The value ó2(X) = .000629 is in "squared" units and is very difficult to interpret. The standard deviation is more useful: ó = (.000629).5= .0251 or 2.51%.
n: Explain the use of conditional expectation in investment applications.
As we know, other factors can play a role in how a stock reacts to a given set of news. A conditional expected valueis a refined forecast that uses additional or new information to appropriately adjust the probabilities that make up a forecast.
Example:Suppose the probability of falling short, meeting or exceeding expectations depends upon some external event like weather conditions. If the weather in the relevant time period has been "good," the probabilities are P(fall short I good) = 0.10, P(meet I good) = 0.50, P(exceed I good) = 0.40. If the weather has been "poor," the corresponding probabilities are 0.3, 0.4, 0.3. For each type of weather, the conditional expected value is:
Good weather: E(X I good) = -.03? * .10 + .01 * .50 + .04 * .40 = .018
Poor weather: E(X I poor) = -.03 * .30 + .01 * .40 + .04 * .30 = .007
o: Calculate an expected value using the total probability rule.
Thetotal probability rule for expected valuesays that the unconditional probability is the weighted a
verage of the conditional probabilities.
Example:Continuing with our good vs. poor weather example from LOS 2.C.n:
E(X) = E(X I good) * P(good) + E(X I poor) * P(poor)
E(X) = [.018 * 0.5] + [.007 * 0.5] = .0125
We can apply this procedure to any set of mutually exclusive and exhaustive scenarios S1, S2,...Sn. The total probability rule for expected value is then represented by:
E(X) = E(X1I S1) + E(X2I S2) * P(S2) + E(X3I S3) * P(S3) +...+ E(XnI Sn) * P(Sn)
p: Define, calculate, and interpret covariance.