This document provides contact information for professors and teaching assistants of the TASAS Finanzas II course. It includes emails and websites for each instructor. It also lists references and resources for the course, including recommended textbooks. The document outlines the course structure, assignments, and expectations for participation. Key topics to be covered are also listed, such as spot rates, forward rates, yield curves, and the theories of expectations, liquidity preference, and market segmentation.

1. TASAS Finanzas II - LAE Alejandro M. SALEVSKY Juan M. CASCONE Pablo TECHERA Sabrina REY Adrián ECKER

2. INDICE Pautas del curso. Contactos Noticias Repaso de Tasas Spot & Forward Rates / Yield Curve

3. PAUTAS DEL CURSO Grupos y data acquiring Parciales Test de lectura Casos Concepto: participación en clase y blog Bibliografía Material de clase Asistencia Tips: trabajo en clase / soporte after class / seguimiento de slides con bibliografía

4. CONTACTOS Ezequiel Calviño Mail & Google Talk: [email_address] MSN: [email_address] http://www.multitag.com.ar Alejandro M. Salevsky Mail & Google Talk: [email_address] MSN: [email_address] http://www.multitag.com.ar Juan Manuel Cascone Mail & Google Talk: [email_address] MSN: [email_address] http://www.multitag.com.ar Sabrina Rey Mail: [email_address] Pablo Techera Mail & Google Talk: [email_address] MSN: [email_address] Adrián Ecker Mail & Google Talk: [email_address] http://condensadordeflujo.wordpress.com

5. BIBLIOGRAFIA Investments . William Sharpe, Gordon Alexander, J. Bailey. Prentice Hall. 6th Ed. Chapter 5: Page 108 - 138. Foundations of Financial Markets and Institutions . Frank Fabozzi, Franco Modigliani, Michael Ferri. Prentice Hall. 2nd Edition. ISBN 0-13-86056-7. Ch 12 The Term Structure of Interest Rates. Pg 223. Brealey & Myers . Chapter 23 Valuing Debt. ó Capítulo 21 Valoración de los diferentes tipos de deuda

6. REPASO Interes simple vs. compuesto TNA VS. TEA Tasa equivalente Tasa de interés vs. tasa de descuento Tasa nominal vs. Tasa Real

7. YTM – YIELD TO MATURITY Generalidades Es la tasa de retorno promedio anual que se obtendrá por una inversión si se la mantiene desde hoy hasta su vencimiento (maturity date) Es la tasa de mercado que hace que el flujo de fondos descontado de un bono sea igual a su precio . Ejemplo Se tiene un bono con un valor nominal de $100, tasa cupón del 10% (anual) y madurez a 5 años (amortización total a fin del período). Calcular el precio (valor actual) del bono si YTM=10.00% YTM=12.00% YTM=8.00% RTA: 100.00 92.79 107.99 ¿Qué relación existe entre la actividad económica de un país y sus niveles inflacionarios? ¿Qué relación existe en un país entre los niveles inflacionarios y los ? ¿Qué relación existe entre el valor de un bono (inversión), la tasa cupón (tasa pactada) y la YTM (tasa de mercado) en una economía?

8. RISK FREE RATE Generalidades Títulos emitidos por el US Department of the Treasury, están respaldados por el gobierno de USA, por lo que son considerados por todos como títulos sin riesgo de crédito EEUU al ser mayor emisor de deuda en el mundo y dado gran volumen de cada emisión, hacen que el mercado de estos títulos sea el más activo y el más líquido del mundo Tipos Hay dos categorías de US Treasury securities: discount (vencimiento a 1 año o menos) y coupon Risk Premium Es el rendimiento extra por sobre un bono libre de riesgo. Ej: yield Bono Tesoro: 8% y bono “X”: 9% => riesgo adicional (spread) 100 b asis p oints

9. SPOT RATE Generalidades Es la YTM del bono discount (zero-coupon). Se expresa en forma efectiva anual (TEA). Ej: una S 2 es la tasa efectiva anual de un bono zero-coupon de dos años de madurez. Un bono (inversión) con cupones y/o amortizaciones (pagos) parciales puede transformarse en un bono zero-coupon Ejemplo#1 Calcular la spot rate de un bono zero coupon de madurez 1 año, precio actual de 938.58 y valor nominal de 1.000 Calcular la spot rate de un bono zero coupon de madurez 2 años, precio actual 857.34 y valor nominal de 1.000 Síntetización de bonos cupón Se puede encontrar la tasa spot para más de un año utilizando en bonos con cupon tasas spots conocidas para descontar los flujos anuales previos Ejemplo#2 Se tiene un bono (inversión) que paga 50.00 por año y vence en dos años. Su precio actual es de 946.93. (946.93) 50.00 1.050.00 1+S1=1.07 1+S2=?

10. FORWARD RATE Generalidades Es la tasa de interés, fijada hoy, que se pagará por dinero a ser prestado en el futuro y que será devuelto más adelante aún , en una fecha determinada S 2 =[(1+r)^(1/2)]-1 S 1 =[(1+r)^(1/1)]-1 F 1-2 =[(1+r)^(1/1)]-1 MATURITY STRATEGY ROLLOVER STRATEGY En teoría, en condiciones de equilibrio ambas estrategias deberían generar el mismo rendimiento. (1+S 2 )^2 = (1+S 1 ) * (1+f 1-2 ) m 0 1y 2y

11. FORWARD RATE Ejemplo Se tienen los siguientes bonos emitidos por el gobierno. Determinar la Spot 1 , f 1-2 y f 2-3 Bono m o y1 y2 y3 A B C (909.09) (991.81) (977.18) 1.000 100 100 1.100 100 1.100 Investments. Sharpe 6th edition. Pag 132. Exercise 14

12. YIELD CURVE Generalidades El gráfico que muestra la relación del retorno (yield) de bonos con la misma calificación crediticia (bonos del Tesoro USA), pero con diferentes vencimientos (maturities La yield curve está armada a partir de observaciones de precios y retornos en el Treasury market, porque 1) Treasury securities son libres de default risk 2) al ser el mercado más grande y activo, hay pocos problemas de iliquidez http://www.ustreas.gov/offices/domestic-finance/debt-management/interest-rate/yield.shtml

13. YIELD CURVE

14. LAS FORMAS DE LA YIELD CURVE ¿Cuál esta asociada con una recesión en el futuro? ¿Con el riesgo asociado al tiempo? ¿una transición económica? ¿Qué relación existe entre la pendiente y la brecha de rendimientos corto/largo plazo? t r NORMAL t r HUMPED t r INVERTIDA t r FLAT ¿Qué relación existe entre la actividad económica de un país y sus niveles inflacionarios? ¿Qué relación existe en un país entre los niveles inflacionarios y los ?

15. TEORÍA DE LAS EXPECTATIVAS Generalidades Ejemplo Si un bono zero coupon ofrece a dos años una YTM del 6.00% y un bono zero coupon ofrece a dos años una YTM del 7.00% ¿cuál es la forward rate para el año 3? Si la tasa real exigida por los inversores para dicha inversión dado su riesgo es del 4.00% , ¿cuál es la inflación esperada? (1+S 2 )^2 = (1+S 1 ) * (1+f 1-2 ) donde (1+f 1-2 ) = (1+r) * (1+ φ 1-2 ) La forward rate representa la opinión promedio de la futura spot rate La única razón para que la pendiente sea positiva es que los inversores esperan que los tasas de corto plazo en el futuro sean mayores que las actuales El mercado espera que la spot rate cambie porque la tasa real o la tasa de inflación va a cambiar

16. TEORÍA DE LA PREFERENCIA DE LA LIQUIDEZ Generalidades Ejemplo Spot rate a un año 7.00% . Spot rate a dos años 8.00% . Forward rate año 1-2 8.60% . Si el mercado se encuentra arbitrado en estos valores, ¿existe prima de liquidez? Calculela (1+S 2 )^2 = (1+S 1 ) * (1+f 1-2 ) donde (1+f 1-2 ) = (1+r) * (1+ φ 1-2 ) * (1+l) Parte del supuesto que inversores prefieren inversiones de corto plazo , por si llegan a necesitar pesos antes. Un inversor a 2 años, tal vez prefiera rollover strategy, pues puede obtener $$ a fin año 1. Para invertir a 2 años, el retorno debe ser mayor ¿Los prestamistas, pagarán esa mayor tasa por 2 años? Sí, porque se evitan gastos y papeleo

17. TEORÍA DE SEGMENTACIÓN DE LOS MERCADOS Generalidades Los inversores tienen habitats preferidos , (corto o largo plazo), a los cuales están restringidos por ley, preferencias o costumbre Los bonos corto plazo demandados por bancos. Bonos largo plazo demandados por fondos de pensión. Cada grupo demanda diferentes plazos, entonces el mercado se segmenta Inversores y prestamistas no están dispuestos a cambiar de un sector a otro para tomar ventaja de oportunidades que surjan Las spot rates están determinadas por las condiciones de la oferta y la demanda de cada mercado Una curva con pendiente positiva tiene lugar cuando la intersección de la oferta y la demanda para fondos a corto plazo ocurre a menores tasas que para los fondos a largo plazo

18. UTILIDAD DE LA YIELD CURVE ¿Qué relación existe entre la actividad económica de un país y sus niveles inflacionarios? ¿Qué relación existe en un país entre los niveles inflacionarios y los costos de financiamiento? ¿Un aumento de los US Securities puede tener implicancias en el la economía local? ¿Qué variables cree Ud. que pueden ser obtenidas usando como proxy la YC? ¿Qué relación existe entre la actividad económica de un país y sus niveles inflacionarios? ¿Qué relación existe en un país entre los niveles inflacionarios y los costos de financiamiento? ¿Un aumento de los US Securities puede tener implicancias en el la economía local? ¿Qué variables cree Ud. que pueden ser obtenidas usando como proxy la YC? ? ARBITRAJE Se utiliza para analizar posibilidades de arbitraje entre distintos securieties (especialmente bonos) Securities de misma duration y mismo riesgo deben tener mismo rendimiento De caso contrario el mercado arbitra. 1 PREDICTOR ECONOMIA La yield curve puede ser entendida como las expectativas que tiene el mercado sobre el valor futuro de las tasas A niveles de rendimiento real constante, perspectivas inflacionarias (deflacionarias) elevaran (disminuirán) la tasa de interés y viceversa. 2

19. Inflation Rate: 6.44% Inflation Rate: 14.76% NORMAL INVERTED http://www.stockcharts.com/charts/YieldCurve.html http :// inflationdata.com / inflation / inflation_rate / HistoricalInflation.aspx?dsInflation_currentPage =1 YIELD CURVES VS INFLATION (yoy)

20. Inflation Rate: 4.60% Inflation Rate: 2.26% NORMAL FLAT http://www.stockcharts.com/charts/YieldCurve.html http :// inflationdata.com / inflation / inflation_rate / HistoricalInflation.aspx?dsInflation_currentPage =1 YIELD CURVES VS INFLATION (yoy)

21. Inflation Rate: 2.82% Inflation Rate: 2.54% STEEP FLAT http://www.stockcharts.com/charts/YieldCurve.html http :// inflationdata.com / inflation / inflation_rate / HistoricalInflation.aspx?dsInflation_currentPage =1 YIELD CURVES VS INFLATION (yoy)

22. Inflation Rate: 3.41% Inflation Rate: 1.64% FLAT STEEP http://www.stockcharts.com/charts/YieldCurve.html http :// inflationdata.com / inflation / inflation_rate / HistoricalInflation.aspx?dsInflation_currentPage =1 YIELD CURVES VS INFLATION (yoy)

23. Inflation Rate: 3.17% FLAT Inflation Rate: 3.24% HUMPED http://www.stockcharts.com/charts/YieldCurve.html http :// inflationdata.com / inflation / inflation_rate / HistoricalInflation.aspx?dsInflation_currentPage =1 YIELD CURVES VS INFLATION (yoy)

24. CASO DE ACTUALIDAD S E C U R I T I Z A C I O N S A V N D G S D F G G H J K R E R F C V B F R T W Q S D S D S S U B P R I M E F I O Y A E R M T Y U B S D W Q A I A X A C B N S T R O S Q R C V B N F D E E W Q R T G A G T R S C D R E C E S I O N S W Q A S S V B T R E S O I V O N N F E R G B H Y T S D A X Z A Z A E T R T E F F V O J U I F G G K R E A L E S T A T E B U B B L E K L E E D E C V F S G S S D S A Q X C V B V H J U J I G B N H O H N Z G N M K J M T G R F E O E D S C S C V B V B H J N J U J B C A L I F I C A D O R A S T B T R F V F G B D C D X S X A Z Q E W E T Y U I Brainstorming y creación colaborativa de concepto

25. YIELD CURVE EN ARGENTINA (ACTUAL) (YTM real) ¿Por qué la Yield Curve de bonos en dólares tiene menor pendiente que la Yield Curve de los bonos en pesos? ¿Qué implicancias debería tener sobre el tipo de cambio ARS/USD? ¿Qué relación existe entre la actividad económica de un país y sus niveles inflacionarios? ¿Qué relación existe en un país entre los niveles inflacionarios y los ?

26. Back up

27. Yield To matuirity Yield to maturity (YTM) is the yield promised by the bondholder on the assumption that the bond will be held to maturity, that all coupon and principal payments will be made and coupon payments are reinvested at the bond's promised yield at the same rate as invested. It is a measurement of the return of the bond. This technique in theory allows investors to calculate the fair value of different financial instruments. The YTM is almost always given in terms of annual effective rate . The calculation of YTM is identical to the calculation of internal rate of return. If a bond's current yield is less than its YTM, then the bond is selling at a discount. If a bond's current yield is more than its YTM, then the bond is selling at a premium. If a bond's current yield is equal to its YTM, then the bond is selling at par . Risk Free Rate The theoretical rate of return of an investment with zero risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. In theory, the risk-free rate is the minimum return an investor expects for any investment because he or she will not accept additional risk unless the potential rate of return is greater than the risk-free rate. In practice, however, the risk-free rate does not exist because even the safest investments carry a very small amount of risk. Thus, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free rate. Spot Rate The yield to maturity of a zero-coupon bond, usually a Treasury bond, which is used as a benchmark for other bond yields and valuations. Because a zero-coupon bond has no coupon payments, there is no reinvestment risk and, therefore, the precise yield to maturity of the bond can be known. The construction of a spot rate Treasury yield curve is used to demonstrate the arbitrage-free relationship between spot rates and forward rates known as the term structure of interest rates. Spot rates are also used in the calculation of a zero-volatility spread (Z-spread) used to price certain fixed-income securities.

28. Trying To Predict Interest Rates Most investors care about future interest rates, but none more than bondholders. If you are considering a bond or bond fund investment, you must ask yourself whether you think interest rates will rise in the future. If the answer is yes then you probably want to avoid long-term maturity bonds or at least shorten the average duration of your bond holdings; or plan to weather the ensuing price decline by holding your bonds and collecting the par value at maturity. (For a review of the relationships between prevailing interest rates and yield, duration, and other bond aspects, please see the tutorial Advanced Bonds Concepts .) The Treasury Yield Curve In the United States, the Treasury yield curve (or term structure ) is the first mover of all domestic interest rates and an influential factor in setting global rates. Interest rates on all other domestic bond categories rise and fall with Treasuries , which are the debt securities issued by the U.S. government. To attract investors, any bond or debt security that contains greater risk than that of a similar Treasury bond must offer a higher yield. For example, the 30-year mortgage rate historically runs 1% to 2% above the yield on 30-year Treasury bonds. Below is a graph of the actual Treasury yield curve as of December 5, 2003. It is considered normal because it slopes upward with a concave shape: Consider three elements of this curve. First, it shows nominal interest rates. Inflation will erode the value of future coupon dollars and principal repayments; the real interest rate is the return after deducting inflation. The curve therefore combines anticipated inflation and real interest rates. Second, the Federal Reserve directly manipulates only the short-term interest rate at the very start of the curve. The Fed has three policy tools, but its biggest hammer is the federal funds rate , which is only a one-day, overnight rate. Third, the rest of the curve is determined by supply and demand in an auction process. Sophisticated institutional buyers have their yield requirements which, along with their appetite for government bonds, determine how these institutional buyers bid for government bonds. Because these buyers have informed opinions on inflation and interest rates, many consider the yield curve to be a crystal ball that already offers the best available prediction of future interest rates. If you believe that, you also assume that only unanticipated events (for example, an unanticipated increase in inflation) will shift the yield curve up or down.

29. Long Rates Tend to Follow Short Rates Technically, the Treasury yield curve can change in various ways: it can move up or down (a parallel shift), become flatter or steeper (a shift in slope), or become more or less humped in the middle (a change in curvature). The following chart compares the 10-year Treasury yield (red line) to the one-year Treasury yield (green line) from June 1976 to December 2003. The spread between the two rates (blue line) is a simple measure of steepness: Consider two observations. First, the two rates move up and down somewhat together (the correlation for the period above is about 88%). Therefore, parallel shifts are common. Second, although long rates directionally follow short rates, they tend to lag in magnitude. Specifically, when short rates rise, the spread between 10-year and one-year yields tends to narrow (curve of the spread flattens) and when short rates fall, the spread widens (curve becomes steeper). In particular, the increase in rates from 1977 to 1981 was accompanied by a flattening and inversion of the curve (negative spread); the drop in rates from 1990 to 1993 created a steeper curve in the spread, and the marked drop in rates from March 2000 to the end of 2003 produced a very steep curve by historical standards. Supply-Demand Phenomenon So what moves the yield curve up or down? Well, let's admit we can't do justice to the complex dynamics of capital flows that interact to produce market interest rates. But we can keep in mind that the Treasury yield curve reflects the cost of U.S. government debt and is therefore ultimately a supply-demand phenomenon. (For a refresher on how increases and decreases in the supply and demand of credit affect interest rates, see the article Forces Behind Interest Rates .)

30. Supply-Related Factors Monetary Policy If the Fed wants to increase the fed funds rate, it supplies more short-term securities in open market operations. The increase in the supply of short-term securities restricts the money in circulation since borrowers give money to the Fed. In turn, this decrease in the money supply increases the short-term interest rate because there is less money in circulation (credit) available for borrowers. By increasing the supply of short-term securities, the Fed is yanking up the very left end of the curve, and the nearby short-term yields will snap quickly in lockstep. Can we predict future short-term rates? Well, the expectations theory says that long-term rates embed a prediction of future short-term rates. But consider the actual December yield curve illustrated above, which is normal but very steep. The one-year yield is 1.38% and the two-year yield is 2.06%. If you were going to invest with a two-year time horizon and if interest rates were going to hold steady, you would, of course, do much better to go straight into buying the two-year bond (which has a much higher yield) instead of buying the one-year bond and rolling it over into another one-year bond. Expectations theory, however, says the market is predicting an increase in the short rate. Therefore, at the end of the year you will be able to roll over into a more favorable one-year rate and be kept whole relative to the two-year bond, more or less. In other words, expectations theory says that a steep yield curve predicts higher future short-term rates. Unfortunately, the pure form of the theory has not performed well: interest rates often remain flat during a normal (upward sloping) yield curve. Probably the best explanation for this is that, because a longer bond requires you to endure greater interest rate uncertainty, there is extra yield contained in the two-year bond. If we look at the yield curve from this point of view, the two-year yield contains two elements: a prediction of the future short-term rate plus extra yield (i.e., a risk premium) for the uncertainty. So we could say that, while a steeply sloping yield curve portends an increase in the short-term rate, a gently upward sloping curve, on the other hand, portends no change in the short-term rate - the upward slope is due only to the extra yield awarded for the uncertainty associated with longer term bonds. Because Fed watching is a professional sport, it is not enough to wait for an actual change in the fed funds rate, as only surprises count. It is important for you, as a bond investor, to try to stay one step ahead of the rate, anticipating rather than observing its changes. Market participants around the globe carefully scrutinize the wording of each Fed announcement (and the Fed governors' speeches) in a vigorous attempt to discern future intentions. Fiscal Policy When the U.S. government runs a deficit, it borrows money by issuing longer term Treasury bonds to institutional lenders. The more the government borrows, the more supply of debt it issues. At some point, as the borrowing increases, the U.S. government must increase the interest rate to induce further lending. However, foreign lenders will always be happy to hold bonds in the U.S. government: Treasuries are highly liquid and the U.S. has never defaulted (it actually came close to a default in late 1995, but Robert Rubin, the Treasury secretary at the time, staved off the threat and has called a Treasury default "unthinkable - something akin to nuclear war"). Still, foreign lenders can easily look to alternatives like eurobonds and, therefore, they are able to demand a higher interest rate if the U.S. tries to supply too much of its debt.

31. Demand-Related Factors Inflation If we assume that borrowers of U.S. debt expect a given real return, then an increase in expected inflation will increase the nominal interest rate (the nominal yield = real yield + inflation). Inflation also explains why short-term rates move more rapidly than long-term rates: when the Fed raises short-term rates, long-term rates increase to reflect the expectation of higher future short-term rates; however, this increase is mitigated by lower inflation expectations as higher short-term rates also suggest lower inflation (as the Fed sells/supplies more short-term Treasuries, it collects money and tightens the money supply): An increase in feds funds (short-term) tends to flatten the curve because the yield curve reflects nominal interest rates: higher nominal = higher real interest rate + lower inflation. Fundamental Economics The factors that create demand for Treasuries include economic growth, competitive currencies and hedging opportunities. Just remember: anything that increases the demand for long-term Treasury bonds puts downward pressure on interest rates (higher demand = higher price = lower yield or interest rates) and less demand for bonds tends to put upward pressure on interest rates. A stronger U.S. economy tends to make corporate (private) debt more attractive than government debt, decreasing demand for U.S. debt and raising rates. A weaker economy, on the other hand, promotes a "flight to quality", increasing the demand for Treasuries, which creates lower yields. It is sometimes assumed that a strong economy will automatically prompt the Fed to raise short-term rates, but not necessarily. Only when growth translates or overheats into higher prices is the Fed likely to raise rates. In the global economy, Treasury bonds compete with other nations's debt. On the global stage, Treasuries represent an investment in both the U.S. real interest rates and the dollar. The euro is a particularly important alternative: for most of 2003, the European Central Bank pegged its short-term rate at 2%, a more attractive rate than the fed funds rate of 1%.

32. Finally, Treasuries play a huge role in the hedging activities of market participants. In environments of falling interest rates, many holders of mortgage-backed securities, for instance, have been hedging their prepayment risk by purchasing long-term Treasuries. These hedging purchases can play a big role in demand, helping to keep rates low, but the concern is that they may contribute to instability. Conclusion We have covered some of the key traditional factors associated with interest rate movements. On the supply side, monetary policy determines how much government debt and money are supplied into the economy. On the demand side, inflation expectations are the key factor. However, we have also discussed other important influences on interest rates, including: fiscal policy (that is, how much does the government need to borrow?) and other demand-related factors such as economic growth and competitive currencies. Here is a summary chart of the different factors influencing interest rates: