LA LEY DE UN PRECIO PARA MERCADOS FINANCIEROS

 En el COMERCIO GLOBAL existe el concepto académico de LA LEY UN PRECIO.  Es decir, retirando ruidos y restricciones de transporte, aranceles, impuestos, almacenamiento y tasas de cambio. El precio de la misma mercancía o activo es IGUAL, en cualquier lugar del mundo....


En los mercados financieros, existe una conceptualización matemática, que implica la ausencia e imposibilidad de arbitraje intertemporal, dado que, llevados a un mismo punto en el tiempo ... Todos los precios de referencia de un mismo activo , negociados en MERCADO BURSÁTIL, arrojarán como resultado , el mismo precio.... De aquel, del punto de partida o comparación....

Dadas las tasas o tipos de interés de referencia y las primas por riesgo, en determinado punto en el pasado , no existe la posibilidad de "almuerzo gratis" ... La rentabilidad que se obtuvo en un periodo de tiempo, reflejó el costo del dinero y los riesgos del activo, atrás, cuando este activo se adquirió

Conceptualmente, tenemos para la renta variable o acciones:

Po =  P1+D1        en donde:    P1 =  P2+D2
        ---------                                   --------
          (1+ro)                                      (1+r1)


Po = precio de una acción en este instante, P1=precio de la acción en fecha posterior a Po en la que se paga dividendo, D1= dividendo que se paga en la misma fecha en la que ocurre P1, ro=la tasa de interés de mercado que existía en la fecha de Po , P2 y D2 = son el precio  y dividendo de referencias que ocurrirán en fecha inmediatamente posterior a P1 y D1, r1=la tasa de interés de mercado que existía en la fecha de ocurrencia de P1

Por qué esta fórmula y no aquella del modelo de crecimiento de Gordon?

La fórmula del modelo de Gordon tiene el inconveniente de que: el dividendo siempre se paga periódicamente en los mismos intervalos de tiempo y aumenta o disminuye siempre, en un factor constante o que tal dividendo permanence constante hasta el final de la vida de la Emisora

Ejemplo:

Grupo Energia Bogota SA ESP Dividend History (GEB)- Investing.com

Grupo Energia Bogota SA ESP Historical Price Data (GEB) - Investing.com

y usando precios de cierre....

el 29 de octubre de 2021, el precio de cierre = 2720 (Po), El 16 de diciembre de 2021: P1 = 2595 y D1 = 47,5 y el 27 de Mayo de 2022: D2 = 96 y P2 = 2280

Cuáles tasas usó el mercado para descontar precios y dividendos futuros, a los efectos de definir precios?

ro = -2,8492647058823529411764705882353% acumulado para 49 días o -0,0589753405538906% diario


r1= -8,4393063583815028901734104046243% acumulado para 163 días o -0,0540762416974316% diario

La iliquidez del mercado, la fuga de capitales, el cambio de GOBIERNO NACIONAL, la pérdida del GRADO DE INVERSIÓN del país, cambios en la oferta y demanda, nos arroja que la tasa de descuento caiga en terreno NEGATIVO

Pero qué ocurre si la Emisora no paga dividendos o no ejecuta recompras accionarias anuales?

La ortodoxia nos indica que la acción debe tasarse vía valoración de la Empresa o Corporación, usando el método de flujo de caja libre y descontado...

Las fórmulas expuestas arriba no son conmutativas, ni modulativas .... Los precios futuros NO DEBEN definirse como función de los precios del pasado....

Hasta la próxima!

Sources & Acknowledgements:  

www.its.caltech.edu/~cvitanic/PAPERS/All slides.pdf

Pricing Options with Mathematical Models | edX

THE SHARPE RATIO (OLD & NEW) IN THE GLOBAL MARKET

It has been more than a year since the latest article. Today, I will be explaining The Sharpe Ratio (old & new) when deployed within a global market, or if your investments, or a global corporation has assets in several currencies or several economies... 

1. Returns of your venture or ventures must be computed after converting past and current local values in US dollars... IRR or ROI must be a percentage after US dollars ... And likewise, the volatility must be computed with a us dollar base , the same you got for the average of your returns 

2. Under the old Sharpe ratio , there is the risk free ratio, there is one yield acceptable to compare all of your ventures ... You must go to the sovereign bond market, look for the 10 year market .... You should use as your risk free rate , that of the country with the lowest value....

For instance, 

 https://tradingeconomics.com/bonds 

3. Under the new Sharpe ratio , the risk free rate is dropped in favor of "the market return" ... Back in the day this was a huge hurdle ... Now your global market return rate could be this:

 https://www.cnbc.com/quotes/.WORLD 

4. if you are not an optimizer your formulas, under the old Sharpe ratio paradigm, will be: 

(Ra-Rf)/Sa , (Rb-Rf)/Sb , (Rc-Rf)/Sc against (MSCI-Rf)/Sm 

 where: Ra, Rb, Rc are the return rates in US dollars for assets/ventures a, b and c 

 MSCI is the return rate for the MSCI (Morgan Stanley Index) 

Rf is the return rate for the 10 year , lowest risk, sovereign bond (either the swiss or japanese bond) 

Sa, Sb, Sc are the standard deviations for the returns of assets/ventures a, b and c plus Sm, the standard deviation of the MSCI returns. 

 If your ratios are beating the market ratio.... You are fine .... 

5. Are you a daily optimizer of your assets? things are a bit different .... Your optimal portfolio return (never the standalone assets): Rp must be compared to a theoretical optimal MSCI portfolio. 

So thus: (Rp-Rf) / sp against (MSCI*-Rf) / sm 

where sp and sm are optimal standard deviations of the returns for optimal expected Rp and MSCI* 

 again, is your optimal sharpe ratio beating that of the market's optimal sharpe ratio? 

well, you are beating the global reference portfolio 

 6. Can I or any corporation make an outright comparison against the market??? YES!!! IN 1994, THE NEW SHARPE RATIO was born!!! 

7. What's the new deal or change in regarding the classic ratio? Well, the risk free rate as a benchmark is gone and the standard deviation of your asset or porfolio, too .... 

 The new formula for the ratio: (RP-MSCI) / TSD(RPt-MSCIt) 

 where: RP is you average asset, investment or optimal portfolio's return, MSCI is the local market or global portfolio average return and TSD(RPt-MSCIt) is the TARGET SEMIDEVIATION .... Such a target semideviation is the square root of a summatory of differentials among daily returns of your portfolio and the daily returns of your reference index or MSCI ... A modified definition of a standard deviation; the main difference: a standard deviation involves a constant, a population or sample mean .... 

TSD involves no constant.... 

8. How do you compute TSD numerically ??? 

 for a ten day period a global portfolio returns were: 0.05% , 0.1%, 0.2%, 0.3%, 0.4%, 0.5% , 0.6% , 0.7%, 0.8%, 0.9% 

 for a ten day period the MSCI returns were: 0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.7% , 0.8% , 0.9% , 1.0% 

 First, quadratic summatory of differentials: (0,0005-0,001)^2 + (0,001-0,002)^2 ... the remaining differentials are all equal to the second argument , summatory = 0.00000925, 

now our target semivariance = 0.00000925/10 = 0.000000925,  

our target semideviation = (0.000000925)^(1/2) = 0.000961769203083567 

 or in percentage = 0.096176920308357% 

 9. And the value for the new sharpe ratio would be??? before that we would need , the average return for each portfolio: (0.00455-0.0055) = -0.00095 so, the new sharpe ratio is equal to: -0.00095/0.000961769203083567 = -0.9878 (rounded) 

10....Buh, buh, but what can you conclude? YOU ARE NOT BEATING THE MARKET! probably, you are beating the reference risk free rate but not the MSCI nor the S & P 500 if you are all invested in the USA .

The old Sharpe ratio studies ventures in isolation .... While the new Sharpe ratio allows for integration into a single formula and the noise of the risk-free asset is gone.....

If you are a portfolio optimizer it is better if you consolidate your ventures as if they were a single asset ... It will be easier for computing deviations and differentials 

if MSCI is not your idea of a complete market (your ventures are not in the area covered) you can use S & P 1200 Global Index:

Download SPG1200 Data | S&P Global 1200 Index Price Data | MarketWatch

The above it is the most holistic and complete worlwide benchmark you can find , nowadays.... I used MSCI because it it the oldest of global indexes for shares activity

All yours.... 

Sources & Acknowledgements: 

https://web.stanford.edu/~wfsharpe/art/sr/SR.htm 

https://www.cmegroup.com/education/files/rr-sortino-a-sharper-ratio.pdf 

 

https://learn.canvas.net/courses/1772

The University of Chicago Booth School of Business

 

TEMPORARY STRUCTURE OF INTEREST RATES: THE 2 REGRESSION MODELS

Eviction Notice: This is going to be the last article I will be posting in a long time. I am devoted to get a DATA SCIENTIST badge and a not related diplomatic distinction.... 


There are several algorithms to compute the Temporary structure of interest rates.  Nowadays, computational models are closer to reality than "mathemagic" models. Usual "mathemagic" devices include: bootstrapping, splines, Nelson-Siegel function and polynomial interpolation.

For this article, the polynomial regression and cubic regression will be used as an alternative to the minimalist bootstrapping method and as it is suggested by International Monetary Fund.

Any given market will exhibit more than one treasury or sovereign bond per maturity term i.e. 1, 2, 3, 4,5,6,7,8,9,10,15,20,30 year bonds

So thus, bootstrapping method will left out vital information , even if you consolidate similar maturities into a single hypothetical bond per maturity.

Polynomial interpolation works as a holistic model, by integrating the market as an interdependent unit rather than a "given term" dependent on the shorter maturities... For instance:

https://docs.google.com/spreadsheets/d/11RtCOu7TrJIgXCO7AtEEwFui8x6tNiOd/edit#gid=438735182

As you can read there, on the upper part , there is the market price of the bonds for 13 years of maturities.  Beside, you are getting the face value and outstanding coupons.  You must make up a temporary structure of interest rates for 13 years.  Bearing in mind there are several bonds for a particular year.

Yup!  First you must run a polynomial regression whereas :  y = the current market price and the values for x = coupons and face value adding zeros if nothing happens.

if you are too lazy to write a code on a programming language or your spreadsheet is not supporting polynomial regressions... You can resort to this:

https://www.wessa.net/rwasp_multipleregression.wasp

The first column of data is going to be your Y (the spot market price)  and the following columns will be reserved for the values of X

if everything run fine, you will get the raw gross rates per term.  You will need to re write them in effective annual and percentage notation .

This first proxy is not the end of it all.  A second regression is still needed, to smooth the curve:

https://docs.google.com/spreadsheets/d/11RtCOu7TrJIgXCO7AtEEwFui8x6tNiOd/edit#gid=1014033820

But, such a regression is a cubic regression.  If you spreadsheet is not running a cubic regression or you are still lazy to write a code on a programming language...Yet, you can still resort to this:

https://www.wessa.net/rwasp_multipleregression.wasp

Whereas, your Y = the rates you got from the previous regression and your X = time to maturity to the power of 1, 2 and 3

What is the idea?

To get the values of a cubic, four argument, equation.  The constant alpha and 3 intercepts....

Once you have got the 4 constant values of this cubic equation... You can proceed to smooth the curve by plugging the variables which they are , time to maturity, known  beforehand, already

The new values for Y are going to be the final values , for your structure of interest rates....


WARNING:  in the same vein of bootstrapping method, polynomial interpolation fails to account for the negotiated volumes of each "treasury" .... In the case studied, there is an alleged equality in the market transactions of each "sovereign bond" or "treasury"


See You Soon!

Sources & Acknowledgements:  
International Monetary Fund & Alex Ho, PhD      https://www.edx.org/bio/alex-ho
Patrick Wessa, PhD     

PCA CORRELATION: A BRIEF INTRODUCTION TO DIMENSION REDUCTION (A Brute Force Mean Variance Standardization)

DISCLAIMER:  This blog's author is not a stakeholder of Chevron Texaco, nor this article is a formal and staid financial advice.

Have you ever wondered why covariance & correlation are so numerically different?   Can they converge?  On the following lines I will be explaining a crucial part of PRINCIPAL COMPONENT ANALYSIS: an early tool for dimension reduction and data noise removal.  The tool has more than 100 years, so,  in terms of today standards is obsolete and plenty of caveats.

The below URL displays prices for the CHEVRON-TEXACO share, high and low prices were taken into account against TEXAS WTI reference price, all of them in a spreadsheet:

https://1drv.ms/x/s!ApxRazJ7xJyUf9ZPugnE4Jenbuc


click on: CVX tab, there you will get amounts of raw data...What is the trick? 

1. I got continuously compounded returns, their average and their standard deviation

2. MEAN VARIANCE STANDARDIZATION ... Of those values, by resorting to this formula:             Z = (x - x̄) / s

3. Once you get your Z statistics, out of the returns; bear in mind that, the mean for a standard normal distribution = 0 and its standard deviation = 1.  So thus, COVARIANCE & CORRELATION values are the same for 2 data sets.

Now, click on: COVARIANCE-CORRELATION  tab, you will get products of 2 data sets: high & low returns, high returns & Texas WTI price change, low returns & Texas WTI price change.

2 dimensions are now 1 for numerical purposes.  For the particular case of CHEVRON TEXACO, There is strong positive correlation for the variations involving the highest and lowest intraday price returns...While the relationship of such returns is moderately positive against the changes on the Texas WTI reference price...

The company is, perhaps, not hugely affected by changes in the price of CRUDE OIL due to investment diversification...

CAVEAT:   By turning all of the values from your data sets into a standard normal distribution , we are assuming PERFECT NORMALITY .   No values falling out of the tails or black swans are part of the ensemble or they are assumed as PERFECTLY NORMAL.

To solve the above problem, Variation Autoencoders from the field of Machine/Deep Learning are a more accurate exit.  Mathematical Models are quite inferior to Data Models in terms of today technology.

Sources & Acknowledgements:  
Shingai Manjengwa from Fireside Analytics Inc.
Mikhail Lakirovich, Greg Filla, Armand Ruiz &  Saeed Aghabozorgi from IBM


https://www.tastytrade.com/tt/learn/correlation

A QUICK MARKET MODEL FOR A DISCOUNT RATE. UN MODELO RÁPIDO DE MERCADO PARA UNA TASA DE DESCUENTO.

An elementary market model for a discount rate has 3 arguments. / Un modelo elemental de mercado para una tasa de descuento tiene 3 argumentos. 

A risk-free rate, country risk premium and the asset/business risk premium (without liabilities). /  Una tasa libre de riesgo, prima de riesgo país y la prima de riesgo por activo/negocio (sin pasivos) .The country risk premium is all about macroeconomic figures and public money management / La prima de riesgo paìs es toda sobre cifras macroeconómicas y gestión de dinero público.

All of the above in coherence with modern and postmodern portfolio theories / Todo lo anterior en coherencia con las teorías moderna y postmoderna de portafolio.

Not so long ago, it was kind of cumbersome to compute the value to each component. No official market information was publicly released, compelling analysts to run esoteric calculations.
Hasta no hace mucho, era un tanto incómodo computar el valor de cada componente. Información oficial de mercado no era liberada públicamente, obligando a los  analistas a correr con cálculos esotericos.After the 2007-2008 credit crunch, market figures and perceptions MUST BE posted with an authority granting fully fledged status. /  Tras el crujido crediticio en 2007-2008, cifras y percepciones de mercado DEBEN SER publicadas con una autoridad concediendo status de pleno derecho.This is an example studying the fictional country named: "Costaguana" / Este es un ejemplo estudiando al país ficticio llamado: "Costaguana"

For practical purposes the risk free rate must be the inflation/deflation rate or an expectation of it. / Para propósitos prácticos la tasa libre de riesgo debe ser la tasa de inflación/deflación o una expectativa de esa.The tax authority in the Republic of Costaguana and after application of the new taxation act has set a free risk rate at 3.5% a year, though this is not a market rate, it is a fully fledged rate.  / La autoridad tributaria en la República de Costaguana y tras aplicación de la nueva ley impositiva ha establecido una tasa libre de riesgo en 3.5% al año, aunque esta no es una tasa de mercado, es una tasa de pleno derecho.

Now, the country risk premium.   This typically involves the target country and the less risky country in the world both rendered in US dollars, a substraction of the 10 year sovereign bond market rate between the target country and the less risky country in the world. / Ahora, la prima de riesgo país. Esto típicamente involucra el país objetivo y el país menos riesgoso del mundo ambos recreados en dólares americanos, una resta de la tasa de mercado del bono a 10 años entre el país objetivo y el país menos riesgoso del mundo.

WARNING: if you are working in US dollars and you want everything in local currency , a  conversion is mandatory. / ADVERTENCIA:  si estás trabajando en dólares americanos y quieres todo en divisa local, una conversión es obligatoria.Certain page states the country risk premium for Costaguana is 630, this is , 0.063.  / Cierta página estima la prima de riesgo país para Costaguana en 630, esto es, 0,063.

https://www.datosmacro.com/prima-riesgo/colombia

However, the above value is in US dollars, so you must use the proper currency appreciation or depreciation factor.  In Costaguana's currency and after an appreciation, this value translates to 0.0242. / Sin embargo, el valor anterior está en dólares americanos , entonces debes usar  el factor apropiado de apreciación o depreciación de divisa.  
En divisa de Costaguana y tras una apreciación, este valor se traduce a 0,0242.  Our domestic rate should be / Nuestra tasa doméstica debería ser 1.035*1.0242 =1.060047  = 6.00%


Recall , the country risk premium attacks the 10 year sovereign bond. Look at the rate for a domestic t-bond in Costaguana. Not so far from reality. / Acuerdate, la prima de riesgo país ataca el bono soberano a 10 años. Mira la tasa de un t-bono doméstico en Costaguana. No tan lejos de la realidad. 

https://www.grupoaval.com/wps/wcm/connect/grupo-aval/c642b108-5af8-4f22-82d4-9cf0787d4869/rentabilidad-cont.gif?MOD=AJPERES

The final component of this formula , it is the business/corporate risk , a personal premium including the sectorial risk. / El componente final de esta fórmula , es el riesgo corporativo/negocio, una prima personal que incluye el riesgo sectorial.  An oil and fuels company in Costaguana has its risk premium rated at 6 % a year / Una compañìa de petróleo y combustibles en Costaguana tiene su prima de riesgo tasada en 6% al año.

http://www.eleconomista.es/empresa/Ecopetrol/recomendaciones-consenso

So thus, the consolidated discount rate would be / Entonces asì, la tasa consolidada de de descuento sería:  1.035*1.0242*1.06 = 1.12364982 or/o 12,364982%
Such a rate is the minimum rate, potential investors would use to discount the one year future price and on the other side, this is the minimum rate that current owners would expect their equity to yield or the price of their shares to appreciate after one year / Tal tasa es la tasa mínima, los inversionistas potenciales usarían para descontar el precio futuro a un año y del otro lado, esta es la tasa mìnima que los propietarios actuales esperarían su patrimonio rente o el precio de sus acciones se aprecie en un año.

Any positive/negative return in excess is market noise.  A new rate is born daily. / Cualquier rentabilidad positiva/negativa  en exceso es ruido de mercado. Una nueva tasa nace diariamente.


Sources & Acknowledgements:  Professor Erik Simanis
https://www.plusacumen.org/courses/financial-modeling-social-sector

BASEL 3, CAPITAL ADEQUACY & Z-SCORES FOR FINANCIAL INSTITUTIONS. BASILEA 3, ADECUACIÓN DE CAPITAL Y MARCADOR Z PARA INSTITUCIONES FINANCIERAS

When Edward Altman developed his Z-Scores, he never outlined a framework for financial corporations nor financial institutions / Cuando Edward Altman desarrolló sus marcadores Z, él nunca describió un marco de trabajo para corporaciones financieras ni instituciones financieras.


International Monetary Fund developed some metrics to asses a probability of default but keeping in mind all the time BASEL 3 Ratio :  Regulatory Capital / Risk Weighted Assets (RWA), must be above or larger than 10.5% for Advanced Countries &   12% for Developing Countries /  El Fondo Monetario Internacional desarrolló algunas métricas para evaluar una probabilidad de incumplimiento pero manteniendo en mente todo el tiempo el convenio de BASILEA 3 y su razón:  Capital Regulatorio/ Activos de riesgo ponderado (RWA), la cual debe estar por encima o ser mayor de 10,5% para paìses desarrollados y 12% para países en desarrollo.


Regardless of the Z-Score, if the financial system as whole or a credit institution fails to fulfill such a capital adequacy requirement , the Bank Authority or Commission will ask for cash or very liquid assets to the current shareholders, if they refuse or there is not a third party willing to join as a new shareholder; this institution will face foreclosure and liquidation / Sin importar el marcador Z  si el sistema financiero como un todo o una institución crediticia falla en cumplir tal requirimiento de adecuación de capital, la Autoridad Bancaria o Comisión solicitará efectivo o activos muy líquidos a los accionistas actuales, si rehusan o no hay una tercera parte voluntaria de unirse como nueva accionista; esta institución encarará cierre y liquidación


IMF developed three metrics for three different Z- scores / FMI desarrolló tres métricas para tres diferentes marcadores Z


The first proxy is quite simple : Total assets-Total liabilities / Standard deviation of assets or Equity/standard deviation of assets , such value for the standard deviation must be an absolute number not a relative one /  La primera aproximación es bastante simple : Activo total-Pasivo total /Desviación típica del activo o Patrimonio/desviación típica del activo, tal valor para la desviación típica debe ser un número absoluto y no uno relativo.

This second proxy is the most holistic and the one you will need to compute a more realistic value:
(Regulatory Capital/Total Assets + ROA : Net Income after taxes/Average Assets) / Standard deviation of ROA .  All of theses values written on per currency unit.  / Esta segunda aproximación es la más holística y la que se necesitará para computar un valor más realista: (Capital Regulatorio/Activos Totales + ROA: Ingreso neto después de impuestos /Activos promedio)/Desviación Típica de ROA.  Todos estos valores escritos por unidad de divisa.

The Third and last proxy deals with equity, net income and RWA.  This is a worst case scenario
(Current Equity+Net income after taxes-(RWA))/Standard deviation of profits over n years. La tercera y ùltima aproximaciòn trata con patrimonio, ingreso neto y RWA. Este es el peor  escenario (Capital Actual+Ingreso neto despuès de impuestos-RWA)/Desviación tìpica de utilidades netas en n años.

Explanatory Material in English only:

https://courses.edx.org/assets/courseware/v1/ec19d6515cb62ffde0f887af575127e0/asset-v1:IMFx+MDSx+3T2017+type@asset+block@MDSx_M06_SLIDES.pdf

https://www.youtube.com/watch?time_continue=309&v=sml7fu7EBgE

Here , this spreadsheet belonging to IMF in English only:
https://drive.google.com/file/d/14NKKBOnS8rDNx9AW61DKLviMW3d3rvPW/view?usp=sharing

Tabs/Pestañas: Balance Sheet - K ,  Volatility & Summary Table

For such a fictional country system or third world financial institution , several of the parameters and rules of thumb are violated.   The system as  a whole or such a corporation should be taken over, or undergoing Bank Authority/Commission intervention / Para tal sistema de país ficticio o institución financiera de tercer mundo , varios de los parámetros y reglas de pulgar son violadas. El sistema como un todo o tal corporación deberían ser adquiridas hostilmente, o sometiendose a intervención de la Comisión/Autoridad Bancaria.









 
Sources & Acknowledgements: edx.org, Adolfo Barajas: Senior Economist at Institute For Capacity Development & International Monetary Fund

DIVERSIFICATION & HOME BIAS. DIVERSIFICACION Y SESGO DOMÉSTICO.

In terms of risk management, a well diversified portfolio or a portfolio applying 1 fund theorem or 2 fund theorem, will be more eficient than a one risky - higher return investment. /  En términos de gestión de riesgo, un portafolio bien diversificado o un portafolio que aplica Teorema de 1 fondo o Teorema de 2 fondos, será más eficiente que una inversión de alto riesgo y alta rentabilidad.


Due to transaction costs, barriers to capital mobility, double taxation and the risks of default, liquidity and currency; most managers prefer a 100% one currency portfolio.  Debido a los costos de transacción, restricciones a la movilidad del capital, castigos fiscales y los riesgos de quiebra, liquidez y divisa; la mayoría de gerentes prefieren un portafolio de 100% en una sola divisa.


With low transactions costs and no double taxation, the old Sharpe Ratio for a global portfolio excels the old Sharpe Ratio for a 100% home biased portfolio.  This is, the globally diversified portfolio or the 2 fund international portfolio will outperform the 100% one currency portfolio.  Con bajos costos de transacción y sin doble tributación, la razón vieja de Sharpe para un portafolio global supera la razón vieja de Sharpe para un portafolio sesgado al 100% en un solo país.  Esto es, el portafolio globalmente diversificado o el portafolio internacional de 2 fondos excederá el desempeño del portafolio al 100% en una sola divisa.https://www.imf.org/~/media/Websites/IMF/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14187.ashx

https://www.federalreserve.gov/pubs/ifdp/2001/702/ifdp702.pdf

www.bis.org/repofficepubl/arpresearch_fs_200712.03.PDF

www.imf.org/external/pubs/ft/gfsr/2007/01/pdf/text.pdf

https://www.imf.org/external/pubs/ft/wp/2012/wp1229.PDF

Technical aspects/ Aspectos Técnicos:


1. All of the target assets, their prices, must be rewritten in a common currency.  Using an official Exchange rate. / Todos los activos objetivo, sus precios, deben ser reescritos en una divisa común.   Usando una tasa de cambio oficial.


2. After the Price transformation, we can proceed to compute returns , variances, standard deviations and covariances. / Tras la transformación de precios, podemos proceder a computar rentabilidades, varianzas, desviaciones típicas y covarianzas.


3. We will need prices correlations, anyways. To discard positive correlated assets, strongly  /  Necesitaremos correlaciones de precios, de todos modos.  Para descartar activos correlacionados fuertemente positivos.

4. We will compute the  Securities market line or the efficient old Sharpe Ratio for our asset selection.  / Computaremos la línea del mercado de capitales or la razón Sharpe vieja eficiente para nuestra selección de activos.

5.  If any combination of 2 assets yields a higher value for the old Sharpe Ratio, there is no need to buy the whole market .   Unless the assets under management be millions or more, we will have to dillute our asset allocation to no more of 10% on each asset; funds engaged in high frequency trades invest no more than 1% of the money under management per asset.  / Si cualquier combinación de 2 activos rinde un valor más alto para la razón Sharpe vieja, no hay necesidad de comprar todo el mercado.  A menos que  los activos bajo administración sean millones o mas, tendremos que diluir nuestra colocación de activos a no más de un 10% en cada activo; los fondos enganchados a compraventa de alta frecuencia invierten no más de un 1% del dinero bajo administración por activo.

Sources & Acknowledgements:  Adolfo Barajas, Christian Johnson, Evan Tanner at International Monetary Fund.

CORPORATE FINANCE & COMPUTATIONAL FINANCE: THE PROBLEM OF SCALABILITY/FINANZAS CORPORATIVAS Y FINANZAS COMPUTACIONALES: EL PROBLEMA DE ESCALABILIDAD

Financial or Ratio Analysis provide us with a lot of information , in regarding , the health of a Company or a Venture, which we might be interested to invest in.  El análisis financiero o de razones, nos provee con mucha informaciòn, en consideraciòn , la salud de una Compañìa o vehìculo de riesgo, el cual podrìamos estar interesados en invertir.


Out of all ratios, the most relievant, it is not one computed from fundamental down and accross Analysis.  De todas las razones, la màs relevante, no es una computada desde el Anàlisis fundamental vertical y horizontal.

When I was still a bachelor student, the discussion was still in diapers.  Industrial & Operation Engineers, some Accountants and Microeconomists were radical about SCALABILITY or marginal income, marginal costs and marginal. utility.  Cuando yo aùn era un estudiante de pregrado, la discusiòn estaba aùn en pañales.  Ingenieros Industriales  y Operaciones, algunos  Contadores y Microeconomistas eran radicales acerca de ESCALABILIDAD o ingreso marginal, costo marginal y utilidad marginal.


What is SCALABILITY in simple words?/Qué es ESCALABILIDAD en palabras simples?
It is the skill a management team deploys to keep growing revenue above the rate at which costs & related expenditures grow.  Es la habilidad que un  equipo gerencial despliega para mantener creciendo los ingresos por encima de la tasa a la cual costos y gastos relacionados crecen.

The problem:  It seems markets are not punishing shares traded at exchanges, in particular , the potential buyers. El problema: Parece que los mercados no estàn castigando acciones negociadas en bolsas, en particular, los compradores potenciales.

The case:  July 1, 2015.  A share market's price is: 17.40.  2 dividends paid out:  On april 29 and june 30, 2016, they are worth 0.45 and 0.44.  On june 30 2016, the market price is 18

El caso: Julio 1, 2015. El precio de mercado de una acciòn es: 17,4.  2 dividendos pagados: En abril 29 y junio 30, 2016, ellos valen 0,45 y 0,44.  En junio 30, el precio de mercado es 18

After running Professor P.C. code on R/Tras correr el còdigo del Profesor P.C. en R :

f=function(y) 0.45*exp(-304*y)+18.44*exp(-366*y)-17.4
uniroot(f,lower=-4,upper=4)  

and after applying interpolation correction/ y tras aplicaciòn correcciòn por interpolaciòn:

y or the daily discount rate is / y o la tasa de descuento diaria es : 0.000225403472 continuously compounded / compuesta continua.   Daily compounded/Diaria compuesta: 0.00022542887727

You can use goal seek to solve this .  Summing up all of the upcoming cash flows in a single cell and the target value will be the price, one year ago..../ Puedes usar Goal Seek para resolver esto. Sumando todo en una celda y el valor objetivo serà el precio, de hace un año.
For an EAR / Para una tasa anual efectiva:  8.575138416625%  on an ACT/ACT date basis.

From INCOME STATEMENT, the marginal income from 2015 and 2014 was/Del ESTADO DE RESULTADOS, el ingreso marginal entre 2016 y 2014 : 35836112000 and the marginal costs/ y los costos marginales : 35853303000.  For a marginal profit /Para una utilidad marginal : -17191000

If we are at the buying side, how are we punishing the current shareholders?  / Si estamos del lado comprador, còmo estamos castigando a los accionistas actuales ?Out of the dividends, we must account this marginal value / Fuera de los dividendos, debemos contabilizar este valor marginal.

At shareholders' meeting , it was approved dividends grossing/En asamblea de socios, fue aprobado, dividendos engrosando  : 16619 millions / millions.

 We could punish this value by substracting "scalability" / Podrìamos castigar este valor sustrayendo "escalabilidad":  16601809000The number of outstanding shares / El nùmero de acciones en circulaciòn: 18,672,822,217

Punished dividend per share /  Dividendo castigado por acciòn:   16,601,809000/18,672,822,217

=  0.88 (it could be 0.89 but to add some drama , let's drop it 1 cent/ puede redondearse a 0,89 pero para darle algo de drama, bajèmolo un centavo)

The new price / El nuevo precio :   0.44*exp(-304*0.000225403472)+18.44*exp(-366*0.000225403472)= 17.39

Could you figure out if negative scalability is even worse? / Pueden imaginar si esta escalabilidad negativa fuera aùn peor?

Why are we punishing twice? / Por què castigamos 2 veces? We are punishing current shareholders for allowing ongoing inefficiences /Castigamos a los accionistas actuales por permitir ineficiencias continuadas.



Sources & Acknowledgements:  Professor Simon Stockley, Professor Gad Allon, Professor Jan A. Van Mieghem & Professor Pasquale Cirillo. 

ACCOUNTING RETURNS WITH A DIVIDEND/CONTABILIZANDO RENTABILIDADES CON UN DIVIDENDO

If you are holding a share with regular dividend payments, accounting for returns could be a problem.  Si eres el titular de una acción con pago regular de dividendos, contabilizar las rentabilidades podría ser un problema.

 04-01- 2016   0.83

03-31-2016  0.83

03-31-2016  0.83 + 0.02625

03-30-2016 0.87
 
03-29-2016 0.87

03-28-2016 0.88
From the above, you are noticing a value 0.02625 This is a dividend. De lo de encima, estás notando un valor de 0,02625 Este es un dividendo.






You are noticing 1 date accounted twice. Estás notando 1 fecha contabilizada dos veces.


The daily returns for this example are as follows...Las rentabilidades diarias para este ejemplo son como sigue...

 
 04-01- 2016   0 %

03-31-2016  -1.58%
03-30-2016 0%
 
03-29-2016 -1.136%

For April 1, we use an ex-dividend price of yesterday .  For March 31, we use a price embedding such a dividend.  Para Abril 1, usamos un precio ex-dividendo de ayer . Para Marzo 31, usamos un precio incorporando tal dividendo.

A QUICK GUIDE TO REAL OPTIONS/UNA GUIA RÁPIDA A LAS OPCIONES REALES

Real Options are financial options traded OTC whose underlying asset is a business operation; not shares, not raw materials...

Falling into the family of american styled options/Cayendo dentro de la familia de opciones al estilo americano...

Las opciones reales son opciones financieras transadas cara a cara y a la medida cuyo activo subyacente es una operaciòn de negocio; no acciones, no materias primas...Commonly used, three types of real options/Comúnmente usadas, tres tipos de opciones reales:

1. Option To Invest/Opción De Invertir: 
*A call option/una opción de compra
*Exercise Price/Precio De Ejecución: The up-front investment required when you decide
  to go ahead with the project/ El monto desembolsado de contado y mìnimo    
  necesario para iniciar operaciones.
*Value Of The Underlying Asset/Valor Del Activo Subyacente: Present Value of the net
  cash flows from operating the project/ Valor Presente de los flujos de caja netos de la             operación del proyecto.
*Premium/Prima:  What was/will be necessary to spend to establish the option (licenses,   
  legal paperwork, fares) / Lo que fue o será necesario gastar para establecer la opción   
  (licencias,  papeleo y tarifas de tramitación)


2. Option To Expand/Opción De Expandir:
*A call option/una opción de compra
*Exercise Price/Precio De Ejecución: All of the costs involved in the expansion/Todos los 
  costos involucrados en la expansión.
*Value Of The Underlying Asset/Valor Del Activo Subyacente: Present Value of the incremental net cash flows from expanded operations/Valor presente de los flujos de caja incrementales netos de las operaciones expandidas.
*Premium/Prima:  What was/will be necessary to spend to establish the option (empty space purchase, licenses, legal paperwork, fares) / Lo que fue o será necesario gastar para establecer la opción (espacio vacío, licencias,  papeleo y tarifas de tramitación)

3. Option To Abandon Operations/Opción De Abandonar Operaciones:
*A put option/una opciòn de venta*Exercise Price/Precio De Ejecución: The salvage value of the assets that can be sold upon 
  abandonment/El valor de salvamento de los activos que pueden ser vendidos antes de la 
  fecha del abandono total.*Value Of The Underlying Asset/Valor Del Activo Subyacente: Present Value of the net 
  cash flows from continued operations/Valor presente de los flujos de caja netos de 
  proseguir con las operaciones. 
*Premium/Prima:  What was/will be necessary to spend to establish the option (taxes, fines,   legal paperwork, fare) / Lo que fue o será necesario gastar para establecer la   
  opción (impuestos, multas,  papeleo y tarifas de tramitación)


EXAMPLES:
The present value without the option is $10 million, the present value of the
decision tree with the option is $12 million and the cost of expansion is $2m to be paid in 5 years. The discount rate is 10% per annum. What is the exercise price of the embedded option?
Answer: $2 million (simply, the PV of CAPEX to expand)

The present value with the option is $10 million, the present value of the decision tree without the option is $8 million and the estimated salvage value of assets is $2m to be received in 5 years. The discount rate is 10% per annum.   What is the option's premium ?
Answer: $2 million (10-8)
The present value of the decision tree without the option is $9 million, the present value of the decision tree with the option is $11 million and the cost of expansion is $1m to be paid in 5 years. The discount rate is 10% per annum. If the up-front payment required is $11.5m with the option embedded or $8.5m without the embedded option – what would your investment decision be?
Answer:  Invest in project without embedded option (10-11.5 = -0.5  but on the other hand 9-8.5= 0.5)

Five years ago,  "Magenta nipples Ltd"  purchased a block of land to establish manufacturing operations. They spent $1.2 million for the 4 acres of land, which was significantly larger than what they needed to conduct operations at the time. In fact they could have gotten away with spending only $800,000 on a smaller parcel of land. Now they are considering building a new factory on the site in response to an increase in demand for their product. It will cost them $300,000 to construct the new buildings on the previously unused part of their land parcel.

 What was the price paid for the option? $400.000 (1,200,000-800,000)

What is the exercise price of the option? $300.000  (present value of the cost to expand)

Acknowledgements: Sean Pinder & Paul Kofman from The University Of Melbourne
Sources: Bank Of New York-Mellon, Wikipedia, Coursera.org 

A RUBE GOLDBERG & HEAT ROBINSON APPROACH TO PRICE CORPORATE BONDS: ALTMAN Z-SCORE

A quick and dirty formula to price corporate bonds/notes might be given by the following formula:

rf / PS  (it looks like a KLUDGE or some sort of MacGyverism)

rf is the market risk free rate as read from the Temporary Structure Of Interest Rate or Yield Curve.  PS is the probability of success for the Corporation or (1-Probability Of Default)

This is the catch!   Probability of Default or Probability Of Success is not easy to get.  You will need to run an algorithm entitled: Altman Z-Score (by Professor Edward I. Altman) with the following figures belonging to a "Columbian" Corporation listed on BVC:

Working Capital=333,060,600

Total Assets=1312,650,600

EBIT=117,550,800

Sales=2546,934,000

Market value of equity is :744,488,400

Total Liabilites:  470,203,200

Retained Earnings: 587,754,000

T₁ = Working Capital / Total Assets

T₂ = Retained Earnings / Total Assets

T₃ = Earnings Before Interest and Taxes / Total Assets

T₄ = Market Value of Equity / Total Liabilities

T₅ = Sales/ Total Assets

Z score bankruptcy model:

Z = 1.2T₁ + 1.4T₂ + 3.3T₃ + 0.6T₄ + .999T₅

Zones of Discrimination:

Z > 2.99 -“Safe” Zones

1.81 < Z < 2.99 -“Gray” Zones

Z < 1.81 -“Distress” Zones

The Altman Z-Score is a Gaussian statistic and for this corporation  =  4.11522388059702.  This means a probability of success = 0.999980659810466  (you can use NORMSDIST function embedded on any spreadsheet to get this value)

The very same day these Financial Reports were issued, the "Columbian" yield curve for a 10 year Bond is 7.84%   after applying our formula and if we want to issue our Corporate Bond our cost would be 7.8402%

Is this cost a straight jacket or alluring to investors?  maybe not!  you have to compare this one to the cost you would face if you were taking a loan from a bank or an ensemble of them.  So thus, the coupon rate of your bond could be defined by the following interval [rf, ActiveRate]

After all, other than full control and a lower cost of corporate debts you are looking for an arbitrage opportunity.  The cheapest bank in this country is paying on a 10 year CD 8% and for a 10 year loan is collecting 16% a year...Our new coupon rate would be 0.08/0.999980659810466 = 8.000154725%

Either a bank or the yield curve.  The day this debt is issued to be market traded, the market's discount rate will be higher than your coupon rate...Beware of not selling your bonds at a discount rate near or above the cost of a loan from any Bank....

WHAT IF?   By using the yield curve the key reference rate is negative? No problem, at least one of the rates per maturity will be positive....We can use this one to build our Yield curve by applying calculation of the short rate curve

Acknowledgements: Edward I. Altman from NYU & Pasquale Cirillo from TU Delft
Sources: RiskCenter, Investopedia, Wikipedia, EdX.org, Coursera.org

COMPUTATIONAL FINANCE: Internal Rate Of Return for uneven cash flows (The Time Lags).

You wanted to know what was the return of a share last year, but you can not compute it due to dividends?

This is basically a problem of computational finance not one of Economics Engineering nor Financial Mathematics.

There is R, an excellent programming language if you are dealing with statistics and data science....

The following algorithm and source code is a courtesy of Professor Pasquale Cirillo:

#f=function(y) D1*exp(-t0.5*y)+D2*exp(-t1*y)+D3*exp(-t1.5*y)+PT*exp(-T*y)-P0

#uniroot(f,lower=j,upper=k)

This uniroot function is crucial and of capital importance when you are writing the upper and lower values

The following example will clear this up :

On december 18, 2013.  You bought a share of Stock Exchange.  The next 3 dates are dividends and the last date is when you are closing your position...

21.6    18/12/2013
0.78    30/04/2014
0.32    27/06/2014
0.32    31/10/2014
19.2     17/12/2014

Computer work:

f=function(y) 0.78*exp(-133*y)+0.32*exp(-191*y)+0.32*exp(-317*y)+19.2*exp(-365*y)-21.6
uniroot(f,lower=-1,upper=1) 

Your Work:

y=-0.000152587.  This is a daily rate in continuous time .  Year rate= y*365, exp^(-0.055694255)=0.9458283   =>  -1 = -0.0541717

effective rate: -5.41717%

What if...   uniroot(f,lower=-2,upper=2) or -1 and 0 ??

y=-0.0001220703.  This is a daily rate in continuous time. Annual = -0.0445556595
Converting to discrete time =0.9564224-1 = -0.0435776  => -4.35776%

By using a year scale instead of a day scale, the yearly continuous rate is: -0.048047, so thus:
0.953089-1 =-0.046911.  This is -4.6911%

By using interpolation.  Our daily continuous rate is: -0.0001316 or -4.8034% per year but in discrete time this translates to:  -4.68986189% per year


Your effective IRR will be the third computation....These algorithms can be deployed to compute rates for ventures and other financial vehicles with not regular events

Sources: Pasquale Cirillo at TU Delft and R
              http://pbil.univ-lyon1.fr/Rweb/Rweb.general.html  (online computations)

FINCA RAIZ: VISIÓN ECONÓMICO-CONTABLE, VISIÓN MONETARIA Y VISIÓN FINANCIERA

Tasar finca raíz, en particular propiedad horizontal, en su precio justo, al menos en teoría; es y será historia de nunca acabar.

En las siguientes líneas se desarrollarán 3 modelos para valorar inmuebles, que casi siempre arrojan resultados irreconciliables, dados los criterios para determinar el valor presente de tales activos.

Los 3 modelos aquí expuestos se fundamentan en pasado, presente o futuro.  Sin híbridos o sin tocar límites de los otros.

->Desde una perspectiva económico-contable, es decir, el pasado.  El valor de un inmueble vendría determinado por el último valor de transacción ajustado por las valorizaciones y correciones efectuadas por el instituto catastral u oficina de predios.

Ejemplo: si se compra un inmueble directamente al constructor y el valor de transacción fue de 1000 y han pasado 5 años en los que las valorizaciones oficiales a objeto de determinar el impuesto de bienes inmuebles o de predios, han evolucionado así: 5%, 20%, 30%, 10% y 8%.  La valorización acumulada sería: 1.05*1.2*1.3*1.1*1.08=1.945944 o 94.5944%  y el precio teórico justo: (1000-depreciaciones)*1.945944 < 1945,944

->Desde una perspectiva financiera, es decir, el futuro.  El valor de un inmueble vendría determinado por los alquileres que podría generar a futuro y las valorizaciones futuras en dinero de hoy. Incluyendo el valor residual o de remate de la propiedad, según se pueda deducir de la información fiscal.

En el caso anterior, suponga que las rentas anuales del inmueble son de 60 anuales y las valorizaciones de 10 anuales .  Sin incrementos por inflación u oferta/demanda. Aplicando la fórmula de Myron Gordon (GGM) y asumiendo un costo del capital del 12% anual, tendríamos:

70/0.12= 583,333333   a este valor hay que sumarle el valor residual/de remate del inmueble hoy día, que puede ser el mismo valor comercial catastral o el determinado por la oficina de predios y que es de 1000

Lo cual nos arroja un total de 1583,33333

->Desde una perspectiva monetaria, se esperaría una conciliación de las dos posturas anteriores.  El presente determina el aquí y el ahora. No hubo un antes, ni va a haber un después.  El valor de un inmueble queda determinado por la oferta y demanda: inventarios disponibles, número de posibles compradores, cantidad de dinero en la economía  y capacidad de endeudamiento.

Ejemplo no numérico:  suponga que en el microcosmos económico de la ciudad R, la cantidad de dinero es M, la cantidad de inmuebles para la venta es I y el nivel de precios es P.

Si por emisiones de la autoridad monetaria o un aumento en la inversión directa la cantidad de dinero aumenta a M+,  al igual que el número de demandantes y la cantidad de inmuebles para la venta sigue siendo I , es más que claro que P tendría que aumentar.

Por el contrario, si hay fuga de capitales o contracción de la base monetaria y ahora hay M- e igualmente baja el número de demandantes, e I sigue en la misma cantidad, es más que claro que P ha de bajar.

Fuentes: Perry Mehrling de Barnard College y Walter Bagehot: Lombard Street.

STANDARD DEVIATION (DESVIACIÓN TÍPICA) : FROM CONTINOUS TIME TO DISCRETE TIME (DE TIEMPO CONTINUO A TIEMPO DISCRETO)

Heteroskedacity is a problem when we are handling time series data. La discontinuidad en la periodicidad de los datos en las series temporales resulta ser un problema de manipulación. Continous time transformation is needed. Transformación en tiempo continuo es necesaria.  Example (Ejemplo) :

Given the following 10 intraday share prices, what is the standard deviation of the return rates? Dados los siguientes 10 precios intradía, cuál es la desviación típica de las tasas de rentabilidad ?

From last to first, Del último al primero: 3700 , 3740 , 3735 , 3800 , 3735 , 3790 , 3695 , 3705 , 3875 , 3865

AS IS (rates) , COMO TAL (tasas):  0.9893 , 1.0013 , 0.9829 , 1.0174 , 0.9855 , 1.0257 , 0.9973 , 0.9561 , 1.0026

These rates must be turned into continous time rates by using natural logarithm: ln.  Estas tasas deben ser convertidas a tasa en tiempo continuo, usando logaritmo natural: ln.  

-0.0107 , 0.0013 , -0.0172 , 0.0172 , -0.0146 , 0.0254 , -0.0027 , -0.0449 ,  0.0026

We can now apply the classic formula for a sample.  Podemos aplicar ahora la fórmula clásica para una muestra.

STD = 0.0205730233503667  This is a value in continuos time... But reality is nearer to discrete time.  Este es un valor en tiempo continuo... Pero la realidad  es más cercana al tiempo discreto.

e^μ * (e^σ^2 -1)^(1/2)  1 period transformation (fórmula de transformación para un periodo)  

 If (si) μ = -0.00484765137657851 , e = Euler's number (número de Euler) ,σ = standard deviation in continous time (desviación típica en tiempo continuo)

STD in discrete time (en tiempo discreto) = 0.0204757003886505

What is the conceptual difference? Cuál es la diferencia conceptual ?While under continous time, we calculate a standard deviation for a n number of data; under discrete time we have got a standard deviation for an elapsed number of time units.

Mientras que bajo tiempo continuo, calculamos una desviación típica para un número n de datos; bajo tiempo discreto conseguimos una desviación típica para un número transcurrido de unidades temporales. 

Here is the formula for a cumulated, discrete time, standard deviation.  Aquí la fórmula para una desviación típica, acumulada y en tiempo discreto.
e^μ*T * (e^σ^2*T -1)^(1/2) multiperiod transformation

Help yourselves by solving for a 15 day cumulated value.  Sírvanse ustedes mismos, resolviendo para un valor acumulado a 15 días.


Sources/Fuentes: John Cochrane. The University Of Chicago. Asset Pricing.

TASAS DE INTERÉS 7 (INTEREST RATES): TASA AL CONTADO (SPOT RATE), TASA INSTANTÁNEA (SHORT RATE), TASA A FUTURO (FORWARD RATE), SWAP RATE

Warning: spot rates are calculated by employing Central Bank Treasuries only. So therefore, the first spot rate is the Internal Rate Of Return of such a theoretical zero coupon treasury, the following spot rates -on the yield curve- undergo a bootstrapping process.  Precaución: las tasas de interés al contado se calculan empleando títulos del Banco Central únicamente.  Entonces y por lo tanto, la primera tasa al contado es la Tasa Interna De Retorno de un teórico título sin cupones, las tasas al contado siguiente -sobre la curva de rendimientos- se someten un proceso de iteración/recálculo.


La siguiente es la información después de un día de operaciones en el mercado de renta fija en términos anuales.  The following information is given by the fixed rent market after an annualized trading day (Oct. 11, 2012):

Fecha de vencimiento/                  Spot Rate/Tasa al contado (annual effective):
Maturity Date:

          Feb. 15, 2013                                                        0.1250782%

          Aug. 15, 2013                                                       0.3967851%

         Feb. 15, 2014                                                        0.4751252%

         Aug. 15, 2014                                                       0.5253753%

         Feb. 15, 2015                                                        0.5163284%

         Aug. 15, 2015                                                       0.4922074%

         Feb. 15, 2016                                                        0.3917654%

         Aug. 15, 2016                                                       0.537439%

         Feb. 15, 2017                                                        0.8889277%

Para títulos emitidos por el BANCO CENTRAL.  For "treasuries" issued by the Central Bank.

Cuál es la curva de Tasas Instantáneas?  What is the Short Rate curve ?

Time to maturity in years/Plazo al vencimiento en años: 0.3479452, 0.8438356, 1.3479452, 1.8438356, 2.3479452, 2.8438356, 3.3479452, 3.8465753, 4.3506849 

Habrá que reescribir las tasas de descuento en semestre efectivo y no año efectivo/ You will have to rewrite the rates in effective semesters and not years

La primera tasa instantánea es igual a la primera tasa al contado/The first short rate is equal to the first spot rate:  0.0625195% per semester or 0.0435026% until maturity.  r(0,1)

r(1,2) =  (1.001981961^2 / 1.000625195)-1  =   0.334057%  per semester or 0.2910886% per time fraction

r(2,3) = 0.305232% per time fraction or 0.315497% per semester 

r(3,4) = 0.3277799% per time fraction or 0.337568% per semester

r(4,5) = 0.2433175% per time fraction or 0.239787% per semester

r(5,6) = 0.1873067% per time fraction or 0.185672% per semester

r(6,7) = -0.087239% per time fraction or -0.104445% per semester

r(7,8) = 0.7555578% per time fraction or 0.7785148% per semester

r(8,9) =  1.804683% per time fraction or 1.855504% per semester
The short rate curve tells us the market expectation and the expected value for the 3 month rate in 3, 6, 9, 12 months from now and so on OR the annual effective rate in 1, 2, 3, 4 years and so on...../La curva para tasas instantáneas nos dice la expectativa del mercado de un periodo a otro y el valor de la tasa a 3 meses en 3, 6, 9, 12 meses desde ahora y en adelante O la tasa efectiva anual en 1, 2, 3, 4 años y en adelante ... Ahora la curva de tasas a futuro.  Now the forward rate curve.

f(1,2) = 0.3340567% semester ;  f(1,3) = 0.324776% semester ; f(1,4) = 0.329040% semester

f(1,5) = 0.306719% semester ;  f(1,6) = 0.282498% semester ;  f(1,7) = 0.217904% semester

f(1,8) = 0.2978% semester ;  f(1,9) = 0.491202% semester

f(1,9) = (1.004434805^9/1.000625195)^(1/8)  -1

These are the expected spot rates in 0.6958904 semesters, there is no forward rate for nine semesters.  Estas son las tasas al contado esperadas en 0.6958904 semestres, no hay tasa futura para nueve semestres.

Swap rates or spreads. Tasa swap o márgenes diferenciales:

Given an 8 semester forward rate and an 8 semester spot rate.  (0.491201 - 0.2683594)*100  =  22.28416 bps.  Dada una tasa a futuro para 8 semestres y una tasa al contado para 8 semestres....


Sources/Fuentes:  www.oup.com/us/ppt/derivatives/DMCH13.ppt (David Dubofsky & Thomas Miller)
-Finance By Kay Giesecke from Stanford University
-Financial Engineering & Risk Management By Martin Haugh & Garud Iyengar from Columbia University

BUDGETS & OTHER FORECASTS: DCF ANALYSIS TO APPRAISE DIFFERENT PROJECTS (BANG FOR THE BUCK)

Net Present Value is widely deployed to perform contrast and comparison among projects, proven the discount rate, the life expectancy and the initial investment value are all the same.

Could I use discount cash flow (DCF) analysis to appraise projects with different discount rates, amounts and life expectancies??? YES! But with a twist....

Remember? COST-->BENEFIT or the old fashioned ratio: BENEFIT/COST??

Read the following projects:

year/project	A	B	C	D	E	F	G	H
0	-2000000	-10000000	-10000000	-10000	-110000	-17200	-1000000	-350000
1	1000000	4000000	0	300	25000	10000	200000	35000
2	1200000	4000000	0	500	25000	10000	206000	35000
3	1400000	5000000	14000000	1200	25000	10000	212180	35000
4				2000	25000	10000	218545,4	42000
5				2000	25000	10000	225101,76	42000
6					25000	10000	231854,81	42000
7					25000	10000	238810,46	42000
8					25000	10000	245974,77	42000
9					25000	10000	253354,02	42000
10					25000	10000	260954,64	42000
11						10000	268783,28	42000
12						10000	276846,77	42000
13						10000	285152,18	42000
14						10000	293706,74	42000
15						10000	302517,94	42000
16						10000	311593,48	42000
17						10000	320941,29	42000
18						10000	330569,53	42000
19						10000	340486,61	42000
20						10000	350701,21	42000
21								42000
22								42000
23								42000
24								42000
25								42000

These are the free cash flows for every venture. Each of them has a unique market discount rate above the Cost of Capital related to our Investment Bank.....What is/was the best project overall??

"The Bang For The Buck" is the answer.....The discount rates are as follow (%): 4, 4.1, 4.2, 4.5, 5, 10, 8, 10

We know the present value for CapEx, Costs and Investment. Now we need the present value for the net cash income.....They must be read as :

A= 3315600.82 , B= 11965766.65, C= 12374420.65, D= 14061.80, E= 193043.37 , F= 85135.64 , G= 2450008.29     H= 2144175.17 and now: the ratios of efficiency:

A= 1.65780041, B= 1.196576665, C= 1.237442065, D= 1.40618, E= 1.7549397273, F= 4.949746349, G= 2.450008290, H= 6.126214771 Why investment F has the same discount rate than investment H? Although, F life is shorter than H, F is a high tech venture while H is a monopolic public transport service
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NOW, HOW TO DRAW A BUDGET: In most countries, forecasting the last financial statements by using Customer's Price Index rate of change is bylaw.....There is a major flaw: this rate is an average of the economy as a whole, so it might no mirror the change rates of your business....The alternative: Ground Zero Budget

The author's favorite method:

1. You should calculate the historical geometric average for the change rate of your incomes (both operational and non operational)

2.Apply down analysis to calculate the share for costs, expenses, profit/loss

....Now you can forecast these variables and to draw an income statement with an expected profit/loss

3. The expected profit/loss goes to the EQUITY section on the Balance sheet and again ....based on historical calculations you must apply down analysis to draw the pending values for the accounts on the equity section and the accounts on the LIABILITIES SECTION....The share for each account and subaccount are defined by the arithmetical average of previous years

For example: total income for your company last fiscal year was $150 million.....The historical geometric average for the change is 15% a year

Total operational costs, CapEx and non operational Expenditure. Down Analysis tells us that the historical average weight of them is 80%

150*1.15 = 172 .5 expected total income for next year and 172.5 * 0.8 = 138 the total expected costs, CapEx and non operational expenditure (taxes have been discounted, already)

expected net profit = 34.5 Down analysis tells us that the historical average weight for profits is 50% of the equity

expected equity = $69 millions down analysis tells us that the historical average weight of equity on the financial structure for this company is 70%

liabilites are 30% = expected $29.57 millions

total asset : $98.57 millions

See you around!

Sources: Kay Giesecke, Dmitry Smelov, David Luenberger, Jorge E. Burbano, Alberto Ortiz & Stanford U.