Question

You've estimated the following expected returns for a stock, depending on the strength of the economy:

State (s) | Probability | Expected return |

Recession | 0.3 | -0.02 |

Normal | 0.5 | 0.09 |

Expansion | 0.2 | 0.14 |

1. What is the expected return for the stock?

2. What is the standard deviation of returns for the stock?

Answer #1

**1.** Expected return = Respective probabilities
of states * expected return of states

= (0.3*-0.02)+(0.5*0.09)+(0.2*0.14)

= 6.70%

Answer = **6.70%**

**2.** Variance = Product of Deviation Squared and
Probability

State of Economy | Probability | Probable Return | Deviation ( Probable Return- Expected Return) | Deviation Squared | Product ( Deviation Squared* Probability) |

Recession | 0.30 | -2.00 | -8.700 | 75.690000 | 22.7070 |

Normal | 0.50 | 9.00 | 2.300 | 5.290000 | 2.6450 |

Expansion | 0.20 | 14.00 | 7.300 | 53.290000 | 10.6580 |

Variance ( Sum of Product) | 36.01 |

Standard Deviation = Square root of Variance

= 36.01^(1/2)

= 6.00%

Answer = **6.00%**

You've estimated the following expected returns for a stock,
depending on the strength of the economy:
State Probability Expected return
Recession 0.1 -0.01
Normal 0.5 0.1
Expansion 0.4 0.15
What is the standard deviation of returns for the stock?

We know the following expected returns for stock A and the
market portfolio, given different states of the economy:
State (s)
Probability
E(rA,s)
E(rM,s)
Recession
0.2
-0.02
0.02
Normal
0.5
0.13
0.05
Expansion
0.3
0.21
0.09
The risk-free rate is 0.02.
Assuming the CAPM holds, what is the beta for stock A?

We know the following expected returns for stocks A and B, given
different states of the economy:
State (s)
Probability
E(rA,s)
E(rB,s)
Recession
0.2
-0.05
0.05
Normal
0.5
0.1
0.08
Expansion
0.3
0.18
0.12
1. What is the expected return for stock A?
2. What is the expected return for stock B?
3. What is the standard deviation of returns for stock A?
4. What is the standard deviation of returns for stock B?

Based on your research, the following states of economy,
probabilities of states, and returns are forecasted for Stock A and
Stock B:
Return if State Occurs
State of Economy
Probability of state
Stock A
Stock B
Recession
0.65
-0.15
-0.2
Normal
0.3
0.13
0.14
Irrational exuberance
0.05
0.2
0.29
a. What is the expected return on Stock A?
b. What is the expected return on Stock B?
c. Your research also indicates that stock A’s beta is greater
than stock...

Based on your research, the following states of economy,
probabilities of states, and returns are forecasted for Stock A and
Stock B:
Return if State Occurs
State of Economy
Probability of state
Stock A
Stock B
Recession
0.65
-0.15
-0.2
Normal
0.3
0.13
0.14
Irrational exuberance
0.05
0.2
0.29
a. What is the expected return on Stock A?
b. What is the expected return on Stock B?
c. Your research also indicates that stock A’s beta is greater than
stock...

Given the following information, what is the expected rate of
return and the standard deviation for this stock?
State of Economy
Probability of State of Economy
Rate of Return
Boom
0.3
0.23
Normal
0.65
0.14
Recession
0.05
-0.36

The table below shows the expected rates of return for three
stocks and their weights in some portfolio:
Stock A
Stock B
Stock C
Portfolio weights
0.3
0.2
0.5
State
Probability
Expected returns
Recession
0.2
0.08
0.03
0.14
Boom
0.8
0.13
0.05
0.15
1. What is the portfolio return during a recession?
2. What is the expected portfolio return?
3. What is the standard deviation of the portfolio returns?

Given the following information:
State of Economy
Probability
Rate of Return if State Occurs Stock G
Rate of Return if State Occurs Stock H
Boom
0.3
12%
25%
Normal
0.5
15%
10%
Recession
0.2
6%
-18%
Suppose you hold a portfolio with 60% invested in G and 40%
invested in H.
(1) What is the portfolio’s return if each state of the economy
occurs, respectively?
(2) What is the portfolio’s expected return?
(3) What is the portfolio’s standard deviation?

A.
Use the following information on states of the economy and stock
returns to calculate the expected return for Dingaling Telephone:
(Do not round intermediate calculations. Enter your answer
as a percent rounded to 2 decimal places. Omit the "%" sign in your
response.)
State of
Economy
Probability of
State of Economy
Security Return
If State Occurs
Recession
.40
–5.50
%
Normal
.40
11.00
Boom
.20
17.00
B.
Use the following information on states of the economy and stock
returns...

Based on your research, the following states of economy,
probabilities of states, and returns are forecasted for Stock A and
Stock B:Return if State Occurs State of Economy Probability of
state Stock A Stock B Recession 0.65-0.15-0.2 Normal 0.30.130.14
Irrational exuberance 0.050.20.29
a.What is the expected return on Stock A?
b.What is the expected return on Stock B?
c.Your research also indicates that stock A’s beta is greater
than stock B’s beta by 0.5. calculate the expected market risk
premium...

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