Question

6/

A. You own a portfolio that has 4,100 shares of stock A, which is priced at 14.8 dollars per share and has an expected return of 4.97 percent, and 2,100 shares of stock B, which is priced at 24.9 dollars per share and has an expected return of 11.35 percent. The risk-free return is 3.14 percent and inflation is expected to be 2.41 percent. What is the expected real return for your portfolio? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098

B

Your investment portfolio has 15,000 shares of Fairfax Paint, which has an expected return of 10.45 percent and a price of 5.8 dollars per share, and 30,000 shares of Litchfield Design, which has a price of 3 dollars per share. If your portfolio has an expected return of 13.47 percent, then what is the expected return for Litchfield Design? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

C.

What is risk premium for stock A if its expected real return is 7.12%, the expected inflation rate is 4.35%, and the risk-free return is 5.27%?  Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Solution 6-A
		Stock A	Stock B	Total
	No of shares	4,100	2,100
	Share price	$                    14.80	$                      24.90
	Portfolio	=4100*14.8	=2100*24.9
	Portfolio	$                  60,680	$                    52,290	$112,970.00
	Expected return	4.97%	11.35%
	Portfolio value	=60680*(1+4.97%)	=52290*(1+11.35%)
	Portfolio value	$             63,695.80	$               58,224.92	$121,920.71
	Nominal return=			(121920.71-112970)/112970
	Nominal return=			7.92%
	Inflation rate			2.41%
	Real return			((1+7.92%)/(1+2.41%)-1)
	Real return			0.05383
Solution 6-B
		Fairfax	Litchfield	Total
	No of shares	15,000	30,000
	Share price	$                      5.80	$                        3.00
	Portfolio	=15000*5.8	=30000*3
	Portfolio	$                  87,000	$                    90,000	$177,000.00
	Portfolio return			13.47%
	Portfolio value			=177000*(1+13.47%)
	Portfolio value			$200,841.90
	Expected return	10.45%
	Fairfax value	=87000*(1+10.45%)
	Fairfax value	$             96,091.50		$ 96,091.50
	Litchfield value			200841.90-96091.50
	Litchfield value			$104,750.40
	Litchfield return			(104750.40-90000)/90000
	Litchfield return			0.1639
Solution 6-C
	Stock A real return	7.12%
	Expected inflation	4.35%
	(1+real rate)*(1+inflation)=	(1+nominal rate)
	(1+7.12%)*(1+4.35%)=	(1+nominal rate)
	1.1177972	(1+nominal rate)
	Nominal rate=	0.1177972
	Risk free rate=	0.0527
	Risk premium=	=0.1177972-0.0527
	Risk premium=	0.0651