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s have their homogeneous expectations. 24 Derivation of CAPM ? Portfolio of risky assets p? ?p i j ijjninw w???????????1112w i ni : , ,? ??????1The weights If (market portfolio), Mp ????njijMjiM w1)( ??211)(??????? ??niiMMiM w ??The exposure of the market portfolio of risky assets is only related to the correlation between individual assets and the portfolio. 25 M? ?E rMrf?? ?E r0 SML Derivation of CAPM: Security Market Line E(rM)rF iiMMiMi rr ????? 22 1~~ ???? ??i iMM? 2)( irE? ? ? ?? ?E r r E r ri f M fMiM? ??? ?226 Security Market Line (SML) ? ? ? ?? ?E r r E r ri f M fMiM? ??? ?2? ??i iMM? 2? ? ? ?? ?E r r E r ri f i M f? ? ??? ?p i iinw???1 are additive ?? ? ? ?? ?E r r E r rp f p M f? ? ??? Model 27 Understanding Risk in CAPM ? In CAPM, we can depose an asset’s return into three pieces: ifMiifi rrrr ??? ~)~(~ ?????0)~,~(0)~(??iMirC o vrE??where ? Three characteristic of an asset: – Beta – Sigma – Aplha 28 M? ?E rMrf?? ?E r0 SML The market bees more aggressive The market bees more conservative Risk neutral 29 Summary of Chapter Three 1. The Key of Investments ? TradeOff Between Expected Return and Risk 2. Diversification ? Only Systematic Risk Can Get Premium 3. Two Fund Separation ? Any Trade in the Market can be Considered as a Trade Between Two Mutual Funds 4. CAPM — Individual Asset Pricing