Question

“The Dow 10 Strategy” maintains a portfolio of the 10 highest yielding Dow Jones industrial stocks. Consider the data as per table, for the 25 years.

1. Compute the average annual returns for the Dow Jones Portfolio and the Dow 10 Strategy portfolio. Comment about the reward.
2. Compute the sample standard deviation for each portfolio. Comment about risk.
3. Compute the geometric mean Xg of 1+R_j for each portfolio. Compute (Xg)-1. What does this last number represent?
4.   is the equation relating least squares slope , Correlation  r and sample standard deviation. Compute the r for Dow 10 versus Dow Jones.

Note:   Use of calculators and computers is highly recommended.

Year	DJIA*Total Returns	Dow 10 Strategy**Total Return
1972	18.18%	23.32%
1973	-13.16%	3.96%
1974	-23.21%	-0.72%
1975	44.48%	56.03%
1976	22.75%	34.93%
1977	-12.76%	-1.75%
1978	2.62%	0.12%
1979	10.52%	12.99%
1980	21.45%	27.23%
1981	-3.40%	7.73%
1982	25.84%	26.05%
1983	25.68%	38.75%
1984	1.07%	5.75%
1985	32.83%	29.40%
1986	26.96%	34.79%
1987	6.00%	6.07%
1988	15.97%	24.33%
1989	31.74%	25.66%
1990	-0.61%	-7.57%
1991	23.99%	34.02%
1992	7.37%	7.79%
1993	16.74%	26.91%
1994	4.94%	4.05%
1995	36.47%	36.51%
1996	28.58%	28.18%

Answer 1

I have calculated the answers using Excel since Note says Use of computer is recommended (You can use Formulas)

a) Average Annual Return =AVERAGE(all return values selected)

for Dow Jones Portfolio = 14.04%

and the Dow 10 Strategy portfolio = 19.38%

Comment:- Dow 10 Strategy Portfolio has higher Average Annual return thus more rewarding.

b) Standard Deviation =STDEVP(All return values selected)

for Dow Jones Portfolio = 0.166

and the Dow 10 Strategy portfolio = 0.158

Comment:-  Dow 10 Strategy Portfolio has lower Standard Deviation thus Less Risky.

c) Geometric Mean (Xg) of (1+Rj)

Add 1 to all returns, it will look as:-

Year	DJIA*Total Returns	Dow 10 Strategy**Total Return
1972	118.18%	123.32%
1973	86.84%	103.96%
1974	76.79%	99.28%
1975	144.48%	156.03%
1976	122.75%	134.93%
1977	87.24%	98.25%
1978	102.62%	100.12%
1979	110.52%	112.99%
1980	121.45%	127.23%
1981	96.60%	107.73%
1982	125.84%	126.05%
1983	125.68%	138.75%
1984	101.07%	105.75%
1985	132.83%	129.40%
1986	126.96%	134.79%
1987	106.00%	106.07%
1988	115.97%	124.33%
1989	131.74%	125.66%
1990	99.39%	92.43%
1991	123.99%	134.02%
1992	107.37%	107.79%
1993	116.74%	126.91%
1994	104.94%	104.05%
1995	136.47%	136.51%
1996	128.58%	128.18%

Now type in Excel =GEOMEAN( and select this Data Range)

you will get

for Dow Jones Portfolio = 112.76%

and the Dow 10 Strategy portfolio = 118.34%

Comment :- Xg -1 of Dow Jones Portfolio = 112.76% -1 = 12.76%

Xg -1 of Dow 10 Strategy Portfolio = 118.34% -1 = 18.34%

This Number Indicates Return of the respective Portfolios over 25 years.

Average Annual Return ignores Compounding of Return, However this return (Calculated using Geometric mean) takes into consideration Compounding of return as well.

d) Correlation (r) for Dow 10 versus Dow Jones=

=CORREL(All return values of Dow 10 , All return values of Dow Jones)

= 0.9

Happy Learning!