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's beta, you need to compare the stock's rate of return to the rate of return on the market portfolio. The formula for beta is:
Beta = Covariance(Stock Return, Market Return) / Variance(Market Return)
Here's how you can calculate the stock's beta using the given information:
Step 1: Calculate the expected return for the stock by weighting the returns in each state by their respective probabilities:
Expected Return Stock = (Prob.State1 * Ret.on Stock.State1) + (Prob.State2 * Ret.on Stock.State2) + (Prob.State3 * Ret.on Stock.State3) + (Prob.State4 * Ret.on Stock.State4)
Expected Return Stock = (0.1 * 3) + (0.3 * 8) + (0.4 * 20) + (0.2 * 15)
Expected Return Stock = 0.3 + 2.4 + 8 + 3
Expected Return Stock = 13.7%
Step 2: Calculate the expected return for the market portfolio using the same method:
Expected Return Market = (Prob.State1 * Ret.on Market.State1) + (Prob.State2 * Ret.on Market.State2) + (Prob.State3 * Ret.on Market.State3) + (Prob.State4 * Ret.on Market.State4)
Expected Return Market = (0.1 * 8) + (0.3 * 10) + (0.4 * 15) + (0.2 * 20)
Expected Return Market = 0.8 + 3 + 6 + 4
Expected Return Market = 13.8%
Step 3: Calculate the covariance between the stock return and the market return:
Covariance = (Prob.State1 * (Ret.on Stock.State1 - Expected Return Stock) * (Ret.on Market.State1 - Expected Return Market)) + (Prob.State2 * (Ret.on Stock.State2 - Expected Return Stock) * (Ret.on Market.State2 - Expected Return Market)) + (Prob.State3 * (Ret.on Stock.State3 - Expected Return Stock) * (Ret.on Market.State3 - Expected Return Market)) + (Prob.State4 * (Ret.on Stock.State4 - Expected Return Stock) * (Ret.on Market.State4 - Expected Return Market))
Covariance = (0.1 * (3 - 0.137) * (8 - 0.138)) + (0.3 * (8 - 0.137) * (10 - 0.138)) + (0.4 * (20 - 0.137) * (15 - 0.138)) + (0.2 * (15 - 0.137) * (20 - 0.138))
Covariance = (0.1 * 2.863 * 7.862) + (0.3 * 7.863 * 9.862) + (0.4 * 19.863 * 14.862) + (0.2 * 14.863 * 19.862)
Covariance = 2.863 + 23.402 + 55.37 + 27.857
Covariance = 109.492
Step 4: Calculate the variance of the market return:
Variance(Market Return) = (Prob.State1 * (Ret.on Market.State1 - Expected Return Market)^2) + (Prob.State2 * (Ret.on Market.State2 - Expected Return Market)^2) + (Prob.State3 * (Ret.on Market.State3 - Expected Return Market)^2) + (Prob.State4 * (Ret.on Market.State4 - Expected Return Market)^2)
Variance(Market Return) = (0.1 * (8 - 0.138)^2) + (0.3 * (10 - 0.138)^2) + (0.4 * (15 - 0.138)^2) + (0.2 * (20 - 0.138)^2)
Variance(Market Return) = (0.1 * 57.358) + (0.3 * 100.876) + (0.4 * 177.132) + (0.2 * 323.226)
Variance(Market Return) = 5.736 + 30.263 + 70.853 + 64.645
Variance(Market Return) = 171.497
Step 5: Calculate the beta:
Beta = Covariance(Stock Return, Market Return) / Variance(Market Return)
Beta = 109.492 / 171.497
Beta ≈ 0.638
So, the stock's beta is approximately 0.638.