Question

Annual and Average Returns for Stocks, Bonds, and T-Bills, 1950 to 2015.

			Stocks			Long-Term Treasury Bonds			T-bills
1950 to 2015		Average		12.6	%		6.6	%		4.40	%
1950 to 1959		Average		20.9			0.0			2.00
1960 to 1969		Average		8.7			1.6			4.00
1970 to 1979		Average		7.5			5.7			6.30
1980 to 1989		Average		18.2			13.5			8.90
1990 to 1999		Average		19.0			9.5			4.90
2000 to 2009		Average		0.9			8.0			2.70
2010		Annual Return		15.1			9.4			0.01
2011		Annual Return		2.1			29.9			0.02
2012		Annual Return		16.0			3.6			0.02
2013		Annual Return		32.4			−12.7			0.07
2014		Annual Return		13.7			25.1			0.05
2015		Annual Return		1.4			−1.2			0.21
2010 to 2015		Average		13.4			9.0			0.06

You have a portfolio with an asset allocation of 50 percent stocks, 26 percent long-term Treasury bonds, and 24 percent T-bills. Use these weights and the returns given in the above table to compute the return of the portfolio in the year 2010 and each year since. Then compute the average annual return and standard deviation of the portfolio. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Rp(2010)=50%*15.1%)+(26%*9.4%)+(24%*1%)=
10.23%
Rp(2011)=(50%*2.1%)+(26%*29.9%)+(24%*2%)=
9.30%
Rp(2012)=(50%*16%)+(26%*3.6%)+(24%*2%)=
9.42%
Rp(2013)=(50%*32.4%)+(26%*-12.7%)+(24%*7%)=
14.58%
Rp(2014)=(50%*13.7%)+(26%*25.1%)+(24%*5%)=
14.58%
Rp(2015)=(50%*1.4%)+(26%*-1.2%)+(24%*21%)=
5.43%
Average annual return on the portfolio=
Sum Rp s/6
(10.23%+9.30%+9.42%+14.58%+14.58%+5.43%)/6=
10.59%
Standard deviation of the returns of the portfolio from Portfolio Av. Returns
Sq. rt. Of(sum of (Rp-Av. Rp)^2)
((10.23%-10.59%)^2+(9.30%-10.59%)^2+(9.42%-10.59%)^2+(14.58%-10.59%)^2+(14.58%-10.59%)^2+(5.43%-10.59%)^2)^(1/2)=
7.85%

In the above, Average returns have been done for the years 2010 to 2015 , for each year & standard deviation of portfolio returns calculated---

Same way, it had been done for the range of years also

tabulated with calculations ---- Table below

The mean /average return for the block of years ranging from 1950-1959 to 2010-2015 is

9.29%

&

Std. deviation of returns during the period 1950 to 2015 is

10.27%

Years	Stocks-R%	LT T-Bonds-R%	T-bills-R%	Rp=Weighted Portfolio return	Variance
1	2	3	4	5=(50%*2)+(26%*3)+(24%*4)	6=(Rp-9.29%)^2
1950 to 1959	20.9	0	2	10.93%	0.000269
1960 to 1969	8.7	1.6	4	5.73%	0.0012702
1970 to 1979	7.5	5.7	6.3	6.74%	0.0006482
1980 to 1989	18.2	13.5	8.9	14.75%	0.0029768
1990 to 1999	19	9.5	4.9	13.15%	0.0014869
2000 to 2009	0.9	8	2.7	3.18%	0.0037357
2010 to 2015	13.4	9	6	10.59%	0.000169
			Sum	65.06%	0.010556	Sum variance
			Average	9.29%	10.27%	Std. deviation
			Sum/7			(Variance)^(1/2)