Calculate the expected rate of return and standard deviation of expected returns of stocks when the probability distribution of expected return are given.

1. Stocks X and Y have the following probability distributions of expected future returns:

PROBABILITY X Y Rate of return Y Rate of return X
10% -10% -35% -4% -1%
20% 20% 0% 0% 4%
40% 12% 20% 8% 5%
20% 20% 25% 5% 4%
10% 38% 45% 5% 4%


a.  Calculate the expected rate of return, khat, for Stock Y (expected return for Stock X, Kx hat, equals 12%).


b. Calculate the standard deviation of expected returns for Stock X.  (that for Stock Y is 20.35%).  Now Calculate the
coefficient of variation for Stock Y.  Is it possible that most investors might regard Stock Y as being less risky than
Stock X?  Explain.


2.  Shalit Corporation's 2002 sales were $12 million.  Sales were $6 million 5 years earlier (in 1997).

a.  To the nearest percentage point, at what rate have sales been growing?
b.  Suppose someone calculated the sales growth for Shalit Corporation in part a as follows:
"Sales doubled in 5 years.  This represents a growth of 100 percent in 5 years, so dividing 100 percent by 5, we find the growth rate
to be 20 percent per year".  Explain what is wrong with this calculation.