Question

Annual and Average Returns for Stocks, Bonds, and T-Bills, 1950 to 2015 Long-Term Treasury B onds 6.6% .0 1.6 5.7 13.5 Stocks 12.6% 9 28. 8.7 7.5 18.2 19.0 0.9 15.1 2.1 16. 32.4 13.7 1.4 1950 to 2015 Average 1950 to 1959 Average 1960 to 1969 Average 1970 to 1979 Average 1980 to 1989 Average 1990 to 1999 Average 2009 to 2009 Average 2010 Annual Return 2011 Annual Return 2012 Annual Return al Return 2013 Annual Return 2014 Annual Return 2015 Annual Return 2010 to 2015 Average 9.5 8.0 T-bills 4.40% 2.00 4.09 6.30 8.90 4.90 2.78 0.01 8.02 0.02 8.07 0.85 0.21 0.06 29.9 3.6 -12.7 You have a portfolio with an asset allocation of 50 percent stocks, 38 percent long-term Treasury bonds, and 12 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.) real in Portfolio Return 2010 2011 2012 2013 2014 2015 Average Standard deviation 5.56

Answer 1

PAGE NO. SOLUTION GIVEN Weight of stock (W) = 50% Weight of long treasury bond (WB)=38% 1200 of ( Weight of t-bills twtb : 12% Return for 2010 Return = Wsx return of stock + WB x return of s long treaswey bond t W + 6x return sooo of t-bille sox. 15.0 + 0.38 *9.4%.+ 0.12x 0.01% = 7.558.73.57%+0.0012%. - 111.12 %. SOHO as Return for 2011 to Return = Wst Rust WB XR B t W o xhtb - 0.5% 21%.+ 0.38 x 29.97 + 0.12X0.02), => 1.05% + 11.36% +0.0024% -> 12.41%. Return for 2012 Return = Ws Xhg + WB X RB t W tb XRtb 5) 0.5% 16% +0.38 x 3.67.+ 0.1270.02% - 8% + 1.368% + 0.0024% - 19.37%

Return for 2 013 Return - Ws x Rs & WB x R B t W tb XRtb. >0.50 x 32,47 +0.38*(-12.7%.) +0.12 x 0.073 >> 16.2%. +(-4.8267) + 0.0084%. → 11.18% Return for 2014 Return = Wg X Rg + WB X RB + Wtbx Rzb =0.506 13.7%+0.38x 25.0%+0.12 x 0.05% > 6.85%+ 9.538% + 0.0060% > (16.395) Revorm for 2015 Return = Wsx Rs 7 WB & B Bt Web XRtb - 0,50x2,4%+ 0.38% (-1.2%) + 0.12 +0.21% 7 0.7%+ (-0.45607) + 0.02527 -> 10.27% Average returns 2010 to 2015 Return = Ws X RS + WB X RB t W tb XRtb. - 0.50x 13.4%.7 0.38% 9%+0.124 0.06%. → 6.7%+ 3.42% + 0.0072% - [10.13%

Average annual Return of from 1950 to 2015 the Portfolio Criven: Ws = 50%. WB =387. Wto = 12% R = 12.6%. RB = 6.6%. Rab 4.40% Returns = Wg x R S + WBX RB + WEB XR tb =) OS X 12.6%+0.38x6.6% +0.12 x 4.42 = 6.3%.1 2.508% + 0.52807. - 9.3366%or 19.39%
The return of all the different assets are given in the table, and are stated as Rs ( return for stock), Rb (return for long treasury bond) , Rtb ( return for t-bills).In order to calculate the average annual return for portfolio since 1950 to 2015 and 2010 to 2015 , we multiply weight of different assets with their respective reurn as given in the table.