Question

Stock ABC has beta of 1.2. The risk-free rate is 5%, and the market expected rate of return is 14%. My estimation shows that the stock of ABC has alpha of 3% over a one-year period horizon. I have $20,000 in my account and I also want to use “buy on margin” as well to buy ABC as much as possible. Initial margin requirement is 50% and I am supposed to pay back 5% annually compounded interest on it. How would be the rate of return of my investment on ABC in a period of one year?

Please Do not use Excel to solve this, I want the formulas seen and the steps so I can understand the concept.

Answer 1

As per CAPM Model,

Expected Return on ABC = 5 + 1.2(14 - 5)

Expected Return on ABC = 15.80%

Alpha = 3%

So,

Total Return on ABC Stock = 3 + 15.80 = 18.80%

Initial Amount in Account = $20,000

Initial margin = 50%

Total Purchase Value = $40,000

Return Rate = 18.80%

For one year,

Final Value = 40,000(1 + 0.188)

Final Value = $47,520

Interest paid on Margin = 0.05(20,000)

Interest Paid = $1,000

So,

Return Rate = (Final Value - Initial Value - Interest Paid)/Amount Invested

Return Rate = (47520 - 40000 - 1000)/20000

Return Rate = 32.60%

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