During this session we extended the binomial tree methodology to the pricing of European Puts and American Options. Remember that it is never optimal to exercise before expiry an American Call (w/o dividends). However, it may be optimal to exercise an American put (w/o dividends).
We also reviewed Delta (how the premium of the option changes when the price of the underlying asset changes). We saw how to form a Delta Neutral position by hedging with options and what is the role of Delta when calculating the hedging ratio.
Have a look at the presentation here and to an example of Delta Neutral portfolio here.
Showing posts with label hedge. Show all posts
Showing posts with label hedge. Show all posts
Tuesday, October 21, 2014
Friday, September 12, 2014
Session 4 - Derivatives - 2014
During this session we reviewed what type of dealers we can find in the Derivatives Markets (hedger, speculators, arbitrageurs) and we also had a look at how we could hedge with Futures. We gave an example of how a hedger/arbitrageur can become a speculator.
We focused on how to hedge a position. Hedging means buying or selling a financial instrument to offset potential losses/gains that may be incurred by a companion investment.
Usually, if the underlying asset of the Future and the asset that we want to hedge are the same, to determine the amount of contracts that we should buy/sell we should divide the amount (units) of the underlying asset that we want to hedge (in the example, 2,000,000 gallons of jet fuel) by the amount (units) of each contract (in the example, 42,000).
However, if the underlying asset of the Future and the asset that we want to hedge are not the same, we will have to do cross-hedging. When we cross-hedge, two questions arise:
1) What is the hedge ratio that we should apply to determine the number of contracts that we have to buy/sell?
- We use a linear regression where the variable to be explained (y) is the change in price of the asset that we want to hedge and the exogenous variable (x) is the change in price of the Future. With this analysis, we will determine how "y" moves when "x" moves.
- The hedge ratio will be equal to the beta parameter of the regression line (beta = correl. coef * sigma "y" / sigma "x"). Beta means how many units "y" moves when "x" moves by 1 unit.
- In our example, beta = 0.77 (meaning that when "x" moves by 1, "y" moves by 0.77). Then, the number of contracts that we will have to long (I am short the underlying asset, if prices go up, my P&L would be lower) would be 0.77 * 2MM / 42k.
2) How good will the hedge be?
- To determine how good the hedge will be, we must calculate R^2 (R^2 = (Covariance / (Sigma "y" * Sigma "x"))^2.
- Values above 0.75 should indicate that the hedge is quite good.
In the second part of the class, we reviewed how to extrapolate cross-hedging to hedge equity portfolios or single stocks with Futures on an Index.
Why would I want to hedge an equity portfolio?
Typically, if I am long an equity portfolio I would be convinced of the potential positive performance of the portfolio. Then, if I am thinking about hedging, maybe I should sell my portfolio and buy later... There are three reasons to hedge:
- Transaction costs (produced by selling and buying again) may be high.
- Hedging with a Future on an Index would eliminate systematic risk (market risk). I would only be exposed to the relative performance of the portfolio vs. the Index.
- The investment is designed for the long run, while I want to hedge the short run (maybe we are waiting for bad news).
The process of cross-hedging is very similar to the prevous case. First, we must determine the beta of the portfolio. To calculate the beta of the portfolio, we calculate a value-weighted average of the betas of the securities in the portfolio. The betas of the securities that compose the portfolio will be available in Reuters or Bloomberg as beta is a fundamental component of CAPM.
To hedge completely the portfolio, we should long/short a number of contracts equal to beta * Value of Portfolio / Euro Value of Future. Remember that to obtain the Euro Value of the Future we must use the Future multiplier. If I hedge completely my portfolio the beta of my new portfolio (old portfolio + Future) will be equal to zero (it does not matter how the market moves, my new portfolio will not move).
I can also change the beta of the portfolio (reduce/increase it). For instance, if the beta of my portfolio is 1.003 and I want to take it to 2, I will have to long a number of contracts equal to (Objective beta - Current beta) * Value of Portfolio / Euro Value of Future.
You can find the presentation used in class here. You can find the Excel file used in class here. You can find how beta minimizes the variance of the new portfolio here.
We focused on how to hedge a position. Hedging means buying or selling a financial instrument to offset potential losses/gains that may be incurred by a companion investment.
Usually, if the underlying asset of the Future and the asset that we want to hedge are the same, to determine the amount of contracts that we should buy/sell we should divide the amount (units) of the underlying asset that we want to hedge (in the example, 2,000,000 gallons of jet fuel) by the amount (units) of each contract (in the example, 42,000).
However, if the underlying asset of the Future and the asset that we want to hedge are not the same, we will have to do cross-hedging. When we cross-hedge, two questions arise:
1) What is the hedge ratio that we should apply to determine the number of contracts that we have to buy/sell?
- We use a linear regression where the variable to be explained (y) is the change in price of the asset that we want to hedge and the exogenous variable (x) is the change in price of the Future. With this analysis, we will determine how "y" moves when "x" moves.
- The hedge ratio will be equal to the beta parameter of the regression line (beta = correl. coef * sigma "y" / sigma "x"). Beta means how many units "y" moves when "x" moves by 1 unit.
- In our example, beta = 0.77 (meaning that when "x" moves by 1, "y" moves by 0.77). Then, the number of contracts that we will have to long (I am short the underlying asset, if prices go up, my P&L would be lower) would be 0.77 * 2MM / 42k.
2) How good will the hedge be?
- To determine how good the hedge will be, we must calculate R^2 (R^2 = (Covariance / (Sigma "y" * Sigma "x"))^2.
- Values above 0.75 should indicate that the hedge is quite good.
In the second part of the class, we reviewed how to extrapolate cross-hedging to hedge equity portfolios or single stocks with Futures on an Index.
Why would I want to hedge an equity portfolio?
Typically, if I am long an equity portfolio I would be convinced of the potential positive performance of the portfolio. Then, if I am thinking about hedging, maybe I should sell my portfolio and buy later... There are three reasons to hedge:
- Transaction costs (produced by selling and buying again) may be high.
- Hedging with a Future on an Index would eliminate systematic risk (market risk). I would only be exposed to the relative performance of the portfolio vs. the Index.
- The investment is designed for the long run, while I want to hedge the short run (maybe we are waiting for bad news).
The process of cross-hedging is very similar to the prevous case. First, we must determine the beta of the portfolio. To calculate the beta of the portfolio, we calculate a value-weighted average of the betas of the securities in the portfolio. The betas of the securities that compose the portfolio will be available in Reuters or Bloomberg as beta is a fundamental component of CAPM.
To hedge completely the portfolio, we should long/short a number of contracts equal to beta * Value of Portfolio / Euro Value of Future. Remember that to obtain the Euro Value of the Future we must use the Future multiplier. If I hedge completely my portfolio the beta of my new portfolio (old portfolio + Future) will be equal to zero (it does not matter how the market moves, my new portfolio will not move).
I can also change the beta of the portfolio (reduce/increase it). For instance, if the beta of my portfolio is 1.003 and I want to take it to 2, I will have to long a number of contracts equal to (Objective beta - Current beta) * Value of Portfolio / Euro Value of Future.
You can find the presentation used in class here. You can find the Excel file used in class here. You can find how beta minimizes the variance of the new portfolio here.
Monday, September 16, 2013
Clase 5 curso 2013-2014 - Coberturas y tipos de interés
En el día de hoy, dividimos la clase en dos partes:
- Durante la primera parte, revisamos los ejercicios que había pendientes. He publicado mi solución en la pestaña 'Ejercicios'. Los ejercicios tenían que ver con la forma de cubrirse con futuros y con los resultados de estas coberturas (qué pasa si la cobertura no es perfecto, qué pasa si sobrecubro, qué ocurre si cubro con futuros de IBEX en vez de futuros del Mini IBEX).
- En la segunda parte , comenzamos a ver cómo valorar futuros y forwards: vimos qué es 'ponerse corto' de una acción, qué distintos mercados de tipos de interés existen, cómo funcionan los tipos LIBOR y cómo afecta la composición a los tipos de interés. Recordad que durante el curso asumiremos composición continua. En general, en los derivados no colateralizados utilizaremos para el descuento la curva LIBOR y en los derivados colateralizados usaremos la curva EONIA.
Os dejó la presentación aquí.
- Durante la primera parte, revisamos los ejercicios que había pendientes. He publicado mi solución en la pestaña 'Ejercicios'. Los ejercicios tenían que ver con la forma de cubrirse con futuros y con los resultados de estas coberturas (qué pasa si la cobertura no es perfecto, qué pasa si sobrecubro, qué ocurre si cubro con futuros de IBEX en vez de futuros del Mini IBEX).
- En la segunda parte , comenzamos a ver cómo valorar futuros y forwards: vimos qué es 'ponerse corto' de una acción, qué distintos mercados de tipos de interés existen, cómo funcionan los tipos LIBOR y cómo afecta la composición a los tipos de interés. Recordad que durante el curso asumiremos composición continua. En general, en los derivados no colateralizados utilizaremos para el descuento la curva LIBOR y en los derivados colateralizados usaremos la curva EONIA.
Os dejó la presentación aquí.
Wednesday, September 11, 2013
Clase 3 y 4 curso 2013-2014 - Mercados de Futuros y Coberturas
Durante la tercera clase de este año estuvimos viendo algunas de las características de los Mercados en los que se cotizan los productos derivados. La más importante, y la que diferencia a los Mercados OTC de los Mercados Organizados, es la existencia de un margen diario que asegura a las contrapartidas contra un posible “default” de la contrapartida.
Vimos, igualmente que hay bastantes elementos a determinar cuando se está definiendo un contrato de futuro: el activo subyacente, el tamaño, cómo será la cotización, límites de precios, límites de posición…
Introdujimos la primera situación en la que el arbitraje nos ayudaba a determinar cómo debía comportarse el precio de un activo: para que no exista arbitraje, el precio del futuro y del activo deben converger a vencimiento.
En términos de regulación, destacamos la normativa EMIR, de reciente creación, que está obligando a muchas contrapartidas a negociar sus derivados a través de Mercados Organizados.
Durante la cuarta clase vimos que hay tres tipos de actores en el Mercado: coberturistas, especuladores y arbitrajistas. Nos centramos en la operativa de los coberturistas, que utilizan los derivados para fijar el precio de la producción o de algunas materias primas. Estudiamos cómo realizando una operación en el Mercado del activo y otra en el Mercado de Futuros podíamos cubrir nuestra posición.
Vimos que no todas las coberturas son perfectas. De hecho vimos cómo realizar un análisis de correlación para determinar el número de contratos a comprar/vender, cuando el futuro y el activo no tienen un “match” perfecto. Posteriormente, vimos cómo extender este tipo de análisis al caso de un portfolio de Equity y usarlo para aumentar o disminuir la Beta de un Portfolio.
Subscribe to:
Posts (Atom)