Question

Joyce Bromfield has $30,000 to invest for 5 years. She will allocate her money to government Treasury Bills (T-Bills), mutual fund A, and mutual fund B as follows: $4,500 in T-bills; $13,500 in A and $12,000 in B. Fund A has a front-end fee of 5%, MER of 2% and no rear-end fee. Fund B has no front-end fee, MER of 2.5%, and rear-end fee of 5%. Assume that the appropriate discount rate to compare fund fees is 5%.

The expected rates of return and standard deviations of the funds are as follows:

	Expected Return (%)	Standard deviation (%)
A	10	20
B	13	25
T-bill	3	0

The correlation coefficients between A and B is 0.4 .

Required:

1. What is the expected rate of return of her portfolio?
2. What is the standard deviation of her portfolio?
3. If her portfolio’s return is normally distributed, what is the probability
4. That she will lose money next year?
5. That she will earn at least 15% next year?

4. What is the annual fee of each of the funds, A and B, if she holds the funds for 6 years?  

Answer 1

a. Computation of the expected rate of return of portfolio:

First compute the weights:

Weight of T-bills = $4,500 / $30,000

= 0.15  

Weight of A = $13,500 / $30,000

= 0.45

Weight of B = $12,000 / $30,000

= 0.40

Expected :

Expected return of A = 10%

Expected return of B = 13%

Expected return of T-bill = 3%

Formula used to compute the expected return of the portfolio,

Expected return of portfolio = Expected return of A*Weight of A + Expected return of B*Weight of B + Expected return of T-bills*Weight of T-bills

Put the values in above formula,

Expected return of portfolio = 10%*0.45 + 13%*0.4 + 3%*0.15

= 10.15%

Hence, the expected return of portfolio is 10.15%.

b. Computation of standard deviation of portfolio:

SD of A = 20

SD of B = 25

SD of T-bills = 0

Coefficient of Correlation = 0.4

Formula used to compute SD of portfolio,

σP = (wA2σA2 + wB2 σB2 + 2wAwBσAσBρAB)^(1/2)

Here,
σP = is the portfolio standard deviation;
ωB = weight of asset B in the portfolio;
σA = standard deviation of asset A;
σB = standard deviation of asset B; and
ρAB = correlation coefficient between returns on asset A and asset B.

Put the values in above formula,

σP = ((0.45*20)^2 + (0.4*25)^2 + 2*0.4*0.45*20*25)1/2

= 253^(1/2)

= 15.91%

Hence, the standard deviation of portfolio is 15.91%.

c. Normal distribution is the distribution which is symmetric about the mean. The resulting mean of the population will lie within the same range of the standard deviation. Here, more than 68% chance that the portfolio will earn within the range of 10.15% +( +15.91% or -15.91%).

The return of the portfolio will be lied between 26.06% or -5.76%. And according to this, 15% return of the portfolio Is possible.

a. Computation of annual fee of each of the fund:

Annual fee of Fund A:

Invested amount = $13,500

Total fees paid = 7% (2% + 5%)

Annual fees = $13,500 *0.07

= $945

Annual fee of Fund B:

Invested amount = $12,000

Total fees paid = 7.5% (2.5% + 5%)

Annual fees = $12,000 *0.075

= $900

Hence, the annual fees paid for investin in Fund A and Fund B are $945 and $900 respectively.