The historical returns for Microsoft Corporation (MFST) were -8%, 10% and 22%. The returns for the market portfolio were 6%, 18% and 24% during this same time period. Calculate the beta for Microsoft.Correct!
Question
The historical returns for Microsoft Corporation (MFST) were -8%, 10% and 22%. The returns for the market portfolio were 6%, 18% and 24% during this same time period. Calculate the beta for Microsoft.Correct!
Solution
To calculate the beta for Microsoft, we need to follow these steps:
Step 1: Calculate the average return for Microsoft (MFST) and the market portfolio.
For Microsoft: (-8% + 10% + 22%) / 3 = 8%
For the market: (6% + 18% + 24%) / 3 = 16%
Step 2: Calculate the variance of the market returns.
Variance = [(6%-16%)^2 + (18%-16%)^2 + (24%-16%)^2] / 3 = [(-10%)^2 + (2%)^2 + (8%)^2] / 3 = [100 + 4 + 64] / 3 = 56
Step 3: Calculate the covariance of returns between Microsoft and the market.
Covariance = [(6%-16%)(-8%-8%) + (18%-16%)(10%-8%) + (24%-16%)(22%-8%)] / 3 = [(-10%-16%) + (2%*2%) + (8%*14%)] / 3 = [160 + 4 + 112] / 3 = 92
Step 4: Calculate the beta.
Beta = Covariance / Variance = 92 / 56 = 1.643
So, the beta for Microsoft is 1.643.
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