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Assume the volatility of Microsoft and the S&P500 is 20% and 15%, respectively. Thecovariance between Microsoft and the S&P500 is 200(%2), Calculate the beta of Microsoft

Question

Assume the volatility of Microsoft and the S&P500 is 20% and 15%, respectively. Thecovariance between Microsoft and the S&P500 is 200(%2), Calculate the beta of Microsoft

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Solution

Sure, I can help with that. The beta of a stock is calculated by dividing the covariance of the returns of the stock and the market by the variance of the market returns. In this case, the market is represented by the S&P500.

Here are the steps to calculate the beta of Microsoft:

  1. Convert the given volatility of Microsoft and the S&P500 into variances. The variance is the square of the volatility. So, the variance of Microsoft is 0.20^2 = 0.04 and the variance of the S&P500 is 0.15^2 = 0.0225.

  2. Convert the given covariance into a decimal form. The covariance is given as 200(%^2), which means it is 200/10000 = 0.02.

  3. Now, calculate the beta of Microsoft by dividing the covariance of Microsoft and the S&P500 by the variance of the S&P500. So, the beta is 0.02/0.0225 = 0.8889.

So, the beta of Microsoft is approximately 0.89. This means that Microsoft's returns are expected to move in the same direction as the S&P500's returns, but at about 89% of the rate.

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