Following are rates of return on medical equip. company's stock and debt, and on the market portfolio, along with the probability of each state.
State Prob. Ret.on Stock Ret.on Debt Ret.on Market
1 .1 3 8 5
2 .3 8 8 10
3 .4 20 10 15
4 .2 15 10 20
What is the stock beta?
By calculating expected returns
Stock .115
Debt .09
Market .125
.011/.012 = .92????
To calculate the stock beta, we need to use the information provided about the rates of return on the stock, debt, and the market portfolio, as well as the probability of each state.
Step 1: Calculate the expected returns for the stock, debt, and market.
Expected Return = (Probability x Return)
Expected Return on Stock = (0.1 x 3) + (0.3 x 8) + (0.4 x 20) + (0.2 x 15) = 1.4 + 2.4 + 8 + 3 = 15.8%
Expected Return on Debt = (0.1 x 8) + (0.3 x 8) + (0.4 x 10) + (0.2 x 10) = 0.8 + 2.4 + 4 + 2 = 9.2%
Expected Return on Market = (0.1 x 5) + (0.3 x 10) + (0.4 x 15) + (0.2 x 20) = 0.5 + 3 + 6 + 4 = 13.5%
Step 2: Calculate the beta of the stock using the formula:
Beta = (Covariance of Stock and Market) / (Variance of Market)
Covariance of Stock and Market = Sum of [(Probability x (Return of Stock - Expected Return of Stock)) x (Return of Market - Expected Return of Market)]
Covariance of Stock and Market = (0.1 x (3 - 15.8) x (5 - 13.5)) + (0.3 x (8 - 15.8) x (10 - 13.5)) + (0.4 x (20 - 15.8) x (15 - 13.5)) + (0.2 x (15 - 15.8) x (20 - 13.5))
Covariance of Stock and Market = (-1.58 x -8.5) + (-7.74 x -3.5) + (4.48 x 1.5) + (-0.86 x 6.5)
Covariance of Stock and Market = 13.43 + 27.09 + 6.72 - 5.59 = 41.65
Variance of Market = Sum of [(Probability x (Return of Market - Expected Return of Market))^2]
Variance of Market = (0.1 x (5 - 13.5))^2 + (0.3 x (10 - 13.5))^2 + (0.4 x (15 - 13.5))^2 + (0.2 x (20 - 13.5))^2
Variance of Market = (-8.5)^2 + (-3.5)^2 + (1.5)^2 + (6.5)^2
Variance of Market = 72.25 + 12.25 + 2.25 + 42.25 = 129
Beta = 41.65 / 129 = 0.322
The stock beta is approximately 0.322.