Question

The following questions are in order:

Question 1 1 pts The following data applies to Questions 1 to 3 Consider two risky assets: a stock fund and a bond fund with the following probability distributions. Scenario Severe recession Mild recession Normal growth Boom What is the expected return for the bond fund? Your answer should be in percentage points and accurate to the hundredth. For example, if your answer is 10.2511%, then type in 10.25 Probability 0.05 0.25 0.40 0.30 Stock Return (%) Bond return (%) -40 -14 17 15 -5 0.05 Question 2 1 pts What is the standard deviation of the bond fund? Your answer should be in percentage points and accurate to the hundredth. Question 3 1 pts What is the correlation coefficient between the stock returns and the bond returns? Your answer should be in decimal values and accurate to the hundredth (NOT in percentage points So 0.24 if the correlation is 0.2410)

Answer 1

Q1.

The Expected Return of the Bond Fund
Scenario	Probability	Bond Return %	Probability * Bond Return %
Severe Recession	0.05	-9	-0.45
Mild Recession	0.25	15	3.75
Normal Growth	0.4	8	3.2
Boom	0.3	-5	-1.5
			5

Expected Return of Bond Portfolio = ∑ Probability * Bond Return %

Q2. Standard Deviation of a Bond Fund

Scenario	Probability	Bond Return %	Probability * Bond Return %	Bond Return - Expected Return	Bond Return - Expected Return ^2	(Bond Return - Expected Return ^2) * Probability
Severe Recession	0.05	-9	-0.45	-14	196	9.8
Mild Recession	0.25	15	3.75	10	100	25
Normal Growth	0.4	8	3.2	3	9	3.6
Boom	0.3	-5	-1.5	-10	100	30
			5			68.40

Standard Deviation of a Bond Fund = ∑[(Bond Return - Expected Return ^2) * Probability] ^ (1/2)

                                                                 = 68.40 ^ (1/2)

                                                                = 8.27

Q3. Calculation of Correlation Coefficient between Stock return and Bond Return

For the calculation of Correlation Coefficient between Stock return and Bond Return, we will require Standard Deviation of Bond Returns and Stock Returns. Standard Deviation of Bond Returns is already calculated in Q2.

Standard Deviation of Stock Returns:

Scenario	Probability	Stock Return %	Probability * Stock Return %	Stock Return - Expected Return	(Stock Return - Expected Return) ^2	(Stock Return - Expected Return ^2) * Probability
Severe Recession	0.05	-40	-2	-51.2	2621.44	131.072
Mild Recession	0.25	-14	-3.5	-25.2	635.04	158.76
Normal Growth	0.4	17	6.8	5.8	33.64	13.456
Boom	0.3	33	9.9	21.8	475.24	142.572
			11.2			445.86

Standard Deviation of a Stock Fund = ∑[(Stock Return - Expected Return ^2) * Probability] ^ (1/2)

                                                                 = 445.86 ^ (1/2)

                                                                = 21.11

Also, we will require the Covariance Between Stock Returns and Bond Returns.

Probability	Bond Return %	Probability * Bond Return %	Bond Return - Expected Return	Stock Return %	Probability * Stock Return %	Stock Return - Expected Return	Probability * (Bond Return - Expected Return) *(Stock Return - Expected Return)
0.05	-9	-0.45	-14	-40	-2	-51.2	35.84
0.25	15	3.75	10	-14	-3.5	-25.2	-63
0.4	8	3.2	3	17	6.8	5.8	6.96
0.3	-5	-1.5	-10	33	9.9	21.8	-65.4
		5			11.2		-85.6

Covariance = ∑ Probability * (Bond Return - Expected Return) *(Stock Return - Expected Return)

                     = -85.6

Correlation Coefficient between Stock Returns and Bond Returns =

Covariance Between Stock Returns and Bond Returns / (Standard Deviation of Stock Returns x Standard Deviation of Bond Returns)     

=                    ____-85.6_____
                       8.27 x 21.11

=                          - 0.49