Saturday, May 5, 2018

Markowitz efficient frontier : backtesting.

The aim of the analysis is to build the efficient frontier that compares the average return (y) to the risk or standard deviation (x) of the top 100 Italian stocks (the market cap is the proxy of the size). Secondly, I will build one hundred portfolios (each portfolio is composed by one stock and each stock has the same weight, for simplicity), by decreasing order of best risk-reward ratio.
Thirdly, I will test the following assumption : the order of best risk-reward ratio should be the same also for the future performances (at least, substantially). 
In this way, the third step will be the backtesting that will cover a medium/long time frame, for obvious reasons and it will be a continuous updating.

The time frame of the past returns is 5 years : it means sixty returns (monthly returns), from April 30, 2013 to April 30, 2018. The source of the data is the following (historical data) :
The source of the stock screener is the following : Stock Screener -

About the data, I converted the monthly returns into annual returns, for greater significance. 

Average Return (annual) = Average Return (monthly) * 12
Standard Deviation (annual) = SQRT [(Standard Deviation (monthly) )^2*12]

So, I adjusted the return for the risk (Standard Deviation), through the following formula : 

Risk Adjusted Return = Average Return / Standard Deviation

Finally, I ranked the stocks, according to the abovementioned ratio (best risk-reward ratio). 
For simplicity, I built ten groups, always respecting the previous order. 
According to the portofolio theory (please consult the links : Markowitz efficient frontier ; images), the best stocks are those with the best ratio : they offers a greater return, given a risk rate or they offers a lower risk, given a return rate. Then, we have the following assumption : the expected returns and the expected risks are based on the past data. Of course, this is a limit and the aim of the analysis is also to implement a backtesting and to test the assumption. 

The following chart shows the efficient frontier. 

The following tables show the ten groups, by decreasing order of best risk-reward ratio (--> ranking).

In the future, I will test the assumption, as mentioned. The stocks with good past performance (with given risk) should outperform the others.