In this workout, we're asked to calculate the expected portfolio return and expected portfolio risk for a portfolio constructed of apple and Facebook shares only.

With the information that we're provided with.

And the information that we're provided with gives us the expected return of apple and Facebook to be 3% and 4% respectively their risks to be 6.5 and 6.4. So that's the volatility of returns within a portfolio weights of 60% in apple and 40% in Facebook and the covariance and correlation between Facebook and apple of 21.8 and 0.6% respectively.

To calculate the portfolio return. All we need to do is multiply the expected return by the weight that the asset has in the portfolio. So 3% return for Apple times these 60% weight. It has in the portfolio plus the expected return of Facebook 4% times the weight that it will have in the portfolio of 40% that gives us an expected return.

Somewhere between Apple and Facebook's return on their own but slightly biased towards the apples return of 3% because they've got slightly more weight in the portfolio.

To calculate portfolio risk is a much more involved calculation.

What we need to do is first of all identify that the risk calculation is the square root of the variance. So let's put that in there to begin with so we can take the square root of the portfolio variance calculation and the way we get the portfolio variance is first of all, we take the risk what we need to square that take it to the power of two.

for Apple and we need to multiply this by the portfolio weights also squared.

For apple and then we needed the same thing for Facebook. So the portfolio risk.

squared multiplied by the weight in the portfolio Square the final seven that we need to add is two times.

the risk of one assets Times by the risk of the other assets multiplied by the weight in the portfolio of one of our assets times the weight in the portfolio of the second assets multiplied by the correlation coefficient between so we really have three elements to this formula.

The first element is looking at the variability of Apple's Returns on their own.

The second element is then looking at the variability of Facebook's stock price performance on its own and the third element is then the interrelationship between Apple and Facebook's share price.

Overall, this gives us portfolio risk of 5.7% And the interesting element here is that the risk of each asset on their own was around 6.46.5% But by combining these two together in a portfolio where they are not perfectly positively correlated does give us some diversification benefits.

So although the return is the average of the two returns expected on their own the risk of the portfolio is not simply the average of the Returns on the individual stocks because they both won't be going up and be going down at the same points in time. So there will be some diversification benefits giving us this overall expected portfolio risk of only 5.7% less than the 6.5 or 6.4 of apple or Facebook on their own.