2. An investor is evaluating a two-asset portfolio of the...

2. An investor is evaluating a two-asset portfolio of the following two securities. \begin{itemize} \item Portfolio A: 75\% Ooredoo and 25\% Woqod \item Portfolio B: Investor has QAR 100,000 and will invest QAR 50,000 in Woqod \item Expected returns and risks: \end{itemize} \begin{tabular}{|l|l|l|} \hline Security & Expected Return & Expected Risk ($\sigma$)\\ \hline Ooredoo & 12.50\% & 26.40\% \\ Woqod & 10.80\% & 22.50\% \\ \hline \end{tabular} \begin{itemize} \item The correlation between Ooredoo and Woqod is 0.72. \item Calculate: \begin{itemize} \item[a.] Expected return of both the portfolios \end{itemize} \end{itemize}

Transcript

00:01 So here we are talking about portfolios, right? and we know something about two stocks, right? so a has an expected return to a is 25%, 0 .25.

00:15 And the variance of a, right, sigma squared a, is equal to 15%.

00:24 For b, we have the expected value of b is equal to 0 .2 .3.

00:30 15 and the variance of b is equal to 0 .09, right? so b is safer, which means that you get a lower risk, but lower return.

00:42 So let's define the portfolio as a new random variable p.

00:50 And the p is that we're spending 60 % of our money in a, which means we are putting 40 % of our money in b.

00:58 So we are and defining this new random variable, which is 60 % a and 40 % b.

01:04 So the expected return to the portfolio is the expected return of 0 .6a plus 0 .4b.

01:13 And this is expectation as a linear operator.

01:16 So this simplifies down to the weighted average of the individual expectations, right? so this is going to be 15, sorry, 0 .15 .5.

01:29 15 plus 0 .06 is equal to 21%, or if you prefer 0 .21.

01:37 That's the easy part, right? we just define a new random variable.

01:40 We take the expectation and now we're off to the races.

01:44 The variance of p is a little bit more tricky, right? when we think about the variance of 0 .6a plus 0 .4b, we need to think a little bit about how this breaks up, right? we need to understand some rules for variance.

02:04 And variance is a quadratic operator, not a linear operator.

02:16 So this is gonna come out to be 0 .6 squared times the variance of a, plus 0 .4 squared times the variance of b.

02:28 And that's only the case if these things are independent, right? in general, they are not independent.

02:36 We know in this particular case they're not independent because we're given a correlation coefficient, right? we say that they are correlated.

02:49 And the missing term that goes in here reflecting that correlation is twice, and this would be the variance, i'm sorry, the covariance, covariance of the individual parts, 0 .6.

03:05 A and 0 .4b, right? and now we need to get those constants out of there, but i'm going to sub in, right? so this is 0 .6 squared times the variance of a.

03:16 The variance of a is 15%.

03:21 This is going to be 0 .16 times 0 .09.

03:26 That's the, this term is taken care of.

03:28 This term is taken care of.

03:29 But what we're given is the correlation coefficient, not the covariance.

03:34 But my argument is that we can by understanding the correlation coefficient, which is defined as the covariance between x and y over the standard deviation of x and the standard deviation of y, right? that is the definition of the correlation coefficient...

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