Answer: b. The beta of the portfolio is higher than the highest of the three betas
Explanation:
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.
