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【正文】 s ofnu m be r :11crr cp e r i o dannual ???% 0 9 )0 0 ( 52 ?????a n n u a lr% 2 9 )( 32 ?????a nn u alrWeekly return of %: 18month return of 20%: GROSS AND NET RETURNS Gross returns Expenses Net returns PRETAX AND AFTERTAX NOMINAL RETURN Pretax nominal return Taxes Aftertax nominal return NOMINAL RETURNS AND REAL RETURNS ? ?? ? ? ?? ?%)()()1()1(1%)()()1(11%)()()()1()1(1)1(??????????????????????????????????r e a lr e a lr e a lrFr e a lrFrrrrRPrrrRPrr??VARIANCE AND STANDARD DEVIATION OF A SINGLE ASSET ? ? ? ?221221221ssTRRsTRTttTtt???????????????Sample Population VARIANCE OF A PORTFOLIO OF ASSETS ? ?? ?? ? ? ?? ???? ???????????????NiNjijijijiiiNjijijiNiiiPPRRC o vwwRV a rwRRC o vwwRwV a rRV a r1 ,1,21,12,?Variance can be determined for N securities in a portfolio using the formulas below. Cov(Ri, Rj) is the covariance of returns between security i and security j and can be expressed as the product of the correlation between the two returns (ρi,j) and the standard deviations of the two assets, Cov(Ri, Rj) = ρi,j σiσj. EXAMPLE 54 RETURN AND RISK OF A TWOASSET PORTFOLIO Assume that as a . investor, you decide to hold a portfolio with 80 percent invested in the Samp。P 500 . stock index and the remaining 20 percent in the MSCI Emerging Markets index. The expected return is percent for the Samp。P 500 and percent for the Emerging Markets index. What will be the portfolio’s expected return and risk given that the covariance between the Samp。 P 500 P or tfolio Emer g ing Mar ke ts ?? = 0 .093 10% 20% Sta nd a rd Dev ia t io n o f P o r t f o lio ?p Expected Portfolio Return E (Rp) 20% 10% 30% EXHIBIT 55 RISK AND RETURN FOR . ASSET CLASSES BY DECADE (%) 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2 0 0 0 s * 1926 –2020 L ar g e co m p a n y s to ck s R etu r n – 0 .1 9 . 2 1 9 . 4 7 . 8 5 . 9 1 7 . 6 1 8 . 2 – 3 . 6 9 . 6 R is k 4 1 . 6 1 7 . 5 1 4 . 1 1 3 . 1 1 7 . 2 1 9 . 4 1 5 . 9 1 5 . 0 2 0 . 6 S m all co m p a n y s to ck s R etu r n 1 . 4 2 0 . 7 1 6 . 9 1 5 . 5 11. 5 1 5 . 8 1 5 . 1 4 . 1 1 1 . 7 R is k 7 8 . 6 3 4 . 5 1 4 . 4 2 1 . 5 3 0 . 8 2 2 . 5 2 0 . 2 2 4 . 5 3 3 . 0 L o n g ter m co r p o r ate b o n d s R etu r n 6 . 9 2 . 7 1
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