Question

Campbell's father holds just one stock, G Co., which he thinks is a very low risk security. Campbell agrees that the stock is relatively safe, but he wants to demonstrate to his father that he could still reduce his risk by diversifying. He obtained the return shown below on G and E Corp. Both have had less variability than most other stocks over the past 5 years.

Year	G	E	Portfolio: 50% G and 50% E
2015	0.40	0.40
2016	-0.10	0.15
2017	0.35	-0.05
2018	-0.05	-0.10
2019	0.15	0.35
Average return	0.15	0.15
Std dev.s	0.2264	0.22264

a. Measured by the standard deviation of returns, by how much would historical risk have been reduced if G and E were held in a portfolio consisting of 50% in G and the rest of the money in E? (Hint: this is a sample, not a complete population, so the sample standard deviation formula should be used. You can use excel or a calculator to complete the table above)

b. Why is the risk reduced?

Answer 1

Year	G	E	dg=G- MeanG	de=E- MeanE	dg * de
2015	0.40	0.40	0.25	0.25	0.0625
2016	(0.10)	0.15	(0.25)	-	-
2017	0.35	(0.05)	0.20	(0.20)	(0.0400)
2018	(0.05)	(0.10)	(0.20)	(0.25)	0.0500
2019	0.15	0.35	-	0.20	-
TOTAL					0.0725

Covariancege = dg * de / n

= 0.0725 / 5

= 0.0145

Correalationge =  Covariancege / SDg * SDe

= 0.0145 / (0.2264 * 0.22264)

= 0.2877

Since COR is not 1, formula for standard deviation formula is

SDp = √ (SDg)2(Weight.g)2 + (SDe)2(Weight.e)2 + 2*(SDg)*(Weight.g)*(SDe)*(Weight.e)*COR

= √  (0.2264)2 (0.50)2 + (0.22264)2 (0.50)2 + 2* (0.2264) (0.50) (0.22264) (0.50) (0.2877)

= √ 0.0128 + 0.0124 + 0.00725

= √ 0.0324

= 0.18

(b) Since the portfolio consists of two stocks and not just one, the risk is spread and thus the standard deviation is reduced.