1. Considering the uncertainty of the future, there is a 5% chance that economy will be in boom; 92%...

Question

1. Considering the uncertainty of the future, there is a 5% chance that economy will be in boom; 92% chance that economy will be normal and the remaining possibility of economy to be in recession. If you buy XYZ company stock, you are expected to earn 22% return, if economy is in boon; or you will earn 15% return if economy is normal. However, if economy is in recession, your stock will make a loss of 2 What is the expected rate of return on this stock?

2. Calculate the expected return; Variance and standard deviation of a ABC Inc. stock if the economy is expected to be very good with 6% chance and expected to be normal with 60% chance and likely to be in recession with 34% chance and the expected return on this stock are likely to be 8.4%; 8.9% and 9.2% respectively if economy is in Boom; Normal or in Recession.

3. Calculate the rate of return on the following portfolio. (Hint: First calculate the weight of each stock value as a percentage of total dollar investment)

STOCK	Number of Shares	Price per Share	Expected Return
A	400	$24	13.6%
B	300	$13	14.8%
C	100	$33	7.4%
D	100	$54	2.1%

4. Calculate the expected return on the portfolio that has invested 30% is stock A, 40% in stock B; and 30% in stock C.

		Rate of Return in each State
State of Economy	Probability	Stock A (%)	Stock B (%)	Stock C (%)
Boom	4%	18.4	11.4	26.1
Normal	93%	9.6	7.9	17.6
Recession	3%	3.8	4.6	-28.7

5. You have four securities in your portfolio Security A, B, C and a Treasury Bill (Risk-free). The total value of this portfolio now is $76,000. The risk of this portfolio is comparable to the Market risk and therefore this portfolio could be used a proxy for the market. (Hint: Beta of market portfolio is 1) Calculate the beta of Stock C, given the following information and the CAPM?

Security	Value	Beta
A	$13,800	1.21
B	$48,600	1.08
C	$8,400	?
T-Bill (risk Free)	?	?

6. Using CAPM (capital Asset Pricing Model), find the Beta of stock A if this stock A has required return of 14.3% and risk free rate is 3.9%. It is also given that the Market risk premium (Market Return – Risk Free Return) is 7.8%

7. You have invested $4,000 in stock A, $4,000 in stock B, and $2,000 in stock C. The risk free rate of return is 4.03% (expected return on T-Bills). Given the following information, calculate the return on this portfolio and then calculate the portfolio risk premium.

State of Economy	Probability	Rate of Return
State of Economy	Probability	Stock A (%)	Stock B (%)	Stock C (%)
Boom	5%	7	15	28
Normal	80%	9	12	17
Recession	15%	10	2	-35

8. Stock A and Stock B have the same reward to risk ratio. Expected rate of return on stock A is 14.4% and stock A has a Beta of 1.21. Stock B has expected rate of return of 12.87% and a beta of 1.06. Calculate the risk free rate of return.

Sweety · Accepted Answer

QUESTION 1
	SOLUTION TO QUESTION 1:  CALCULATION OF EXPECTED RETURN OF PORTFOLIO
		STATE OF ECONOMY	PROBABLITY	RETURN OF
XYZ CO. STOCK	EXPECTED RETURN OF THE STOCK 
(%)
		Boom	5%	22%	1.10%
		Normal	92%	15.0%	13.80%
		Recision	3%	-2%	-0.06%
					14.84%
	Expected Return Of the Stock=		(Expected return in boom economy*probablity)+(Expected return in normal economy*probablity)+(Expected return in boom economy*probablity)
	                                                           =		14.84%
		 
QUESTION 2
		SOLUTION TO QUESTION 2:  CALCULATION OF EXPECTED RETURN, STANDARD DEVIATION & VARIANCE
				STATE OF ECONOMY	PROBABLITY
(A)	 RETURN OF
XYZ CO. STOCK IN EACH STATE OF ECONOMY
(B)	EXPECTED RETURN OF THE STOCK (taking into account all state of economy)
(%) ( C )	ACTUAL RETURN LESS
EXPECTED RETURN
(D)	STANDARD 
DEVIATION	VARIANCE
				Good	6%	8.40%	0.50%	-0.57%	0.14	0.02
				Normal	60%	8.90%	5.34%	8.90%	6.9	47.61
				Recision	34%	9.20%	3.13%	9.20%	5.36	28.73
							8.97%		12.40	76.36
				EXPECTED RETURN OF THE STOCK IS 8.97%
				STANDARD DEVIATION OF STOCK IS 12.40
				VARIANCE OF STOCK IS 76.36
		FORMULAS UNDELYING THE ABOVE CALCULATION ARE
	I)	Expected Return Of the Stock=			(Expected return in boom economy*probablity)+(Expected return in normal economy*probablity)+(Expected return in boom economy*probablity)
QUESTION 3
	SOLUTION TO QUESTION 3: CALCULATION OF EXPECTED RETURN OF FOLLOWING PORTFOLIO
		Stock	Number of Shares
(A)	Price per Share
(B)	Total Value of share
(A*B)
( C )	Weight
(D)	Expected Return
(E)	Expected Return
(D*E)
(F)
		A	400	$   24.00	$   9,600.00	0.43	13.60%	5.9%
		B	300	$   13.00	$   3,900.00	0.18	14.80%	2.6%
		C	100	$   33.00	$   3,300.00	0.15	7.40%	1.1%
		D	100	$   54.00	$   5,400.00	0.24	2.10%	0.5%
		TOTAL			$   22,200.00	$   1.00		10.1%
		 Expected Return of portfolio= 10.1%
		NOTES
		I) Formula underlying above calculation are as follows
		     Expected Return of the portfolio  = (WA*ERA)+(WB*ERB)+(WC*ERC) +(WD*ERD),Where
                                                                                                                                                                                      
		      WA= Weight of A   = (No. of share of A*Price per share of A)/Total value of portfolio.
		      WB= Weight of B   = (No.

1. Considering the uncertainty of the future, there is a 5% chance that economy will be in boom; 92% chance that economy will be normal and the remaining possibility of economy to be in recession. If...

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