**Capital Structure Arbitrage Definition**

Capital structure arbitrage refers to a strategy used by companies where they take advantage of the existing market mispricing across all securities to make profits. In this strategy, there is buying undervalued securities and selling of the same company’s overvalued securities. The main objective is to make use of the pricing inefficiency to make a profit when a company issues its capital structure. There is anticipation that the pricing difference, will at some point cancel out.

**A Little More on What Capital Structure Arbitrage**

In most cases, opportunities for mispricing exists between debt-linked and equity-linked securities. Mispricing is usually short-term and happens because both the equity and the debt markets have different market structures and participants. The two create different price discovery speeds as well as processes.

**How it Works (Example)**

For instance, if a company surprisingly reports disappointing earnings in the stock market, there will be an immediate drop in the company’s stock at 10 percent. However, when it comes to the company’s bond price, similar information will not be reflected immediately.

It takes a few days for the bond’s price to go down, mostly at 2 percent. What does this mean for a company? It is possible for a company that takes advantage of the market dynamics and mispricings to make immediate profits.

**Volatility vs. Debt Price & Equity Securities**

Fund managers have the responsibility of comparing prices and determining value. Where a manager identifies more value compared to the reflected price, it becomes a valuable opportunity to increase the company’s profits.

In most cases, the managers will look at the difference in valuation between a company’s equity and debt securities. However, to be able to understand the two financial liabilities’ relationship, they have to incorporate what we call volatility.

Under Volatility, there is a division of the company’s assets value between its equity and debt securities. Where a company has no net debt, the company’s equity price will equal its assets’ value.

However, if the capital structure happens to have net debt, equity will automatically become a call option on the assets of the company. The call option’s price will then equal that of the debt’s face value. Similarly, the behavior in prices reflects that of assets’ value less than the call option’s value.

Here is the formula;

Debt + Equity = Assets

(Assets – Call) + Call = Assets

Generally, volatility is an essential ingredient when it comes to the value of both equity and debt securities a corporation issue. Volatility increases with an increase in option prices. In other words, the equity value increases only if the volatility of returns on company assets increases, holding other things equal.

Note that a change in volatility does not change the asset’s value. So, asset and equity value risk happen to be the same if a company is fully financed with equity.If for example, a bank buys debt obligations, the financing of this debt obligation will be done using a bank capital and bank borrowing.

Generally, the amount held against a loan by a bank is what we call equity risk. For every capital a bank uses to finance a loan, it must earn a hurdle rate to come up with a loan that reflects the credit risk. Since there is a high equity risk with loans below investment grade, the level of equity a lender uses to finance the loan must be high.

**How to Create Synthetic Credit Risky Debt**

To hedge and replicate risks, we can use derivatives contracts. The same applies when hedging credit risks. To replicate credit risky debt’s performance, most managers would use Credit Default Swaps (CDS). Those who are not able to transact CDS contracts can use a combination of securities in cash listed derivatives markets as an alternative. The combination may include the following:

- US treasury bonds
- Company issued stock
- The company issued stock and listed options

The above are combined reflect the company debt obligations’ performance. The following relationship is important to be able to achieve this.

Debt = Cash + Put or Debt = Asset – Call

Note that you cannot buy company assets or options on such assets. However, you can use the Company’s equity as a proxy on the equity. Generally, lenders always expect a certain level of recovery in case of a default. For this reason, the recovery act can be a put option because it acts as a floor to the credit risk debt’s value. Therefore, the replication of a credit risky debt performance can be through:

- Purchasing equity
- Selling a call
- Buying a put

Here is the formula;

Debt = Cash + Put or Debt = Asset – Call

In theory, the capital structure arbitrage trade is less risky compared to one long security. A number of capital structure arbitrage strategies require leverage for a company to be able to achieve its target. For this reason, a trade which goes against this can be overwhelming.

**References for Capital Structure Arbitrage**

http://www.businessdictionary.com/definition/capital-structure-arbitrage.html

http://www.mkllp.com/insights-news/capital-structure-arbitrage-making-sense-of-the-pieces

https://www.investopedia.com/university/guide-pairs…/arbitrage-and-pairs-trading.asp

**Academic Research for Capital Structure Arbitrage**

How profitable is **capital structure arbitrage**?, **Yu, F. (2006). ***Financial Analysts Journal***, ***62***(5), 47-62. **This paper examines the return and risk of capital structure arbitrage that exploits mispricing in an equity price and credit default swap of a company. The author uses the model of CreditGrades Benchmark which is a trading strategy of convergence type. At the individual trades level, losses may be faced because of the low correlation between the equity price and the CDS spread. The bank proprietary trading and hedge funds, in current years, are a great reason for increasing the capital structure arbitrage or debt-equity trading. The author suggests consistency of the returns with statistical arbitrage, a long-horizon profitability notion which does not depend on any asset pricing theory.

And now for **capital structure arbitrage**, **Currie, A., & Morris, J. (2002). ***Euromoney, December***, ***38***, 43. **Banks have been crushed by the markets this year, however, some have made a profit by arbitraging debt against capital. This is, no doubt, a smart trick. Even smarter will be to turn it to a sustainable business. The United States benchmark ten-year bonds of consumer finance company hit 800 bp over. They were launched at a spread of one hundred and fifty-five basis points last year on United States Treasuries. Default swap prices were wider at even 900 bp over. In many investment banks, as the traders say, capital structure arbitrage is gaining ground rapidly as the coming big trading technique.

The determinants of **capital structure **choice, **Titman, S., & Wessels, R. (1988). ***The Journal of finance***, ***43***(1), 1-19. **This article evaluates the explanatory power of recent optimal capital structure models. The paper extends statistical work on capital structure model in 3 ways. 1st, it investigates a broader set of relevant theories, out of which no one has yet analyzed many empirically. 2nd, as the theories imply empirically different with respect to different debt instruments, the authors make an analysis of a measure of convertible, long-term and short-term debt instead of an aggregate measure of the whole debt. 3rd, this paper applies a factor-analytic method which reduces the measurement issues faced while using proxy variables.

Dynamic **capital structure **choice: Theory and tests, **Fischer, E. O., Heinkel, R., & Zechner, J. (1989). ***The Journal of Finance***, ***44***(1), 19-40. **This research presents an approach of the choice of dynamic capital structure with the recapitalization costs. The model discusses the optimal policy of dynamic recapitalization as a function of company-specific features. The findings are that even minor recapitalization costs cause wide swings in the ratio of a firm’s debt over time. Instead of static leverage measures, the authors use a firm’s debt ratio limit as a statistical measure of capital structure relevance. The results of statistical tests relating companies’ debt ratio range to company-specific characteristics strongly favour the theoretical model of choice of relevant capital structure in a dynamic framework.

**Capital structure arbitrage**: model choice and volatility calibration, **Bajlum, C., & Larsen, P. T. (2008). **With the help of credit default swap information, this article addresses two problems, faced by the arbitrageurs, i.e. positions on the basis of mismeasured inputs and model misspecification. Despite the assumptions differences governing calibration and default, the authors find an accurate structure model associating the markets with timely major inputs. The findings are that the gains are highest in the speculative-grade segment and we cannot elaborate them from the factors of systematic market risk. Though the model may look appealing at an aggregate level, there can be high risk in the positions on single obligors.

Optimal **capital structure**, endogenous bankruptcy, and the term **structure **of credit spreads, **Leland, H. E., & Toft, K. B. (1996) . ***The Journal of Finance***, ***51***(3), 987-1019.** This paper evaluates the optimal capital structure of a company which can select both the maturity and amount of its debt. The authors determine the bankruptcy endogenously instead of the cash flow constraint or imposing a condition of positive net worth. This approach predicts credit spreads, leverage, write-downs and default rates that closely match with historical averages. While the exploitation of tax benefits is not with short term debt as compared to long term debt, it tends to provide incentive compatibility in equity holders and debt holders.

On the pricing of corporate debt: The risk **structure **of interest rates, **Merton, R. C. (1974). ***The Journal of finance***, ***29***(2), 449-470. **This paper explains and extends the BSM (Black-Scholes Model. The same fundamental approach can be implemented in presenting a pricing mechanism for corporate liabilities generally. The author develops the fundamental equation for the financial instrument pricing with Black-Scholes lines. The author applies this model to the corporate debt in its simplest form. He proposes a discount bond in which there are no coupon payments to make. He presents a formula for estimating the risk structure of rates of interest and uses comparative static’s to design graphs of the risk structure. Finally, he extends the MM theorem (Miller & Modigliani) to include callable bonds and coupon.

Agency costs, risk management, and **capital structure**, **Leland, H. E. (1998). ***The Journal of Finance***, ***53***(4), 1213-1243.**This paper examines the joint determination of investment risk and capital structure (of optimal, reflecting the tax benefits of agency costs incurring on asset substitution and the debtless default costs). The agency costs limit the debt maturity, leverage and raise yield spreads, but their significance is small for the environments range taken into consideration. The author also examines risk management. Hedging allows for higher leverage. Even if a firm is not able to pre-commit for hedging, it still does so. Hedging benefits are mostly greater in case of low agency costs.

The fragile **capital structure **of hedge funds and the limits to **arbitrage**, **Liu, X., & Mello, A. S. (2011). ***Journal of Financial Economics***, ***102***(3), 491-506.** When investors, in a financial crisis, need accurate prices and liquidity, their arbitrage positions are cut by hedge funds and cash hoarding starts. This paper argues that the fragile capital structure of hedge funds along with low market liquidity develops a coordination risk in redemptions among their investors which extremely limits arbitrage capabilities of hedge funds. The authors propose a hedge funds model for optimal allocation of assets when the coordination risk is present among investors. The findings are that the managers of hedge funds conservatively behave, even avoiding market participation when coordination risk factors in their investment decisions. Finally, the model suggests a new limits source to arbitrage.

The insignificance of bankruptcy costs to the theory of optimal **capital structure**, **Haugen, R. A., & Senbet, L. W. (1978). ***The Journal of Finance***, ***33***(2), 383-393. **Twenty years ago, MM (Miller and Modigliani) showed that the capital structures are irrelevant to the firm value in the tax less world. Later, they provided evidence that debt financing raises the firm value by what amounts effectively to a state subsidy. Many researchers have followed the MM results in less restrictive conditions. Particularly, MM research is intact even when there is a positive costless bankruptcy probability. Stieglitz has provided more general evidence. He puts forward a costless financial intermediary who has right to reconstitute the firm that changes its debt-equity ratio. The author states that in the optimal capital structure theory, the bankruptcy costs are unimportant.

A theory of **capital structure **relevance under imperfect information, **Heinkel, R. (1982). ***The journal of finance***, ***37***(5), 1141-1150. **Companies raise equity capital and debt for financing a positive net current value project in the capital markets of perfect competition. Their insiders know the function creating the random cash flow of the firm but potential capital suppliers have no idea. Considering the insiders’ incentives to misrepresent their company type, the capital suppliers try to make financing mixes of equity and debt which remove the insiders’ adverse incentives and price securities correctly. The author develops important conditions for a costless equilibrium to show that the debt amount, the firm uses, has monotonic relation to the unobservable true value.