Question

Ramona Sanjuan is planning to invest $10-million of her own money but she is undecided among the following two alternative portfolios:

• Portfolio 1: Investing $4-million in a North-American Market Index fund “A” and the rest in a European market index fund “B”

• Portfolio 2: Investing $7-million in fund “A” and the rest in fund “B”
  The predicted returns over the next year for fund “A”, fund “B”, and T-bills are as follows:

		Returns (Annualized)
Economic Scenario	Probability	North- American Index Fund “A”	European Index Fund “B”	T-bills
Recession	1/3	-14%	8%	2.5%
Normal	1/3	19%	-6% %	2.5%
Expansion	1/3	34%	22%	2.5%

Given above information, determine:

1 a) The expected return on fund “A” and fund “B”, respectively. [2 points]
1 b) The standard deviation of fund “A” and fund “B”, respectively [2 points] 1 c) The covariance between the returns on fund “A” and fund “B” [2 points] 1 d) The correlation coefficient between both funds [2 points]

For portfolio 1, determine:

2 a) The expected return [2 points]

2 b) The risk of the portfolio (standard deviation). [2 points] 2 c) The reward to variability (RTV) ratio. [2 points]

For portfolio 2, determine

3 a) The expected return [2 points]
3 b) The risk of the portfolio (standard deviation). [2 points]
3 c) The reward to variability (RTV) ratio. [2 points]
4) Which of the two portfolios should Ramona choose? Why? Justify your answer. [2 points]

Answer 1

Risk free rate is 2.5%

	Probability	Noth america	european	P(n)	P(E)	(North-13)^2*P	(European-8)^2*P	Covariance of AB	COV
Recession	0.333333333	-14.00	8	-4.666667	2.666667	243.00	0	(-14-13)(8-8)*o.3333	o
Normal	0.333333333	19.00	-6	6.333333	-2	12	65.33333333	(19-14(-6-8)*0.3333	-6.33333
expansion	0.333333333	34.00	22	11.33333	7.333333	147	65.33333333	(34-13)(22-8)*0.33333	11.6655
				13	8	402.00	130.6666667		5.332173
				Expected return a	Expected return B

1(A) expected return on Noth america(a) is 13
Expected return on european (B) is 8
1(B) variance of A is 402
variance of B is 130.666
standard deviation of A is square root of 402=20.05
standard deviation of b is square root of 130.6666=11.43
Covariance is 5.332173
for portfolio 1
2(A)Expected return
A investment -4 million
B investment -6 million

	Weight	expected return	W*return
A	0.4	13	5.2
B	0.60	8	4.8
		Expected return	10

2(b) standard deviation
wA*(SDA)^2+wB*(SDB)^2+2WaWbcoviance of ab
(0.4*402)+(0.6*130.6666)+2*0.4*0.6*5.3321
241.759368
variance is 241.7594
SD is square root of 241.7594=15.55
SD is 15.55
For portfolio 2
3(A)Expected return
A investment -7 million
B investment -3 million

A	Weight	expected return	W*return
B	0.7	13	9.1
	0.3	8	2.4
		Expected return	11.5

3(b) standard deviation
wA*(SDA)^2+wB*(SDB)^2+2WaWbcoviance of ab
(0.7*402)+(0.3*130.6666)+2*0.7*0.3*5.3321
322.839462
variance is 322.8395
SD is square root of 241.7594=17.96
SD is 15.55

	Expected return	SD	Coffeicent of variation
A	13	20.05	154.2307692
B	8	11.43	142.875
Portfolio 1	10	15.55	155.5
Portfolio 2	11.5	17.96	156.173913

Portfolio 1 is better

Investing fullin B is very good