Question

Risk. Suppose you are considering the risk of a portfolio made up of 70% company A stock and 30% company B stock.

Stock A

Stock B

2011

10.00%

6.00%

2012

7.00%

2.00%

2013

15.00%

5.00%

2014

-5.00%

1.00%

2015

8.00%

-2.00%

Calculate the average annual return for each. (5 points)

Calculate the volatility of returns for each. (5 points)

Calculate the range of values we can be 95% sure returns will fall within for each. (4 points)

Suppose you build a portfolio of 25% in A and 75% in B, calculate expected returns, volatility, and a 95% confidence interval for the portfolio. (10 points)

Answer 1

Following are the data derived from the question:-

	2011	2012	2013	2014	2015	Portfolio %age
Stock A	10%	7%	15%	-5%	8%	70%
Stock B	6%	2%	5%	1%	-2%	30%

A) Calculate the average annual return for each.

Sol:- Average annual return will be calculate by summing all the return year wide and then divide it by 5.

	2011	2012	2013	2014	2015	Portfolio %age	avg annual Return
Stock A	10%	7%	15%	-5%	8%	70%	7.00%
Stock B	6%	2%	5%	1%	-2%	30%	2.40%

B) Calculate the volatility of return for each.

sol:- Following are the table shown all the calculation and steps to calculate the volatility (Variation).

	2011	2012	2013	2014	2015	Portfolio %age	avg annual Return	Summation of all the Deviation Squared/no. of observation
Stock A	10%	7%	15%	-5%	8%	70%	7.00%
Stock B	6%	2%	5%	1%	-2%	30%	2.40%
Deviation from avg Return Stock A	3.00%	0.00%	8.00%	-12.00%	1.00%
Deviation from avg Return Stock B	3.60%	-0.40%	2.60%	-1.40%	-4.40%
Deviation Squared Stock A	0.09%	0.00%	0.64%	1.44%	0.01%			0.436%
Deviation Squared Stock B	0.13%	0.00%	0.07%	0.02%	0.19%			0.082%

Steps to be followed:-

a) Calculate the average price for the number of periods of observations.

b) Determine each period's deviation.

c) square each period's deviation.

d) sum the squared deviation.

e) divide this sum by number of observation. This will give you the volatility of the particular stock.

f) the standard deviation is the square root of that number.

C) Calculate the range of values we can be 95% sure return will fall within for each.

Sol:-

	2011	2012	2013	2014	2015	Portfolio %age	avg annual Return	95% Sure return Data
Stock A	10%	7%	15%	-5%	8%	70%	7.00%	6.65%
Stock B	6%	2%	5%	1%	-2%	30%	2.40%	2.28%

The value for return can be vary for stock A is 7% to 6.65% and for stock B is to 2.40% to 2.28%.