Question

a) Financial engineering has been disparaged as nothing more than paper shuffling. Critics argue that resources used for rearranging wealth (.e. bundling and unbundling financial assets) might be better spent on creating wealth (i.e. creating real assets) Evaluate this criticism. (15 Marks) b) You are given the following data about available investments: State of the Economy Probability Return (A) Return (B) Strong Boom 0.15 -0.60 0.75 Weak Boom 0.20 -0.30 0.50 Average 0.05 -0.10 0.15 Weak Recession 0.40 0.20 -0.10 Strong Recession 0.20 0.80 -0.35 Compute and fully interpret the following for these investments: I. II. III. IV. Mean rate of return for each investment (5 Marks) Standard deviation for each investment. (5 Marks) Coefficient of variation for each investment. (3 Marks) Covariance among the rates of return. (4 Marks) Correlation coefficient of the rates of return. (3 Marks) Briefly explain the difference in assumptions underlying Portfolio Theory and the Capital Asset Pricing Model (CAPM) Cheet link (5 Marks) [TOTAL: 40 MARKS] VI.

investment analysis

Answer 1

1. Mean rate of return

		Actual return		Expected return= Probability* actual return
state	probability	A	B	A	B
strong boom	0.15	-0.60	0.75	-0.0900	0.1125
weak boom	0.20	-0.30	0.50	-0.0600	0.1000
average	0.05	-0.10	0.15	-0.0050	0.0075
weak recession	0.40	0.20	-0.10	0.0800	-0.0400
strong recession	0.20	0.80	-0.35	0.1600	-0.0700
			Total	0.0850	0.1100

For strong boom , A: expected return = 0.15*-0.06, weak boom = 0.20*-0.30 and so on.

For strong boom ,B: expected return = 0.15*0.75, weak boom = 0.20*0.50 and so on.

So the return for A= 8.50 %

And B= 11.00%

2. Standard deviation

Standard deviation = [( actual return-expected return)²* ( probability)]^1/2

		Actual return		Expected return		S= (Given return - expected return) ^2		D= S*P
state	probability	A	B	A	B	A	B	A	B
strong boom	0.15	-0.60	0.75	0.0850	0.11	0.4692	0.4096	0.0704	0.0614
weak boom	0.20	-0.30	0.50			0.1482	0.1521	0.0296	0.0304
average	0.05	-0.10	0.15			0.0342	0.0016	0.0017	0.0001
weak recession	0.40	0.20	-0.10			0.0132	0.0441	0.0053	0.0176
strong recession	0.20	0.80	-0.35			0.5112	0.2116	0.1022	0.0423
			Total	0.0850	0.1100			0.2093	0.1519

Standard deviation = D^1/2
A:	=(0.2093)^1/2
	=0.4575
B:	=(0.1519)^1/2
	= 0.3897

Here, for strong boom , in A: S= (-0.60-0.085))^2

Weak boom = (-0.30-0.085)^2

And so on

Similarly for B:

for strong boom , in B: S= (0.75-0.11))^2

Weak boom = (0.50-0.11)^2

And so on

And for D: for A:

Strong boom= 0.15*0.4692

Weak boom = 0.20*0.1482

And so on.

3. Coefficient of variation:

coefficient of variation (COV)= standard deviation/ expected return rate

for A:

SD= 0.4575

Expected return = 8.50%

COV= 0.4575/0.085

= 5.38

for B:

SD= 0.3897

Expected return = 11%

COV= 0.3897/0.11

=3.54

4. Covariance of portfolio = ∑[probability*(given return of A- expected return of A)* (given return of B- expected return of B)]

		Actual return		Expected return		V= (Given return - expected return)		C= P* (V of A)*(V of B)
state	probability	A	B	A	B	A	B
strong boom	0.15	-0.60	0.75	0.0850	0.11	-0.69	0.64	-0.0658
weak boom	0.20	-0.30	0.50	0.0850	0.11	-0.39	0.39	-0.0300
average	0.05	-0.10	0.15	0.0850	0.11	-0.19	0.04	-0.0004
weak recession	0.40	0.20	-0.10	0.0850	0.11	0.12	-0.21	-0.0097
strong recession	0.20	0.80	-0.35	0.0850	0.11	0.72	-0.46	-0.0658
							Total sum	-0.1716

So the C for strong boom will be = 0.15*-0.69*0.64= -0.065

Weak boom = 0.20*-0.39*0.39=-0.03

And so on

So Covariance= -0.1716

5. Correlation coefficient of portfolio = Covariance / (Standard deviation of A* Standard deviation of B)

= -0.1716/(0.4575*0.3897)

= -0.9625