1. Affine Term Structure Models and Short-Selling: A Liberal Case against Prohibitions* Vicente Jakas (Deutsche Bank AG)** * This presentation is an integral part of Chapter 35 in Greg N. Gregoriou, Handbook of Short Selling © 2012, Elsevier Inc. A list of the literature used in this presentation is provided in the book at the end of the chapter. ** This chapter expresses solely the authors opinion and not that of Deutsche Bank AG or DB Research.

2. Reading Questions Why is Macroeconomic Risk Management Important? What are Affine Term Structure Models? How can Macroeconomic Risks Affect Government Surpluses? What is the Fiscal Theory of the Price Level? What is Sovereign Debt Roll-Over Risk? What is Multiple Equilibria? What is naked-short selling? What does market-making activities mean? Why are Prohibitions Distortionary and Ineffective?

3. Introductory Remarks Motivation is mainly due to recent developments on Southern European sovereigns and the resulting Merkel Prohibition on naked short-selling on certain stocks and EU-Members securities. Speculative attacks can only be controlled by addressing the underlying macroeconomic risks in advance.

4. Macroeconomic risk refers to the uncertainty an economy has as a result of unfavorable shocks stemming from macroeconomic variables Example I: Consumption Based Asset Pricing Models: The macroeconomic risk is the aggregate consumption growth. Example II: Vasicek or Cox-Ingersoll-Ross Models: The macroeconomic risk is the overnight rate or the target rate or the interbank borrowing rates. 4 Macroeconomic Risks

5. Objectives of Macroeconomic Risk Management Ensure Government securities continue to provide a hedge for investors when aggregate consumption growth declines Ensure that Governments are able to continue to have enough financial resources to undertake counter-cyclical policies without increasing their deficits A countrys inherent macroeconomic risks affect the yield curve, thus the cost of debt refinancing, because it affects its future expected surpluses 5

6. Affine Term Structure Models Affine Term Structure Models are models that explain changes in asset values as a consequence of shocks or innovation on macroeconomic variables. Affine term structure models assume that the investors act within a competitive environment and that there are no arbitrage possibilities. A representative investor will try to anticipate changes in government bond yields and this will be done by observing interdependencies across macroeconomic variables 6

7. Structural Model 7 for x t being the state space vector with macroeconomic data comprising for example unemployment, consumer confidence index, production price index and monetary aggregate (possibly M3). y t (N) is a N × 1 column vector of observed yields, A(N) is a N × 1 vector of constants, B(N) is a N × N matrix of parameters betas. The assumption is that the disturbance term of ε t (N) is independently and normally distributed with zero mean and constant variance. The model is simple: the greater the B(N) term, the greater the risk.

8. Fiscal Theory of the Price Level (1/2) The fiscal theory of the price level says that the price level is determined by the ratio of nominal debt to the present value of real primary surpluses: 8 For B denote a zero coupon bond outstanding at the end of the period that matures in N. Y is y t (N), for y t (N) is affine as derived from previous slide. π t denote the price level and s t the real primary surplus

9. Fiscal Theory of the Price Level (2/2) 9 Making the previous identity more formal and accounting for an infinite number of periods results in: For B t (N) denote a zero coupon bond outstanding at the end of period t-1 that matures in N. β (N) is the discount factor and β (N) = 1/(1+y t (N) ), for y t (N) is affine as derived from previous slide. π t denote the price level and s t the real primary surplus, and the real primary surplus is also affine:

10. Sovereign Debt Roll-Over Risk 10 Debt roll-over risk refers to the risk of governments being unable to issue new debt to repay the old maturing one without being forced to increase interests or coupons on the new one. In the process of issuing new debt governments face time inconsistencies. In an ideal scenario, governments would not need to increase total debt outstanding and the roll of new debt would only be used to pay back the old maturing one. Governments issue debt to fund budget deficits in order to compensate for the fall in private consumption in times of low aggregate consumption growth. In the process of issuing long term debt they avoid increasing distortionary taxation. Governments can trade current inflation for future inflation when issuing long term debt. In order to issue new debt the government requires to convince investors that current deficit is only temporary and that futures surpluses are expected in order to ensure debt repayment. In times of economic distress, the above conditions are less lax and governments are less credible

11. Multiple Equilibria 11 We have seen how yields and government surpluses are affine and in absence of arbitrage a representative investor will invest in government securities in order to hedge for times of low consumption growth This is because government securities are seen as risk-free assets and thus exhibit higher pay-offs in times of low consumption growth when marginal aggregate utility is high. This is only possible as long as the investor continues to believe that the government security is a risk-free asset. And this will happen only if the price level remains unchanged, thus recalling that the price level is determined by the ratio of nominal debt to the present value of real primary surpluses. However, if the investor believes that the government might have difficulties in rolling debt over as a consequence of a deterioration on markets perception on its future surpluses, the investor will consider the asset to be risky. If governments fail to address the macroeconomic risks affecting their surpluses, it will result in reverting its issuance from risk-free to risky.

12. Multiple Equilibria: The good equilibrium 12 A Government bond yield which is considered risk-free will exhibit a negative relationship to an increase in unemployment. Thus, will exhibit negative B(N) term or beta unemployment coefficient. This is because in times of low consumption growth these assets are dearer, as they perform better than risky assets. Defining two possible equilibriums: the good and the bad equilibrium In a good equilibrium the below relationship must hold: If the above holds, the covariance between the bond yield and expected consumption growth is positively related. Thus negatively related to an increase in unemployment, as an increase unemployment would result in a fall in expected future consumption growth and thus a decrease in government yields.

13. Multiple Equilibria: The bad equilibrium 13 However, a Government bond yield which is considered risk-free will become risky if the previous relationship does not hold hence, if the relationship becomes If the probability of becoming a bad equilibrium increases, the covariance between the bond yield and expected consumption growth become negatively related. Thus positively relation to an increase in unemployment, as an increase unemployment would result in a fall in expected future consumption growth and thus a increase in yields from risky assets.

14. Prohibitions on Short-Selling I Naked short-selling refers to investors borrowing assets from a lender and selling ti to another market participant with the expectation that the price of the asset will fall. In the process of doing so the investor will make a profit. Market-making activities refer to the service whereby a financial intermediary ensure that clients issuances will exhibit enough trading activity, hence liquidity, in order to continue to be attractive to the investors. In order to do this the financial intermediary sometimes needs to short the positions in order to attend market requirements whilst ensure that its balance sheet does not increase. Prohibition on Short-Selling refers to the ban on the above mentioned practices. The ban on short-selling practices can put in danger liquidity in capital markets.

15. Prohibitions on Short-Selling II Prohibition on short-selling is market distortionary Short-selling is a source of funding. Short-selling a way which markets can enforce discipline on the issuer penalising mediocre management or policies. Short-selling is a hedging strategy in cases where there are no alternative hedging instruments and reduces the use of credit default swaps Short-selling reduces informational asymmetries Short-selling prohibitions are difficult to implement, monitor and control Local bans cannot work in a global environment. Prohibitions that result in populist responses reflect the lack of governments ability to restore confidence and represent an act of despair

16. Conclusions and Final Remarks The use of affine term structure models in conjunction with the fiscal theory of the price level show that governments could use these tools in order to identify and address their macroeconomic risks. Governments should understand these risks as well as ensure that these are managed actively in advance in order to avoid speculative attacks, as failure to do so it will give rise to multiple equilibria, thus when the probability of a risk-free bond to become risky is high. The prohibition of naked short-selling of government bonds during times of financial distress are unlikely to be addressed within a global perspective, as the existence of a global supervisor to enforce these measures would not receive the international support required. The prohibition is only a work-around to solve the negative consequences of not addressing macroeconomic risks on an earlier stage or rather a populist measure not aimed to get anywhere.