# Expected Rate of Return and Stock variance and Standard Deviation

1) Given the following data, What is the weight of security 1? Of security 2? 3? What is the expected return on the portfolio?

Security 1 ; $5,000 invested; Expected return 7%

Security 2; $7,000 invested; Expected return 9%

Security 3; $9,000 invested; Expected return 12%

2) The expected possible outcomes for Roxy Stock are below; what is the expected standard deviation of Roxy Stock?

State Probability Return

Super Boom 10% 35%

Boom 15% 20%

Expansion 45% 15%

Recession 30% -5%

https://brainmass.com/business/finance/expected-rate-of-return-and-stock-variance-and-standard-deviation-588528

#### Solution Summary

The weight of three securities are calculated. After completing the calculation, the expected return of the portfolio is calculated. This solution also includes a calculation for variance of a stock based on the four different returns and the probability of the return. After completing the variance calculation, the standard deviation of the stock is calculated.

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.