You hold a portfolio of stocks consisting of the following: Stock Beta Current V

Question

You hold a portfolio of stocks consisting of the following:

Stock Beta Current Value

Blackwater Gas 0.5 $10,000
Tidy Tom’s Cleaners 0.7 $5,000
Globular Grabbus 1.2 $20,000
Creative Crafts 1.0 $4,000
Total: $39,000

a. What is the beta of the portfolio?

b. You have decided to sell Creative Crafts for $4,000 and to use the proceeds to buy $4,000 of International Steel stock with a beta of 2.5. After the transaction is complete, what will be the new beta of the portfolio? (Disregard any commissions on the buy and sell transactions.)

Explanation / Answer

a) To find the beta of the entire portfolio you need to know the beta of the individual stocks you own which you already do. The first step you need to take is to calculate the weighted beta. Take each beta and multiply it by the percentage of you portfolio that the single stock occupies. So for instance, Blackwater Gas has occupies 12.8205 % of your portfolio. (10000+5000+20000+4000+39000 = 78000, then take 10000/78000 = 12.82%) Take that percentage and multiply it by the beta is has. (12.82% * .5 = .064103) This number is your weighted beta for Blackwater Gas. Do this same thing for the rest of your stocks then add all the weighted betas together to find your beta of your portfolio. b) So now that you no longer have Creative Crafts, take that out and just add an extra $4000 to International Steel. Now you have $4,000 of International Steel with a beta of 2.5. Calculate the weighted beta for this new addition, then add all the betas together and that's your new total beta of the portfolio.

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