Question

Michael and Janine are both investors wanting to purchase investment portfolios. The expected return, standard deviation and beta of various investments are shown in the following table:

Investment	Average return over last year (% pa)	Standard Deviation (% pa)	Beta
Apocryphal Industries	16	11	1.8
Bona Fide Ltd	13	9	1.3
Market Index	11	2	1
10 year Bond	5	3	0

Michael wants a portfolio that has an expected return of 12% pa and that contains only Apocryphal Industries and 10 year bonds.

Janine wants a portfolio with a 26% weighting in Apocryphal Industries and a 74% weighting in Bona Fide Ltd shares. The correlation coefficient between the returns of the shares in Apocryphal Industries and Bona Fide Ltd is 0.7.

a)Calculate the percentage of each share that Michael should include in his portfolio to achieve his desired results. Give your answers as a percentage to the nearest percent.

Investment	Percentage to invest
Apocryphal Industries	% pa
Bona Fide Ltd	% pa
10 year Bond	% pa

b)Janine is interested in finding out how risky her portfolio is. Calculate the standard deviation of Janine's portfolio. Give your answer as a percentage to 2 decimal places.

Standard deviation =  % pa

Answer 1

a. Weight of Aprocryphal Industries = w

Weight of 10 Year Bond = 1 - w

Expected Return = w * Return of Aprocryphal Industries + (1-w) * Return of 10 year Bond

12% = w * 16% + (1-w) * 5%

12% = w * 16% + 5% - 5% * w

11% * w = 7%

w = 0.6363

1 - w = 0.3636

Investment	Percentage to invest
Apocryphal Industries	64%
Bona Fide Ltd	0%
10 year Bond	36%

2. weight of apocryphal = 26%

Weight of Bonafide = 74%

SD of Apocryphal = 11%

SD of Bonafide = 9%

Standard Deviation = Sqrt(0.26^2 * 0.11^2 + 0.74^2 * 0.09^2 + 2 * 0.26 * 0.11 * 0.74 * 0.09 * 0.7)

Standard Deviation = Sqrt(0.00792)

Standard Deviation of Janine Portfolio= 8.90%