Question

Below is a spreadsheet for a situation in which a day trader seeks to maximize expected return while minimizing risk for a portfolio consisting of two assets.

	A	B	C	D
1	Day Trading Portfolio
2
3	Probabilities and Outcomes:	Probability	X Index Fund	Y Index Fund
4		0.25	$5	$6
5		0.36
6		0.19	$3
7		0.04	$2
8		0.05	$1	$(4)
9		0.03		$3
10		0.06		$(2)
11		0.01	$(2)	$5
12		0.01	$(3)	$1

38) What is the variance of the X index fund?

A) 8.80

B) 22.78

C) 4.69

D) 16.40

Answer: C

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39) What is the standard deviation of the X index fund?

A) 5.13

B) 2.17

C) 4.77

D) 2.97

Answer: B

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40) What is the variance of the Y index fund?

A) 22.78

B) 4.69

C) 18.66

D) 8.80

Answer: D

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41) What is the standard deviation of the Y index fund?

A) 5.17

B) 4.77

C) 2.17

D) 2.97

Answer: D

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42) What is the covariance between the two assets?

A) 4.64

B) 4.69

C) 4.77

D) 4.81

Answer: A

How we got the results ??

Answer 1

38)

$Var(X)=E(X^{2})-E(X)^{2}$

$E(X)=\sum xp(x)=5(0.25)+3(0.19)+2(0.04)+1(0.05)+(-2)(0.01)+(-3)(0.01)=1.9$

$E(X^{2})=\sum x^{2}p(x)=5^{2}(0.25)+3^{2}(0.19)+2^{2}(0.04)+1^{2}(0.05)+(-2)^{2}(0.01)+(-3)^{2}(0.01)=8.3$

So, $Var(X)=8.3-1.9^{2}=4.69$

Hence option C.

39)

Standard Deviation X = Var(X)^0.5 = 4.69^0.5 = 2.17

Hence option B.

40)

$Var(Y)=E(Y^{2})-E(Y)^{2}$

$E(Y)=\sum yp(y)=6(0.25)+(-4)(0.05)+3(0.03)+(-2)(0.06)+(5)(0.01)+(1)(0.01)=1.33$

$E(Y^{2})=\sum y^{2}p(y)=6^{2}(0.25)+(-4)^{2}(0.05)+3^{2}(0.03)+(-2)^{2}(0.06)+(5)^{2}(0.01)+(1)^{2}(0.01)=10.57$

So, $Var(Y)=10.57-1.33^{2}=8.80$

Hence option D.

41)

Standard Deviation Y = Var(Y)^0.5 = 8.80^0.5 = 2.97

Hence option D.

42)

$Cov(X,Y)=E(XY)-E(X)E(Y)$

$E(XY)=\sum \sum xyp(x,y)=30(0.25)+(-4)(0.05)+(-10)(0.01)+(-3)(0.01)=7.17$

So, $Cov(X,Y)=7.17-(1.9)(1.33)=4.64$

Hence option A.