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Expected returns: You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted to medical school is about 10 percent. If you are accepted to medical school, then your starting salary when you graduate will be $300,000 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $40,000 per year. Without considering the additional educational years or the time value of money, what is your expected starting salary as well as the standard deviation of that starting salary?

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So expected returns are just a little more advanced version of probability - without getting too in detail it uses weighted averages so you do not have to add the same number 17 times.
Let's first define our variables:
E(X) = Expected Return X1 = Variable 1 P1 = Probability 1 (in decimal format so 55% would be .55) X2 = Variable 2 P2 = Probability 2 (P2 is also equal to 1 - P1)
So the expected return formula is as follows:
E(X) = (X1)*(P1) + (X2)*(P2)
Plugging in our given numbers we get E(X) = Expected Return X1 = 300,000 P1 = 10% or .1 X2 = 40,000 P2 = 1 - P1 = 1 - .1 = .9
E(X) = (300,000)*(.1) + (40,000)*(.9) E(X) = 66,000
Now remember this does not include the opportunity cost of spending your four years in college studying biology instead of another degree.

Posted on Mar 01, 2011

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