Question

The following table shows historical end-of-week adjusted close prices (including dividends) for a stock and the S&P 500.

	A	B	C
1	Week	Stock	S&P 500
2	0	39.53	2,758
3	1	40.17	2,700
4	2	43.1	2,742
5	3	42.47	2,783
6	4	39.77	2,836
7	5	42.07	2,762
8	6	43.84	2,829
9	7	39.77	2,768
10	8	40.1	2,866
11	9	40.98	3,019
12	10	42.15	2,982

2. What is the geometric average weekly return for the S&P 500?

3. What is the annualized return for the S&P 500 (EAR)?

4. Calculate the weekly returns. What is standard deviation of weekly returns for the S&P 500?

5. What is the beta of the stock?

Answer 1

	Weekly Return of S&P100 (Week1)	-0.02102973	(2700/2758)-1
	Weekly Return ofWeek(n)=(Closing Price of Week(n)/Closing price of week(n-1))-1
			A	B	C	i	R	(1+R)
		1	Week	Stock	S&P 500	Weekly Return of stock	Weekly Return of S&P500	(1+Weekly return)
		2	0	39.53	2,758
		3	1	40.17	2,700	0.01619	-0.02103	0.97897
		4	2	43.1	2,742	0.07294	0.015556	1.015556
		5	3	42.47	2,783	-0.01462	0.014953	1.014953
		6	4	39.77	2,836	-0.06357	0.019044	1.019044
		7	5	42.07	2,762	0.057833	-0.02609	0.973907
		8	6	43.84	2,829	0.042073	0.024258	1.024258
		9	7	39.77	2,768	-0.09284	-0.02156	0.978438
		10	8	40.1	2,866	0.008298	0.035405	1.035405
		11	9	40.98	3,019	0.021945	0.053385	1.053385
		12	10	42.15	2,982	0.028551	-0.01226	0.987744
					TOTAL	0.0768	0.081658
	Expected(Mean) Weekly Return of Stock	0.007679983	(0.0768/10)	0.768%
	Expected(Mean) WeeklyReturn of S&P500	0.008165833	(0.081658/10)	0.817%					0.027063
2	Geometric Average Weekly Return of S&P500=
	((1+R1)*(1+R2)*(1+R3)…...(1+Rn))^(1/n))-1
	R1,R2,R3 are weekly return in week 1,2,3 ..n
	Geometric average Weekly Return of S&P
	(1+R1)*(1+R2)…....(1+R10)=	1.081218274	(0.97897*1.015556*…...........0.987744)
	Geometric Average Weekly Return of S&P500=	0.007839412	((1.081218^(1/10))-1
	Geometric Average Weekly Return of S&P500=	0.7839%
3	Annualized Return of S&P 500(EAR)
	Expected Weekly Return	0.008165833
	Annualized Return of S&P 500(EAR)=0.008166*52	0.424623339
	Annualized Return of S&P 500(EAR)	42.46%
4	Standard Deviation of Returns of S&P 500	0.027062684	Using STDEV function of excel over weekly returns of S&P 500
	Standard Deviation of Returns of S&P 500	2.71%
5	Beta of Stock is the Slope of the Line with Return of S&P 500 in X axis and Stock Return on Y axis
	Slope of the Line =	0.207310725	(Using SLOPE function of excel with S&P returns as known Xs and Stock returns known y_s
	Beta of Stock	0.207310725