a)
Given:
Now, the covariance matrix or the box matrix for a 5 stock portfolio looks like this:
where the first row and column represents the stock number (1 through 5). It looks complicated but is quite easy to create. Every cell corresponds to a stock pair. Each cell is filled with a term that contains the product of weights of each stock in the stock pair and either:
Now, the variance of the portfolio is calculated by adding all these terms up.
When we substitute the values, the matrix simplifies as shown:
So, all cells take up one of 3 values 0.64, 0.8 or 0.
the variance of the portfolio is simply the sum of all these values. There are 5 terms of 0.64 and 6 terms of 0.8. Rest are zero.
So, variance = 5(0.64) + 6(0.8)
Variance = 8
b)
Portfolio beta is simply the weighted average of individual stock betas.
It is given that betas of stocks 3 and 4 are zero, so they can be ignored totally.
For stocks 1,2 and 5, beta is equal to 1.1 and their weights are 0.2 each. So, their weighted average is calculated as:
Problem 3: You have a portfolio of 5 stocks with equal shares invested in each stock....
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