In a portfolio of three randomly selected stocks, which of the following could NOT be true; i.e., which statement is false?
a. The beta of the portfolio is lower than the lowest of the three betas
b. The beta of the porfolio is higher than the highest ofthe three betas
c. The riskiness of the portfolio is greater than the riskiess ofoneor two of the stocks.
d. The riskiness of the portfolio is less than the riskiness of each of the stocks if they were held in isolation
e. The beta of the portfolio is calculated as a weighted average of the individual stocks' betas.

The beta of a portfolio is calculated as a weighted average of the individual betas of the individual stocks. As such, the highest individual beta will be the upper limit of the portfolios entire beta.

For instance.

3 stocks A, B and C have betas of 1, 1.3 and 2 respectively.

A has a weight of 1%, B has a weight of 1% and C has a weight of 98%.

The portfolio beta will be;

= (0.01 * 1 ) + ( 0.01 * 1.3) + ( 0.98 * 2)

= 1.98

Even if the stock with the highest beta had an advantage of weighing such a high figure, it it mathematically impossible for the portfolio beta to be higher than it.