You have a $5 million portfolio consisting of a $200,000 investment in each of 25 different stocks. The portfolio has a beta of 1.5. You are considering selling $200,000 worth of one stock with a beta of 1.2 and using the proceeds to purchase another stock with a beta of 1.1. What will the portfolio’s new beta be after these transactions?
Answer-
There are 25 stocks of $ 200000 each worth $ 5 million with average beta of 1.5
One stock of $ 200000 is sold which has a beta of 1.2 and another stock is purchaed with a beta of 1.1.
The change in total value of beta
= 25 x 1.5 - (1 x 1.2 )+ (1 x 1.1) [ 25 stocks with 1.5 beta and
one is sold ( beta = 1.2 and one is purchased ( beta = 1.1
]
= 25 x 1.5 - 1.2 + 1.1
= 25 x 1.5 - 0.1
= 37.5 - 0.1
= 37.4
Note- Number of stocks remain the same after the transaction (25)
Therefore the new beta of the portfolio after the
transacions
= Total beta / number of stocks = 37.4 / 25 = 1.496
You have a $5 million portfolio consisting of a $200,000 investment in each of 25 different...
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