= = = = Returns ScenarioProbability Auto Gold Portfolio (75% auto, 25% gold) Recessio 1/3 -8 +20 .75(-8) + .25 (20) = -1.0% Normal 1/3 +5 +3 .75(5) + .25 (3) = +4.5% Boom 1/3 +18 -20 .75(18) + .25 (-20) = +8.5% Expected Return Auto (-8+5+18)/3 = 5% Gold (+20+3-20)/3 = 1% Portfolio (-1+4.5+8.5)/3 = 4% Variance Auto (169+0+169)/3 = 112.7 (std. 10.6%) Gold (361+4+441)/3 = 268.7 (std. 16.4%) Portfolio (25+.25 +20.25)/3 = 15.2 (std 3.9%) Homework: 1) Show expected return & variance of a 90% auto, 10% gold portfolio 2) Show expected return & variance of a 25% auto 75% gold portfolio = =