Question

Monthly adjusted closing prices for Stock A for the months of November, October, Sept, Aug, July, June and May are $98, 100, 90, 100, 110, 105, 100 respectively. The corresponding market index are $100, 105, 110, 115, 118, 120 and 118. Based on the above data,

1. The annualized volatility of stock A is...

2. The beta of stock A is...

3. If the market index goes up from $100 to $120, what is the estimated percentage change in stock A

Answer 1

A	B	C	D	E	F	G	H	I	J
2			Price		Return
3			Stock A	Market	Stock A	Market
4		May	100	118
5		June	105	120	5.00%	1.69%	=(E5-E4)/E4
6		July	110	118	4.76%	-1.67%
7		August	100	115	-9.09%	-2.54%
8		September	90	110	-10.00%	-4.35%
9		October	100	105	11.11%	-4.55%
10		November	98	100	-2.00%	-4.76%
11				Average	-0.04%	-2.69%	=AVERAGE(G5:G10)
12				St. Dev.	8.46%	2.48%	=STDEV.S(G5:G10)
13				Covariance with market	0.051%	=COVARIANCE.S(F5:F10,G5:G10)
14		1)
15
16		Hence the volatility of the Stock A is	8.46%
17
18		2)
19
20		Beta of stock A	= Cov (rA,rM)/ Var(rM)
21			=0.051% / (2.48%^2)
22			0.83
23
24		Hence Beta of stock A is	0.83
25
26		3)
27
28		Return of the market	=($120 - $100)/$100
29			20.0%
30
31		Estimated % change in stock A	=Beta for Stock A*Return on market
32			=0.83*20%
33			16.61%	=D24*D29
34
35		Estimated % change in stock A	16.61%
36