Jill Angel holds a $200,000 portfolio consisting of the following stocks. The portfolio's beta is 0.875. Stock Investment Beta
A $50,000 0.5
B 50,000 0.8
C 50,000 1
D 50,000 1.2
Total $200,000

If Jill replaces Stock A with another stock, E, which has a beta of 1.50, what will the portfolio's new beta be?

a. 1.40
b. 1.29
c. 0.86
d. 0.75
e. 1.08

The options provided are incorrect. The correct answer is given below

New Portfolio beta = 1.125

Explanation:

The portfolio beta is the function of the weighted average of the individual stock betas that form up the portfolio. The formula to calculate the beta of a portfolio is as follows,

Portfolio beta = wA * Beta of A + wB * Beta of B +    +  wN * Beta of N

Where,

w represents the weight of each stock in the portfolio

New Portfolio beta = 50000/200000 * 0.8  +  50000/200000 * 1  +  

50000/200000 * 1.2  +  50000/200000 * 1.5

New Portfolio beta = 1.125

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