In this video I will explain the portfolio diversification effect.
So what is the portfolio diversification effect.
In simple words let's assume you have two stocks and you can invest only in one of them or you can invest
in both and form a portfolio.
And to keep it simple let's assume we invest in both and we have fates of 50 50 so we have equal rights
then the return of the portfolio is simple the mean are the average return of the single stocks however
the risk of our portfolio is less than the mean or the average of the single stocks.
And that's actually a pretty metric.
So let's make an easy example from real world.
Let's assume that you like pizza and ice cream and both give you 100 percent satisfaction when you eat
them.
But on the other hand side pizza and ice cream both have 500 calories and if you eat them separately
for example in the morning ice cream and in the evening pizza you get to two times 100 percent satisfaction
and then total 1000 calories.
However if you eat both together at lunch you also get two times the food satisfaction but your total
calories is only 600 or 700.
And yeah this sounds completely strange and it is but that's how portfolios work.
All right so now let's stop coding and we still have imparted our summary data frame.
Here we have our six constituents and our maximum Sharpe Ratio portfolio or market portfolio.
And we also have here the optimum weights for our stocks so these are the optimum weights to create
the maximum Sharpe Ratio portfolio.
So this is nothing new.
So here now a summary data frame we have the annualized the return and risk and the if we would calculate
the evaded average return of the constituents of uh the M P portfolio.
Then we would probably end up at the return of the MP portfolio so twenty five point five eight percent.
However if we do the same for the risk.
So we calculate the weighted average risk of our constituents.
Then we probably wouldn't end up at the risk of our portfolio here and we can prove this by simply calculating
the weighted average return and weighted average risk uh for our constituents.
So we select our six constituents until the Microsoft stock including and uh we only select the return
and risk and then we are calculating the weighted average with the top method and pass here the optimal
weights and uh we save for the result and the variable weighted average.
So let's do this here.
So this is actually the weighted average return and evaded ever its risks for our constituents of our
best portfolio.
And we can see that the evaded ever its return is the same so twenty five point five eight percent.
However the risk of our weighted average is higher than the risk of our portfolio and that's pretty
significant so here we have twenty five point two five percent.
And actually our portfolio only has about 20 percent risk and we can also create a plot here.
So we are plotting our 100000 portfolios then we are plotting our market portfolio and also we are plotting
our weighted average portfolio.
So let's have a look.
So this is actually nothing new.
Here we can see our market portfolio.
And here in pepper this uh would be uh the hypothetically uh weighted average portfolio.
And we can also offer a more detailed look.
So this is simply the weighted average.
And this is the actual risk of our market portfolio.
And the differential Yes actually the risk uh that we can diversify when we create a portfolio.
And therefore this is also called the and systematic or diversified risk of uh the single stocks.
And as an example let's take the Boeing stock.
So Boeing had recently some technical issues with uh the uh new airplane 7 3 7 Max.
And this would be a so-called and systematic or Boeing specific risk.
And if you form a portfolio with the Boeing stocks and many other stocks you can actually fully diversify
the risk of the technical issues um of uh the new airplane.
So we have our six stocks and we created the best possible portfolio.
However still we have some risks.
So we have a stellar 20 percent and this is actually the systematic risk of so-called market risk and
the market risk cannot be diversified away.
And the best example for the market risk is actually the state of the economy.
So if the whole economy is weak then also the performance of the single stocks this week.
So people buy less on Amazon and also the airlines buy less aircraft from Boeing.
So this is a risk that affects all stocks and therefore by forming a portfolio of stocks this risk cannot
be diversified away.
And therefore it's a systematic non diverse viable risk.
All right now let's go back to our Jupiter notebook and then the following I would like to present a
pretty easy attitude for example of uh risk diversification.
So let's assume we have three stocks A B and C and we actually have uh the returns of a b and c for
10 periods.
So this could be for example a month or years.
So here we have 10 periods.
And uh the return data for the three stocks and that's simply getting graphical intuition how the stocks
A and B perform
so here we have the return of a and b a we have here in blue and B and green.
And actually the average return is about 5 percent.
And whenever a is higher than 5 percent p s lower than 5 percent and whenever a is lower than 5 percent
B is higher than 5 percent.
So A and B are actually negatively correlated.
So whenever a is high P as low and vice versa.
And that's also compared the performance of A and C
and here we can see that both stocks pretty much move together.
So when the return of A is higher than the return of C is also high and vice versa.
And if you have a look at the data at the raw data.
So the return of C is always two times the return of a.
So here we are five and 10 10 and 20 minus two and the minus 4 so the stocks ANC pretty much move together
and in contrast A and B move in the opposite directions.
And if you have look at the single periods so the average of A and B is always 5 percent so you have
5 percent on average and year 10 plus several gifts 5 percent minus two and twelve gifts a 5 percent
on average.
So you could say that poor periods for stock H with low returns are offset by high returns for stock
P and vice versa.
And we can also calculate the correlation between the stocks so the correlation factor and it's no surprise
that a and b are perfectly and negative correlated and the stocks ANC are perfectly positive correlated.
And now let's create portfolios of the stocks A and B and ANC.
And for simplicity reasons we assume equal weights low 50 50 and therefore we can at year two new columns
to our three stocks data frame.
So the portfolio A B and the returns and the returns of a c.
So let's do this let's have a look.
So here we have uh the period returns for the portfolio a and b and a and c and.
We can see here that the portfolio a and b we have in each and every period a stable return of 5 percent.
And we can also see that the portfolio with the stocks a and c is there shows quite a high volatility
and we can also plot this.
So we are applauding the portfolios A B and A C.
So the period returns and they are completely stable for the A B portfolio and they are still pretty
volatile for the A C portfolio.
And now we can also grade these summary data frame with the ever rates return and the standard deviation
of returns and let's have a look so the mean return of the stock is 4.5 and uh the mean return of the
B stock 5.5.
And consequently the portfolio return of a and b is um the average.
So 5 percent and we can also see that the standard deviation of returns all the risk is the five point
four six.
And also 5.5 6 percent for a and b.
And if you create a portfolio with uh both stocks then the risk of uh the portfolio B is 0 because here
we are in each and every period the return of 5 percent.
So there's zero variability here.
And we can also make this more explicitly so we can calculate uh the evaded ever its risk and return
of a and b and this would be 5 percent return and five point for six percent risk.
And let's also calculate the weighted average of the single stocks ANC.
So the weighted average return and risk and the weighted average return of six point seven five and
exactly the same return we have for the portfolio ANC.
And uh we can also see here that the risk of the portfolio ANC is 8 percent and the same we have here
for the weighted average.
So to summarize we can see here for the portfolio a b a huge diversification effect.
So even if the single stocks ANP are risky itself the portfolio has no risk at all.
So by forming a portfolio we fully diversified the risk and the opposite.
We can say for the portfolio a C.
So here we have no portfolio diversification effect at all.
And the reason for this is pretty simple.
So the stocks ANP are perfectly negative correlated and in contrast the stocks ANC are perfectly positive
correlated.
And whenever two stocks are perfectly positive correlated so whenever they have a correlation factor
of one then there is no portfolio diversification effect at all.
Or to put it the other way around whenever the correlation between two stocks is less than one.
So whenever they are not perfectly positive correlated then that is a portfolio diversification effect
and uh therefore we could also have a look at the correlation factors of our six stocks and as we have
here portfolio diversification effects.
So I would assume that the correlation effect does between our six stocks less than one and this is
C or exactly the case.
So for example for our Amazon stock we have a correlation of 0 point 3 6 with Boeing.
So this is clearly less than one.
And also with the Microsoft stock here we have a correlation effect of 0 point 5 and so on but that's
the reason why we a portfolio diversification effect.
So our single stocks are not perfectly positive correlated and with this we are finished here and I
hope to see you also in the next video by.