Question

Below is a table that exhaustively lists the three possible economic growth situations for the next year and the probability corresponding to each economic situation. The Fund 1 (X) return rate in the different economic growth situation is listed in the table

economic growth	Probability	Fund (X) (%).
Recession	?	-20
Stable growth	0.6	12
Strong growth	0.3	24

(a) (1 point) What is the probability of Recession?

1. (b) (3 points) Calculate the expected return rate for Fund 1 and the standard deviation of the return rate for Fund 1.

2. (c) (3 points) There is a Fund 2 with an expected return rate 7.9% and where the standard deviation of the return rate is 10.7238%. Also we know the correlation coefficent of the Fund 1 and Fund 2 is −0.8187. What is the covariance of the Fund 1 and Fund 2?

3. (d) (3 points) A portfolio consists of 55% invested in Fund 1 and 45% invested in Fund 2. Calculate the standard deviation of the return for this portfolio.

Answer 1

a)

b)

The expected value and standard deviation of the return rate is obtained using the formula,

From the data values,

economic growth	Probability, P(X)	Return rate, X	X*P(X)	X-E[X]	(X-E[X])^2	P(X)*(X-E[X])^2
Recession	0.1	-20	-2	-32.4	1049.76	104.976
Stable growth	0.6	12	7.2	-0.4	0.16	0.096
Strong growth	0.3	24	7.2	11.6	134.56	40.368
Total			12.4			145.44

c)

Where standard deviation of fund 1 (X) = 12.0599%, standard deviation of fund 1 (Y) = 10.7238% and correlation = -0.8187.

d)

Using the properties of variance (such that Var(cX)=c*Var(X) and Var(X+Y)=Var(X)+Var(Y))