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 determine the expected return on the stock, the expected return on the market, and their covariance.

First, let's calculate the expected return on the stock. The expected return on the stock is the weighted average of the possible returns on the stock, based on the probabilities of each state:

Expected return on stock = (Prob.1 * Ret.on Stock 1) + (Prob.2 * Ret.on Stock 2) + (Prob.3 * Ret.on Stock 3) + (Prob.4 * Ret.on Stock 4)

= (0.1 * 3) + (0.3 * 8) + (0.4 * 20) + (0.2 * 15)

= 0.3 + 2.4 + 8 + 3

= 13.7%

Now, let's calculate the expected return on the market. Similarly, we'll calculate the weighted average of the possible returns on the market:

Expected return on market = (Prob.1 * Ret.on Market 1) + (Prob.2 * Ret.on Market 2) + (Prob.3 * Ret.on Market 3) + (Prob.4 * Ret.on Market 4)

= (0.1 * 8) + (0.3 * 10) + (0.4 * 15) + (0.2 * 20)

= 0.8 + 3 + 6 + 4

= 13.8%

Now, let's calculate the covariance between the returns on the stock and the market. The covariance measures the co-movement between the stock and the market:

Covariance(stock, market) = (Prob.1 * (Ret.on Stock 1 - Expected return on stock) * (Ret.on Market 1 - Expected return on market))
+ (Prob.2 * (Ret.on Stock 2 - Expected return on stock) * (Ret.on Market 2 - Expected return on market))
+ (Prob.3 * (Ret.on Stock 3 - Expected return on stock) * (Ret.on Market 3 - Expected return on market))
+ (Prob.4 * (Ret.on Stock 4 - Expected return on stock) * (Ret.on Market 4 - Expected return on market))

= (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))

= (0.1 * 2.863 * 7.862)
+ (0.3 * 7.863 * 9.862)
+ (0.4 * 19.863 * 14.862)
+ (0.2 * 14.863 * 19.862)

= 1.995
+ 18.491
+ 56.083
+ 56.237

= 132.806

Finally, we can calculate the stock beta by dividing the covariance by the variance of the market:

Stock beta = Covariance(stock, market) / Variance(market)

To calculate the variance of the market, we need to determine the weighted average of the squared deviations of the market returns from their expected value:

Variance(market) = (Prob.1 * (Ret.on Market 1 - Expected return on market)^2)
+ (Prob.2 * (Ret.on Market 2 - Expected return on market)^2)
+ (Prob.3 * (Ret.on Market 3 - Expected return on market)^2)
+ (Prob.4 * (Ret.on Market 4 - Expected return on market)^2)

= (0.1 * (8 - 0.138)^2)
+ (0.3 * (10 - 0.138)^2)
+ (0.4 * (15 - 0.138)^2)
+ (0.2 * (20 - 0.138)^2)

= (0.1 * 7.868)
+ (0.3 * 9.772)
+ (0.4 * 14.725)
+ (0.2 * 19.722)

= 0.7868
+ 2.9316
+ 5.89
+ 3.9444

= 13.5528

Now, we can calculate the stock beta:

Stock beta = 132.806 / 13.5528

= 9.8

Therefore, the stock beta is approximately 9.8.