Question

Mr. Armstrong and Mr. Spendwell are both investors looking to buy financial assets. Mr. Armstrong prefers assets with the lowest prices while Mr. Spendwell prefers assets on the financial market with higher prices. Each of them currently has GHC 1000 to invest and needs your assistance to know which asset to buy to suit their preference. It turns out that Mr. Armstrong is a risk-averse investor while Mr. Spendwell has a huge risk appetite. After receiving a huge bonus from their employers they both decided to do more investments. Of course, Mr. Armstrong has indicated his preference for low risk assets while Mr. Spendwell also indicated his preference more very high risk assets that offer a high return, given his knowledge in risk and return.

i. Using the following information below, do well to advice these two investors on which asset to invest in, considering their risk preference.

ii. Mr. Knowitall subsequently advised Mr. Armstrong to rather invest 50% of his money in Asset A and 50% in Asset B. As a finance expert, what will you say about this idea and what figures will you show to Mr. Armstrong to convince him that this is actually the way to go?

State      Probability      Return on Asset A      Return on Asset B

1             20%                           5%                      50%

2             30%                          10%                       30%

   3             30%                           15%                      10%

   4             20%                         20%                     -10%

Answer 1

	Asset A
	State of Economy	Probability of state of the economy [p]	Rate of return [%] if the state occurs [r]	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	1	0.20	5	1.00	-7.50	56.25	11.25
	2	0.30	10	3.00	-2.50	6.25	1.875
	3	0.30	15	4.50	2.50	6.25	1.875
	4	0.20	20	4.00	7.50	56.25	11.25
				12.50			26.25
	Expected return			12.50
	Variance			26.25
	SD = 26.25^0.5 =			5.1235
	Coefficient of variation = 5.12/12.5 =		0.4096
	Asset B:
	State of Economy	Probability of state of the economy	Rate of return if the state occurs	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	1	0.20	50	10.00	$                   30	900.00	180
	2	0.30	30	9.00	$                   10	100.00	30
	3	0.30	10	3.00	$                 -10	100.00	30
	4	0.20	-10	-2.00	$                 -30	900.00	180
				20.00			420
	Expected return			20.00
	Variance			420
	SD = 420^0.5 =			20.4939
	Coefficient of variation = 20.49/20 =		1.0245
	Correlation [A,B]:
	State of Economy	Probability of state of the economy	dk*dm	dk*dm*p
	1	0.20	-225	-45
	2	0.30	-25	-7.5
	3	0.30	-25	-7.5
	4	0.20	-225	-45
	Covariance [A,B]			-105.000
	Correlation [A,B] = -105/(5.1235*20.4939) =		-1.00
	ANSWERS:
i]	Coefficient of variation is the indicator of risk. Higher the COV, higher the risk.
	Hence,
	Mr.Armstrong should invest in Asset A as, it has lower risk.
	Mr.Spendwell should invest in Asset B as, it has higher risk and higher return.
ii]	If Mr.Armstrong invests as suggested by Mr.Knowitall, the SD and expected return would be as below:
	SD [Volatility] of a two asset portfolio [asset 'a' and asset 'b'] is given by the formula, sdp = [sda^2*wa^2+sdb^2*wb^2+sda*sdb*wa*wb*Cor(a,b)]^0.5
	Where,
	sda and sdb are the standard deviations, wa and wb are the weights of the two assets in the portfolio and Cor(a,b) the correlation of the returns of the two assets.
	Substituting values, SD of the portfolio = (0.5^2*5.12^2+0.5^2*20.49^^2+2*0.5*0.5*5.12*20.49*-1)^0.5 =	7.69
	Expected return = 12.5*0.5+20.00*0.5 =					16.25
	COV = 7.89/16.25 =						0.47
	As the two assets are perfectly & negatively correlated, the risk of the portfolio is less than the risk of Asset A as
	evidenced by the SDs. Further, the return of the portfolioi is also higher. Hence, Mr.Armstrong can satisfy his requirement
	of low risk and at the same time can get higher returns.