Expected rate of return and standard deviation of return

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.

The solutions shows steps to calculate the expected rate of return and standard deviation of expected returns of stocks when the probability distribution of expected return are given.

... solution explains some questions relating to expected rate of return... average return that we may expect to earn ...return may deviate from the expected return by ...

... Probability Return (%) 0.30 9.5 0.15 12.0 0.25 15.0 0.30 16.0. Calculate the expected rate of return and the standard deviation of the returns. 21. ...

... distribution of all possible expected return based on ... larger the variabtion you can expect investment varies ... estimate the appropriate required rate of return...

... Normal 0.6 15% 8%. Boom .20 .2 0 25% 4%. Returns 13.00% 8.40%. Stock will be preferred as its Expected return is higher Rate of return. 0.026. 0.122. 0.166. ...