Question

Stocks A and B have the following historical returns:

Year
2012	-20.10%	-12.60%
2013	20.50	24.30
2014	17.25	30.90
2015	-3.25	-10.10
2016	29.50	11.40

1. Calculate the average rate of return for each stock during the 5-year period. Round your answers to two decimal places.

   Stock A	%
   Stock B	%

2. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Round your answers to two decimal places.

   Year	Portfolio
   2012	%
   2013	%
   2014	%
   2015	%
   2016	%
   Average return	%

3. Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places.

   	rA	rB	Portfolio
   Std. Dev.	%	%	%

Answer 1

A Average rate of return for each stock during 5 years will be aa follows :-

Stock A = -20.10+20.50+17.25+(-3.25)+29.50/5

= 43.90/5 ,= 8.78%

Stock B = -12.60+24.30+30.90+(-10.10)+11.40/5

= 43.9/5 = 8.78%

Stock A	8.78%
Stock B	8.78%

B. Following will be the Return of portfolio each year and average return :-

Year	Portfolio
2012	-16.35% (-20.10x0.5+-12.60x0.5)
2013	22.40% (20.50x0.50+24.30x0.50)
2014	24.075% (17.25x0.5+30.90x0.5)
2015	-6.675% (-3.25x0.5+-10.10x0.5)
2016	20.45% (29.50x0.5+11.40x0.5)
Average return	8.78% {(-16.35+22.40+24.075+-6.675+20.45)/5}

C . Standard deviation of returns of each stock and portfolio is as follows

	rA	rB	portfolio
Standard deviation	40.21%	39.38%	37.76%

Working note :-

1. Standard deviation for sotck A

m = average return

Year	return (x)	x-m (here m = 8.78)	(x-m)2
2012	-20.10	-28.88 (-20.10-8.78)	834.05
2013	20.50	11.72 (20.50-8.78)	137.36
2014	17.25	8.47 (17.25-8.78)	71.74
2015	-3.25	-12.03 (-3.25-8.78)	144.72
2016	29.50	20.72 (29.50-8.78)	429.32
Total		m = 8.78	1617.19

Standard deviation of stock A = √1617.19 = 40.21%.

Calculation of standard deviation of stock B

Year	return (x)	(x-m)	(x-m)2
2012	-12.60	-21.38 (-12.60-8.78)	457.10
2013	24.30	15.52 (24.30-8.78)	240.87
2014	30.90	22.12 (30.90-8.78)	489.29
2015	-10.10	-18.88 (-10.10-8.78)	356.45
2016	11.40	2.62 (11.40-8.78)	6.86
Total	m = 8.78		1550.59

Standard deviation of stock B = √1550.59 = 39.38%.

Calculation of is standard deviation of portfolio

Year	return (x)	(x-m)	(x-m)2
2012	-16.35	-25.13 (-16.35-8.78)	631.52
2013	22.40	13.62 (22.40-8.78)	185.50
2014	24.075	15.295 (24.075-8.78)	233.94
2015	-6.675	-15.454 (-6.675-8.78)	238.83
2016	20.45	11.67 (20.45-8.78)	136.19
total	m = 8.78		1425.97

Standard deviation of portfolio = √1425.97 = 37.76%