Question

Question 37 Jan $87.69 Feb $84.95 Mar $85.86 Apr $88.04 May $87.12 Jun $94.10 Using the above stock prices, calculate the historical standard deviation of returns for the stock 3.265% 4.631% 3.85796 4.229% 5.50196

Answer 1

Historical standard deviation of returns of stock calculation

Month	Stock Price (Pi)	Return [xi = (P2 -P1)/P1]	(xi- x-bar)	(xi- x-bar)^2
Jan	$87.69
Feb	$84.95	-3.12%	-4.62%	0.21%
Mar	$85.86	1.07%	-0.42%	0.00%
Apr	$88.04	2.54%	1.05%	0.01%
May	$87.12	-1.04%	-2.54%	0.06%
Jun	$94.10	8.01%	6.52%	0.43%
Average Return (x-bar)	1.49%
Sum [∑(xi- x-bar)^2]	0.72%
Variance = [∑(xi- x-bar)^2]/(5-1)	0.18%
Standard Deviation = √variance	4.229%
[Note: as there are 5 data points of stock return, therefore n = 5)

Historical standard deviation of returns of stock is 4.229%

Therefore correct answer is option: 4.229%

Formulas used in excel calculation:

D E (xi-x-bar)^2 1 Month 2 Jan 3 Feb 4 Mar 5 Apr 6 May 7 Jun А B Stock Price (Pi) Return [xi = (P2-P1)/P1] (xi-x-bar) 87.69 84.95 =(B3-B2)/B2 =C3-$C$8 85.86 I=(B4-B3)/B3 =C4-$C$8 88.04 1=(B5-B4)/B4 =C5-$C$8 87.12 =(B6-B5)/85 =C6-$C$8 94.1 I=(B7-B6)/B6 =C7-$C$8 Average Return (x-bar) =AVERAGE(C3:07) Sum [S(xi- x-bar)^2] Variance = [(xi-x-bar)^2]/(5-1) Standard Deviation = Vvariance =D3 D3 =D4*D4 =D5 D5 =D6*D6 =D7*D7 8 9 10 =SUM(E3:E7) =E9/(5-1) =SQRT(E10) 11