El modelo CAPM y la tasa de descuento (Parte 1)

La técnica más utilizada para determinar la tasa de descuento de un proyecto es la derivada del modelo de valoración de activos financieros o CAPM (Capital Asset Pricing Model).

La tasa de descuento de un proyecto se obtiene a través de esta ecuación:

La tasa de descuento está, por lo tanto, en función de los parámetros de la ecuación (rf y rm -rf) y del β proy.

Los parámetros de la ecuación del CAPM (rf y rm -rf) conceptualmente se definen del modo siguiente:

 ·     rf es la tasa libre de riesgo y se define como la tasa que paga hoy un activo libre de riesgo, en este caso un bono soberano.

·     (rm -rf) es el diferencial entre lo que paga una inversión en el mercado (acciones) frente a lo que reditúa una inversión en un activo libre de riesgo. Se le conoce como “prima por riesgo de mercado”. Ese diferencial es la suma algebraica de los promedios geométricos de ambos componentes en el plazo más largo posible.

 Dado que el modelo CAPM está pensado para mercados financieros líquidos, profundos y transparentes los datos (β y parámetros) para aplicar la ecuación del modelo están basados preferentemente en el mercado americano. Obtener a una tasa de descuento aplicable a nivel local implica incorporar a la ecuación el riesgo país.

 Es importante tener en cuenta lo siguiente:

 a)   No se debe confundir el rf que constituye el elemento inicial de la ecuación con el rf de la prima por riesgo de mercado. Tal como se señaló anteriormente el primero es la tasa de rendimiento de un activo libre de riesgo en el momento de la evaluación en tanto que el otro es el promedio geométrico de la rentabilidad de un activo libro de riesgo en el mayor plazo posible.

b)   La tasa del activo libre de riesgo, primer rf de la ecuación, es el correspondiente al rendimiento de dicho activo al plazo más cercano a la duración del proyecto. Sin embargo; algunos analistas utilizan el rendimiento al plazo más largo posible.

c)   El promedio de ambos componentes en la prima por riesgo de mercado debe ser geométrico ya que los rendimientos ganados se van acumulando año tras año de manera similar a una tasa de interés compuesto.

d)   El plazo de la prima por riesgo de mercado debe ser el más largo posible para poder “suavizar” la tendencia de los rendimientos percibidos a lo largo del tiempo.

e)   El riesgo país que se suma a la tasa de descuento es el vigente el día de hoy.

 No hay que perder de vista que la tasa de rentabilidad que entrega la ecuación es una tasa corriente, es decir ese rendimiento incorpora la inflación. Por lo tanto, las tasas de descuento halladas a través del modelo son aplicables únicamente a flujos de caja expresados en dólares corrientes.

Si el modelo de pronóstico del proyecto está en moneda local, la conversión de la tasa de rentabilidad a dicha moneda se efectúa de la manera siguiente:

Se debe enfatizar, nuevamente, que esa tasa es solo aplicable a proyecciones financieras efectuadas en moneda corriente.

A continuación, se presentan las fuentes en donde se pueden obtener los datos de los parámetros de la ecuación del CAPM y los β por sector industrial. Tal como se mencionó anteriormente dichos datos están referidos al mercado americano.

Tasa de rendimiento del activo libre de riesgo:

http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield

El enlace lleva a la página de la Reserva Federal (FED) que detalla el rendimiento (yield) de valores emitidos por el gobierno americano a diferentes plazos.

Como ya se indicó anteriormente el analista debe escoger el rendimiento del activo (bono del tesoro) al plazo más cercano a la vida del proyecto. Alternativamente, se puede considerar el rendimiento del bono con el plazo más largo posible (30 años).

Prima por riesgo de mercado:

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html

La página a la que se accede mediante este enlace presenta las rentabilidades anuales obtenidas desde inicios de 1928 hasta el 2019 para tres clases de activos financieros: i) bonos del tesoro americanos, ii) inversión en la bolsa de valores americana (índice S&P500) y iii) letras del tesoro americano. Asimismo, se entrega el valor anual de una inversión de US$100 efectuada en 1928 en esos tres activos para cada uno de los años del período.

Para el cálculo de la prima por riesgo de mercado sólo interesan el rendimiento de los dos primeros activos. Lamentablemente, el cuadro no detalla el promedio de las rentabilidades; pero es fácil obtenerla si se siguen estos pasos:

Paso 1: Determinar el valor de la inversión inicial y final en el plazo más largo posible.

En el caso de la inversión en acciones:

Inicios de 1928:          US$100

Finales 2019   :           US$502,443.41

Paso 2: Hallar la rentabilidad acumulada en esos años.

Siguiendo el ejemplo anterior:

Rentabilidad acumulada 1928-2019 = (502,443.41/100) – 1 = 5,023.43%

Paso 3: Calcular el promedio geométrico correspondiente.

Continuando con el ejemplo:

Rentabilidad promedio 1928-2019 = (5,023.43%)ˆ(1/92) – 1 = 9.71%

En términos nominales una inversión en la bolsa americana ha rendido en promedio 9.71% anual en los último 92 años.

Similar procedimiento se utiliza para hallar la rentabilidad de un bono del tesoro americano.

Los resultados así obtenidos se suman algebraicamente y se obtiene la prima por riesgo de mercado.

Riesgo país:

http://www.ambito.com/economia/mercados/riesgo-pais/

El riesgo país esta expresado en puntos básicos (pb) o basic points (bp). Dado que 100 puntos básicos equivalen a un punto porcentual, la conversión a términos decimales implica dividirlos entre 10,000.

β sectoriales:

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html

El enlace lleva a un listado de β sectoriales en diversas industrias americanas. Se debe seleccionar el βμ de una actividad similar a la desarrollada por el proyecto.

235 thoughts on “El modelo CAPM y la tasa de descuento (Parte 1)”

  1. Heya i am for the primary time here. I came across this board and I find It truly useful & it helped me out much. I am hoping to present something back and help others like you aided me. Nedi Jeramie Lovell

  2. Thanks for your own work on this website. My mum takes pleasure in setting aside time for research and it is simple to grasp why. We notice all relating to the powerful way you provide very important tips and hints via your website and therefore strongly encourage response from visitors on this theme while our own simple princess is without a doubt understanding so much. Take pleasure in the rest of the year. Your performing a useful job. Marne Stanwood Wey

  3. Thank you for sharing your info. I really appreciate your efforts and I am waiting for your further write ups thank you once again. Mariquilla Aymer Pegg

  4. Yesterday, while I was at work, my sister stole my iPad and tested to see if it can survive a thirty foot drop, just so she can be a youtube sensation. My iPad is now broken and she has 83 views. I know this is totally off topic but I had to share it with someone!| Odella Ambrosi Vinia

  5. I together with my buddies ended up taking note of the nice thoughts located on your web blog while unexpectedly I had an awful suspicion I had not expressed respect to the blog owner for them. All the women are already consequently joyful to learn all of them and have clearly been having fun with them. I appreciate you for being considerably considerate and also for figuring out this sort of terrific guides millions of individuals are really needing to be informed on. Our sincere regret for not expressing appreciation to you earlier. Sibylla Erek Luckin

  6. I usually do not leave discuss article. It seems foolish to do so. I wanted to take a moment to tell you that I located your article to be worthwhile of recommendation. The quantity of information that you consisted of in it is really remarkable and it behaves to see that another person is as thinking about this subject as I am. Kati Christophorus Wolfson

  7. Are able to anyone recommend a very good hair stylist online friends ? Contain tried several, dissatisfied. Willing to travel anywhere in the sex club metro area. Thanks! Rachtades, Dyers Crossing, Lignei-i Kuc milf pussy Habersham Georgia women seeking sex Mortons Gap Dniren Douglas Krischer

  8. jimdofreecrerm

    The road seemed to stretch on endlessly before us, but Alexis assured me that our journey was near an end. We’d turn before long into thick woods and travel through narrow, winding roads until we reached her family’s cabin. I had no choice but to trust her as GPS had given out nearly 20 minutes ago.

    “There’s good wifi and okay reception at the cabin,” she’d told me, “but you can’t get there unless you know the way.”

    So here I was, driving alone in the middle of god knows where with a girl who was my student just a couple of weeks ago. Her and her four best friends had been together from first grade all the way through high school and now they had graduated with very different futures ahead of them. They had decided to kick off “the best summer ever” with a week long stay at Alexis’s family cabin. Alexis and I were heading up before everyone else, the four other girls and four guys.

  9. The road seemed to stretch on endlessly before us, but Alexis assured me that our journey was near an end. We’d turn before long into thick woods and travel through narrow, winding roads until we reached her family’s cabin. I had no choice but to trust her as GPS had given out nearly 20 minutes ago.

    “There’s good wifi and okay reception at the cabin,” she’d told me, “but you can’t get there unless you know the way.”
    https://Dsawesaweropmnbs3421674.jimdofree.com/
    So here I was, driving alone in the middle of god knows where with a girl who was my student just a couple of weeks ago. Her and her four best friends had been together from first grade all the way through high school and now they had graduated with very different futures ahead of them. They had decided to kick off “the best summer ever” with a week long stay at Alexis’s family cabin. Alexis and I were heading up before everyone else, the four other girls and four guys.

  10. The road seemed to stretch on endlessly before us, but Alexis assured me that our journey was near an end. We’d turn before long into thick woods and travel through narrow, winding roads until we reached her family’s cabin. I had no choice but to trust her as GPS had given out nearly 20 minutes ago.

    “There’s good wifi and okay reception at the cabin,” she’d told me, “but you can’t get there unless you know the way.”
    https://medium.com/@carterjoanns26/late-night-rendezvous-pt-01-4af1d5aaf648
    So here I was, driving alone in the middle of god knows where with a girl who was my student just a couple of weeks ago. Her and her four best friends had been together from first grade all the way through high school and now they had graduated with very different futures ahead of them. They had decided to kick off “the best summer ever” with a week long stay at Alexis’s family cabin. Alexis and I were heading up before everyone else, the four other girls and four guys.

  11. The road seemed to stretch on endlessly before us, but Alexis assured me that our journey was near an end. We’d turn before long into thick woods and travel through narrow, winding roads until we reached her family’s cabin. I had no choice but to trust her as GPS had given out nearly 20 minutes ago.

    “There’s good wifi and okay reception at the cabin,” she’d told me, “but you can’t get there unless you know the way.”
    https://notepin.co/shared/ffbqtoc
    So here I was, driving alone in the middle of god knows where with a girl who was my student just a couple of weeks ago. Her and her four best friends had been together from first grade all the way through high school and now they had graduated with very different futures ahead of them. They had decided to kick off “the best summer ever” with a week long stay at Alexis’s family cabin. Alexis and I were heading up before everyone else, the four other girls and four guys.

  12. Takipbonus hakkında duyurular, güncellemeler, paylaşımlar ve en yeni içerikler burada! Instagram takipçi satın al sitesi takipbonus platformunun yeniliklerini ve en güncel indirim kampanyalarını buradan takip edebilirsin!

  13. Instagram takipçi almanın en güvenilir ve hızlı yanı takipbonus.com ile popülerliğe yelken açmaktır! Piyasanın nirvanası panelimiz tüm takipçi ve beğeni hizmetlerinde sonsuz aktarım garantisi vermektedir. Bu sayede hızlıca takipçi kasmak saniyeler içerisinde gerçekleşecektir.

  14. Metin2 pvp serverler ile en eğlenceli pvp oyunları bulabileceğin Forumexe.tc üzerinden istediğin oyun modunu bul ve metin2 heyecanını limitsiz tat! Metin2 pvp server tanıtım forumu üzerinden ücretsiz serverleri incele, sana uygun olanını seçerek anında maceraya katıl!

  15. The road seemed to stretch on endlessly before us, but Alexis assured me that our journey was near an end. We’d turn before long into thick woods and travel through narrow, winding roads until we reached her family’s cabin. I had no choice but to trust her as GPS had given out nearly 20 minutes ago.

    “There’s good wifi and okay reception at the cabin,” she’d told me, “but you can’t get there unless you know the way.”
    https://telegra.ph/An-Unexpected-Break-Pt-02-10-19
    So here I was, driving alone in the middle of god knows where with a girl who was my student just a couple of weeks ago. Her and her four best friends had been together from first grade all the way through high school and now they had graduated with very different futures ahead of them. They had decided to kick off “the best summer ever” with a week long stay at Alexis’s family cabin. Alexis and I were heading up before everyone else, the four other girls and four guys.

  16. The road seemed to stretch on endlessly before us, but Alexis assured me that our journey was near an end. We’d turn before long into thick woods and travel through narrow, winding roads until we reached her family’s cabin. I had no choice but to trust her as GPS had given out nearly 20 minutes ago.

    “There’s good wifi and okay reception at the cabin,” she’d told me, “but you can’t get there unless you know the way.”
    https://rentry.co/f7ctz
    So here I was, driving alone in the middle of god knows where with a girl who was my student just a couple of weeks ago. Her and her four best friends had been together from first grade all the way through high school and now they had graduated with very different futures ahead of them. They had decided to kick off “the best summer ever” with a week long stay at Alexis’s family cabin. Alexis and I were heading up before everyone else, the four other girls and four guys.

  17. Its like you read my mind! You seem to know so much about this, like you wrote the book in it or something.
    I think that you could do with a few pics to drive the message home a bit, but instead of
    that, this is excellent blog. An excellent read.
    I will definitely be back.

  18. The road seemed to stretch on endlessly before us, but Alexis assured me that our journey was near an end. We’d turn before long into thick woods and travel through narrow, winding roads until we reached her family’s cabin. I had no choice but to trust her as GPS had given out nearly 20 minutes ago.

    “There’s good wifi and okay reception at the cabin,” she’d told me, “but you can’t get there unless you know the way.”
    https://txt.fyi/-/20363/dee79bc4/
    So here I was, driving alone in the middle of god knows where with a girl who was my student just a couple of weeks ago. Her and her four best friends had been together from first grade all the way through high school and now they had graduated with very different futures ahead of them. They had decided to kick off “the best summer ever” with a week long stay at Alexis’s family cabin. Alexis and I were heading up before everyone else, the four other girls and four guys.

  19. My spouse and I stumbled over here by a different page and thought
    I might check things out. I like what I see so now i am
    following you. Look forward to looking at your web page yet again.

  20. Wow, amazing blog layout! How long have you been blogging for?
    you made blogging look easy. The overall look of your site is wonderful, as well as
    the content!

Leave a Comment

Su dirección de correo no se hará público.