Friday 5 November 2021

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