Investment Management Equations Rate of re turn on an asset or portfolio Return = (End-of-period wealth - beginn ing -ofperiod weal t h )/( begi n n i n g-of~pe ri od wealth) Actual margin in a stock purchase (nXmp) -[(I-im) X /,p X ,,] am = >I X mp Market price at which a margin purchaser will re ceive a margin call _ (I - ;1>1) X pp mp- - mm Actual margin in a short sale [(spXn) X ( I +im)] -(mpX>l) X mp n am = Market price at which a short seller will receive a margin call Ip X (1 + ;1>1) mp = 1+ mm Expe cted return o n a portfolio ,\' rp = ; =1 Covariance between two securities au = P'jUjU'j Standard deviation of a portfolio Up = v ~ ~ XiXi0';, [ ] 1/2 Standard deviation of a two-asset portfolio '1 ') ~ I /~ U p = XjUI + X,1O'2 + 2XIX"PI2IT ,U 2j 10 The market model "j = Uj + {3;'/ + e, 11 Beta from the market model 'j [ 13, = Uj 12 Securitv variance from the market model u; = l3~u7 + 0';, 13 Security cov,~riance from th e market model U,j = f3if3 jUj 14 Variance of a portfolio (by market and unique risk) IT~ = f3~ u; + u;p 15 Mark et risk of a portfolio v e, = ;L=1 x;f3; 16 Unique risk of a portfolio s L XTu;, j =1 17 Capital Market Line r" = 'j Ii)] u p ( '.11 - + [- - - 0' 11 18 Variance of the market portfolio \' \' L L X,.\,Xj.\fU,j a~, = , =1 j =1 19 Security Market Line (covariance and beta versions) r; = 'j + [( r.1I ~ r/)] Ui.1I fr \1 r; = 'i + (1"11 - Tj)f3, 20 Beta from the CAP:'.I = 17, 11 13 t U ",\1 + (b" hJ2 + [J' 2bjl) Coo( fj f ;) 24 Arb itrage Pricing Theory (two-factor model) 1-;=A o+A,II" +A 211'2 1- i = 'i+ (