Practical Portfolio Optimization with Python - YouTube

hello everyone and welcome to the pythoninvest.com  youtube channel today we will talk about the  

practical portfolio optimization so let's assume  you have a sum sum of money and you want to invest  

into several stocks you may want to get an  optimal split of weights for your investments  

why are going to do this a smart portfolio  management can reduce the overall risk portfolio  

can increase returns per units of risk and  can reduce losses in the worst case events  

we will use this standard library by portfolio  opt you can read the user guide here or you  

can check the detailed collab example i  used a lot of functions from this example  

let's check the plan we'll start from the  preparation works of imports getting the  

financial data and built-in pivot tables then  we will talk about the correlation metrics the  

intuition behind the portfolio optimization  theory then we will see three optimal  

portfolios with mean volatility max share  pressure and mean c var or conditional variance  

portfolios then we will see an efficient  frontier and finally we will um find the the  

best discrete allocation of stocks i also wrote  a detailed article on my website by invest.com  

with a slightly different setup when you do a  repetitive short term trading for three days  

i manually build all combinations of  portfolios and check the portfolio metrics  

and build a scoring model for those metrics  so let's begin first we install y finance and  

get usual imports for panda snappy and matplotlib  we will have 2000 us dollars for our experiment  

here and these stickers to invest they are  actual tickers that i recently tried to invest in

here we we get the daily prices for the stocks for  example last day prices is actually two day and  

for today we have eight different records for  um for the stock values we also generate pivot  

table so that one they represents one line  and we store only close prices for the stocks  

so now with this setup we have eight  different rows which represent time series

stats and we can find the correlation  correlations between those time series  

correlations matrix is a matrix like like this  it is it has one on a diagonal so correlation  

of a stock with itself is always one it is a  symmetrical matrix so correlation of ba with  

with bodies the same is the same as but with with  ba so so we are interested in uh either bottom um  

triangle or upper triangle above the main diagonal  here we have the bottom triangle which is colored  

it is always good to have different colors  or more very variation of a correlations  

so any correlation lies between -1 and 1 and  stocks that have a similar correlation say 0.96.87

is not very good for the purposes of a portfolio  diversification because they tend to move in  

the same direction and the optimization  algorithm will probably try to mix in um  

other stocks that are loosely correlated with  many um top performing stocks so for these set  

of stocks probably ptr is the most important one  because it's not correlated with many other stocks

so now let's uh look at the pi portfolio opt  library we do install it check its version  

and we import some functions and  first we find an expected returns  

for individual stocks there  are a number of options to find  

in the expected returns here i use cpm  underscore return function it can be  

mean historical return or ema  historical return you can read about it  

in the library itself then we we  find the covariance matrix so it's a

unconstrained parameter and constraint matrix for  covariance between each set of each pair of stocks  

and when we have mu and s we can build  an efficient frontier and calculate  

the best performance portfolios we also

show we also

specify weight bounds between 0 and 1 so that  we don't allow short trading with negative  

weights we also buy stocks and go along and then  sell after some period of time um let's check  

what is a minimum volatility portfolio what is  a max sharp ratio and what is a c bar optimal  

portfolio um okay first as we remember its  average returns expected for each stock and  

they can be slightly different uh depending on the  method of estimation but here we see that nvidia  

is actually the top performance stock with 30 uh  39 and all expected returns um also shopify and

b a are top performing stocks  and if we want to optimize  

portfolio and to reduce its minimum volatility  sometimes the most performance stocks like nvidia  

um they will have weight zero probably because  they bring a lot of volatility with the returns so  

the metrics for this portfolio will be expected  and i'll return that is 16.2 percent which is  

uh lower than um many of the returns for the  individual stocks but it has a low volatility of  

8.9 percent and sharp ratio that is expected and  i'll return divided on nl volatility which equals  

to 1.67 next if we want to optimize this sharp  ratio which is expected return pure volatility  

we will see slightly different weights now nvidia  has a weight and va has a weight and with this we  

are adding the top performing stocks where you  are increasing the expected handle return from  

16.2 to 22.4 percent um but the annual volatility  is increasing only from 8.9 to 10.7 so that sharp  

ratio actually is increased from 1.67  to 1.91 and in many cases this portfolio  

will be treated as the optimal portfolio  and last but not least portfolio is

the the one that minimizes uh the losses in  the worst cases so um let's start with the  

um max server portfolio um weights we have these  these weights and calculate for this portfolio  

the daily returns uh distribution so in in  many cases daily returns are lie between  

minus five percent and plus five percent we and  it can be slightly shifted towards left or right  

um but in most of the cases you will see  a bell shy distribution curve then we find  

5 worst cases quantile so here it is somewhere  between minus percent and zero and we take  

average um returns for the worst cases so we  see that um uh the the quantile is actually  

minus 2.56 so it is here and as 5 5 of the  worst cases days they will bring losses that are  

higher than minus 2.56 percent for an optimal  sharper portfolio and if you take average of  

these losses it will be minus four percent you can  improve this uh average of losses and uh optimize  

your portfolio uh for uh to reduce this um average  of uh bad losses from minus four percent to  

um minus three percent but uh you will lose some  of the expected tunnel return and this will be  

a big loss because you are losing from 22 percent  in case of a sharp ratio to 15.8 percent uh for a

optimal civil war portfolio but it's up to you  whether you want to risk more and choose max  

sharper portfolio or you want to reduce volatility  and reduce conditional variance for a portfolio  

to build a highly protective case um now we  will talk about the efficient frontier um you  

you will see um these eight points on on the  chart each point represents one stock um and  

you will see returns and volatility on on  access so if if you are a risky investor  

you you don't need to to make an optimal portfolio  you can just simply choose maximum return stock  

nvidia in this case or you can choose a maximum  return alternative investment as bitcoin and  

um go all in but you know that over the long  term this is a very risky strategy and that's  

why we want to see um some um hatching in in our  portfolio and we are trying to mix in other stocks  

um so if you're adding other other stocks from  these eight we will see later that any combination  

of stocks will deliver some points under this  line which is called an efficient frontier  

it is a convex area and any any point specifically  on this line will be a point on an efficient  

frontier so this optimal uh selection point is  a maximum sharp ratio point when the dungeon  

curve is is optimal on on this line but you can  select any any other point depending on your risk  

return profile so let's try to get this efficient  frontier uh we we are doing um simulations and we  

are building 10 000 of portfolios with various  uh weight splits between stocks with dirichlet  

random distribution um and if you put all lines  from um the simulation or all all points from  

the simulation you will get this this area  so you can approximately understand that um  

the there will be a frontier uh for for  this area and it's always better to select  

higher return um stocks with the given high return  combinations or higher than portfolio with a given  

volatility say you have 15 volatility in  your portfolio so you're ready to risk 15  

of your money you will definitely want to  choose a portfolio that will deliver your  

approximately 30 of of returns highest possible  points and that's why you want to select  

a point on this efficient frontier so last  piece of analysis is a discrete allocation  

let's check why do we need this um we  take last day 8 prices and we take the  

maximum sharp ratio weights if you multiply  prices on on weights you will see that  

you need to buy specifically this amount  of stocks if you have in total just  

dollars and many numbers are not close  to the discrete number of stocks like  

0.48 for a shopify stock um so shopify stock  stocks price now is almost 1500 dollars

so

if you can buy only discrete number of stocks you  can't buy 0.48 you will need to buy at least one  

one stock of shopify and you will spend 1500 out  of 2 000 that is almost all money that you have  

that's why there is another function which  is uh called discrete allocation method  

which will find your um an optimal portfolio  which is close on metrics to the um max sharp  

or another optimal portfolio line on the efficient  frontier but this portfolio will have uh only  

um discrete amount of stocks to buy and this  restriction is often imposed by many brokers  

and you can't buy fractional shares but sometimes  you can buy and it can be an important factor to

to think about when you choose your own broker  thanks for watching and let me remind you once  

again that there is a very detailed article  um on on the portfolio optimization that i  

wrote by myself where you can try to get this  portfolio metrics do the simulation and come  

up with the best performing portfolio with  your own hands and not just call the methods  

from the standard library and not  understanding how they actually  

calculate all those numbers thanks  for watching and see you next time