# 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.

https://brainmass.com/economics/barriers-to-growth/8290

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See attached file for complete answers

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%

14% 16%

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

I calculated 16% for stock X (the instructor said I should have 12%) where did I go wrong?

16%

Your answer is correct for X ( to be more accurate it is 15.6%)

PROBABILITY Y Probability * Y

10% -35% -3.50%

20% 0% 0.00%

40% 20% 8.00%

20% 25% 5.00%

10% 45% 4.50%

Expected return=Average= Σ= 14.00%

PROBABILITY X Probability * X

10% -10% -1.00%

20% 20% 4.00%

40% 12% 4.80%

20% 20% 4.00%

10% 38% 3.80%

Expected return=Average= Σ= 15.60%

b. Calculate the standard deviation of expected returns for Stock X. (that for Stock Y is 20.35%). Now Calculate the ...

#### Solution Summary

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.

Elite Jewellery vs So Lo Supermarkets: Expected rate of return and standard deviation

You have some money to invest for 12 months and are considering purchasing shares in the retail sector. After reviewing the historical performance and future prospects for Elite Jewellery Ltd. and So Lo Supermarkets Ltd, you have prepared the following information that you willuse for your investment decision:

Elite Jewellery Ltd: So Lo Supermarkets Ltd

Current share price $9.00 $11.60

Current EPS $1.20 0.90

Current Beta 0.85 0.60

Elite Jewellery Ltd So Lo Supermarkets Ltd

Probability of Likely return over Probability of Likely return over return next 12 months return nxt 12 months

0.15 -1% 0.10 1%

0.60 12% 0.40 7%

0.25 18% 0.30 10%

0.20 14%

Other relevant information:

Current risk free rate of return: 5% p.a.

Long run average return on market protfolio: 12% p.a.

Required:

1) Calculate the expected return and standard deviation for each company shares.

2) Briefly explain the meaning of expected return and standard deviation and outline what your calculations indicate about a relationship between risk and return?

3) Briefly outline in words that an average person in the street can understand the difference between standard and beta as measures of risk?

4) Calculate the return investors with a diversified portfolio should require from each share?