Previously, we learned how to measure the
variability of a financial security and agreed
this is one of the best measures of risk we
can use.
We learned a volatile stock is much likelier
to deviate from its historical returns and
surprise investors.
That’s excellent.
Now is the time to consider a portfolio of
at least two stocks.
We learned how to calculate the expected rate
of return of portfolios with two or more stocks,
but we haven’t discussed the calculation
of a portfolio variance.
If a portfolio contains two stocks, its risk
will be a function of the variances of the
two stocks and of the correlation between
them.
Remember the example about Facebook, LinkedIn,
and Walmart?
It is reasonable to expect a portfolio containing
Facebook and LinkedIn shares will have a different
risk compared to a portfolio containing Facebook
and Walmart (even if the variances of LinkedIn
and Walmart were the same).
The difference will be given by the relationship
between the prices of the two companies in
the portfolio.
Ok.
Let’s remember basic algebra, shall we?
The sum of a plus b to the second degree is
equal to a squared plus b squared plus two
times ab.
Correct?
Remember that?
So, you did pay attention at school?
Great!
We did too.
Let’s do the same thing for a portfolio
containing two stocks.
The first stock has a weight of “w” 1,
which stands for “weight 1”, and the second
stock has a weight of ”w” 2, which stands
for “weight 2”.
It is important to mention the sum of the
weights is always equal to 1, because the
weights must add up to one, as these are the
two stocks forming the entire portfolio.
100% of it, or simply 1.
The portfolio variance will be given by “weight
1” times the standard deviation of the first
stock plus “weight 2” times the standard
deviation of the second stock to the second
degree.
The result is the same as the formula we have
above.
“Weight 1” times the standard deviation
of the first stock plays the role of a, while
“weight 2” times the standard deviation
of the second stock is b.
And the end result is equal to:
“Weight 1” to the second degree times
the variance of the first stock plus “weight
2” to the second degree times the variance
of the second stock plus two times the product
of ”weight 1”, “weight 2” and the
covariance between the two stocks.
Here it is.
This is how we calculate a portfolio’s variance.
It depends on two things – the standard
deviations of the two stocks and the correlation
between these stocks.
In our next lesson, we’ll apply what we
have learned in practice.
Thanks for watching!
