we are in a situation at the moment where most of many instruments credit spread is compensation for factors other than default, prominent amongst them the cost of financing the position, the possible future volatility of the position, and the liquidity risk of the position.

This leaves some serious issues with equity/credit (aka capital structure arbitrage) models though. The vast majority of these models are based on the assumption that the credit spread is (risk neutral) compensation for the probability of default, and that equity is (some kind of) option on the value of a company struck at the face value of the liabilities. Given these assumptions and a few more besides, a connection between equity prices and credit spreads is established. But if there is a systematic component to credit spreads which varies strongly with time then most of these models are some trouble. And certainly their predictions earlier in the year wouldn’t have ensured career success. As Dizard puts it:

Let’s say you decided at the beginning of the year, with what was left of your limited partners’ capital, to bet that the price of risk in both markets will converge. So, you go short a basket of stocks of investment grade companies, and simultaneously buy the CDX.IG, the index of investment grade credits. However, since, historically, stocks in the form of the S&P 500 are seven times as volatile as the CDX.IG, you levered up the CDX at the multiple required to have a hedged position. Unfortunately for you, in the first week of February, the CDX moved (down) one fourth, not one seventh, as much as equity, as dealers stopped providing liquidity. So your position just died and went to money heaven.

Leaving aside Dizard’s hedge ratio calculation – which is far too naive – he is basically right. And remember you need models like these for a range of wacky convertibles, too, so this is not just a matter of interest to the CSA funds. If nothing else this little market episode will result in some improvements to equity/credit models.

Update. There is further comment from the FT, based on a report by Goldman, here. Some of the examples given here are fascinating:

In the first three weeks of February, the shares of Swedish truckmaker Scania rose 11 per cent. But the spread on its credit default swaps (CDSs) rose 60 per cent… Over the period, spreads on the 155 names in the iTraxx main index of European investment-grade companies widened 55 per cent on average. The figure for 103 names not on the index – including, for instance, Scania – was 41 per cent.

I am not brave enough to opine for certain which market is right. But it is clear that one of them is wrong. And if it is the equity market, there is a lot more pain to come.

The cost of capital December 11, 2007 at 8:17 pm

There will be a fair amount written about the UBS writedown, so I’ll stick with the other part of the story, the mandatory CB it is issuing. This will pay a 9% coupon. Citi on the other hand, is paying 11% on the mandatory issued to plugs its capital hole. Assuming (which is a big leap) that both of them went for par, how do we explain this difference?

Update.To plug its capital hole, WaMu is issueing a perpetual pref convertible into common stock. This is still being priced, but the word is that it will pay a coupon of between 7.5 and 8%. It would be really interesting to get the details of all 3 of these instruments, their levels of subordination, conversion features and so on and put them in a capital structure model. WaMu’s is optional conversion rather than mandatory so it is not immediately obvious how it compares with the Citi and UBS offerings.

Meanwhile Morgan Stanley is paying 9% on its mandatory CB, issued to plug a $5B capital hole after taking a further $5.7B writedown.

Who is getting hurt in equity/credit? July 29, 2007 at 12:57 pm

There are, if not falling cubes, then certainly some falling knives out there. Indeed the current market gyrations seem to suggest a dislocation between the equity and credit markets as well as a weakening of sentiment. As the often amusing Naked Capitalism puts it:

[…] fixed income types speak of truly grim conditions, of the markets for riskier credits having shut down completely, and concerns that the market seize-up could extend its reach to better quality credits. By contrast, many of the equity market participants sounded relatively sanguine, believing that the credit markets are working through a repricing of risk, but that earning yields are sufficiently high so as to be able to withstand an increase in yields.

Meanwhile according to the FT:

Fear now rules the credit markets, where the effective cost of ensuring against a default, in both Europe and the US, has increased by more than half in barely a month. A steady drip of bad news has prompted fears that the subprime debacle could trigger a credit crunch, raising the cost of financing worldwide as investors are forced to sell healthy investments to make good their losses.

Most recently, the equity markets have shown only modest falls, but credit rationing is in full swing, and spreads have moved out markedly, to the extent that they are visible, from the ridiculously tight levels of the first half of the year.

Now this would all be merely interesting, were it not for capital structure arbitrage. CSA posits a relationship between the equity and credit markets, and CSA funds use models based on this relationship to put on equity vs. credit positions. The first generation of these models were based on Merton’s work or elaborations of it. What I would really like to know is how models like these, calibrated to the conditions earlier in the year, are performing at the moment. To end with the FT again:

…we may well be in the middle of a regime shift

In fact it could even be that the new regime was the last four years or so, and what we are seeing now is a return to more ‘normal’ conditions, albeit one that is proceeding in jumps.