Question

An analyst gathers the following return data for two assets and constructs the follow table, R₁ is the return of Asset 1 and R1 is the mean of the return for Asset 1, R₂ is the return of Asset 2 and R2 is the mean of the return for Asset 2.

	Asset 1	Asset 2
Period	R1 (%)	R2 (%)	R1 - R1	(R1 - R1)2	R2 - R2	(R2 - R2)2	(R1 -R1)(R2 - R2)
T1	7.00	16.00	-3.00	9.00	6.00	36.00	-18.00
T2	13.00	4.00	3.00	9.00	-6.00	36.00	-18.00
T3	10.00	10.00	0.00	0.00	0.00	0.00	0.00
SUM	30.00	30.00		18.00		72.00	-36.00
(SUM / N), where N=3	10.00	10.00		6.00		24.00	-12.00
SUM / (N-1), where N = 3				9.00		36.00	-18.00

Based on the information above: the sample standard deviation for the returns of Asset 2 is closest to:

If the investor forms a portfolio comprised of only the two assets with 30% invested in Asset 1, then the correlation of the returns between Asset 1 and Asset 2 is closest to:

If the investor forms a portfolio comprised of only the two assets with 30% invested in Asset 1, then the portfolio's standard deviation of the returns is closest to:

Answer 1

	Asset 1	Asset 2	Asset 1	Asset 1	Asset 2	Asset 2
Period	R1 (%)	R2 (%)	R1 - R1	(R1 - R1)2	R2 - R2	(R2 - R2)2	(R1 -R1)(R2 - R2)
T1	7	16	-3	9	6	36	-18
T2	13	4	3	9	-6	36	-18
T3	10	10	0	0	0	0	0
SUM	30	30		18		72	-36
n	3	3		3		3	3
(Sum / n)	10	10		6		24	-12
	1	Standard Deviation for Asset 2	SUM(R2 - R2)2
					n
					72
					3
					24
	2	Correlation of the returns between Asset 1 and Asset 2
		where investment in Asset 1 is 30%
		Standard Deviation for Asset 1	6
		Standard Deviation for Asset 2	24
		Covariance (Asset 1 Asset 2)	Sum((R1 -R1)(R2 - R2))
					n
					-36
					3
					-12
		Correlation (Asset 1 Asset 2)	Covariance (Asset 1 Asset 2)
					S.D1 * S.D2
					-12
					6*24
					-12
					144
					-0.083
	3	Portfolio's standard deviation	16.74