Question

Jeanne Lewis is attempting to evaluate two possible portfolios consisting of the same five

assets but held in different proportions. She is particularly interested in using beta to compare

the risk of the portfolios and, in this regard, has gathered the following data.

Portfolio Weights

Asset Asset Beta Portfolio A Portfolio B

1 1.3 10% 30%

2 0.7 30% 10%

3 1.25 10% 20%

4 1.1 10% 20%

5 0.9 40% 20%

Total 100% 100%

Answer 1

As per the question, the asset distribution in Portfolio A & B are as follows:

Beta represents the volatility in the stock or the portfolio.

The beta value of 1 represents that the movement of stock value is exactly replicating the movement of the market index. A higher beta value indicates that the stock/portfolio is more volatile and so more risky, as compared to the stock/portfolio with a lower beta value which is having less risk.

However, the stocks/portfolio with higher risk has the potential for higher returns and the stocks/portfolio with lower risk have the potential for lower returns.

For calculating the Portfolio beta, the formula used is as below.

So for Portfolio A

Beta is calculated as follows,

Beta_{Portfolio A} = (1.3*0.1)+(0.7*0.3)+(1.25*0.1)+ (1.1*0.1) + (0.9*0.4)

= 0.935

For Portfolio B,

Beta_{Portfolio B} = (1.3*0.3)+(0.7*0.1)+(1.25*0.2)+(1.1*0.2)+(0.9*0.2)

=1.11

So, from the above calculations, we find that,

So, Portfolio B is riskier as compared to Portfolio A.