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.