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투자론강의노트 04

투자론강의노트 04. 포트폴리오이론. 포트폴리오의 위험과 기대수익률 - Notation. [ 상관계수 ]. ①+ ②+③+ ④. ◦ n-asset case   - Notation - -. - variance-covariance matrix. Diversification ◦ An Example of Gains from Diversification - Investment of $100 on two identical securities.

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투자론강의노트 04

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  1. 투자론강의노트04 포트폴리오이론

  2. 포트폴리오의 위험과 기대수익률 - Notation

  3. [상관계수]

  4. ①+ ②+③+ ④

  5. ◦ n-asset case   - Notation - -

  6. - variance-covariance matrix

  7. Diversification ◦ An Example of Gains from Diversification - Investment of $100 on two identical securities

  8.  - Investment of $50 in A and $50 in B, and independent case( ) ⇒ increasing E(u)

  9. ◦ The Size of Gains from Diversification : depending on the degree of interdependence                  the number of securities

  10. (1) Impact of Interdependence ex)  Sec A : E( ) = 10, Var( ) = 100         Sec B : E( ) = 20, Var( ) = 900

  11. - Pfo결합선( Pfo combination line ) 주식A 주식A 100 주식B 주식A 100

  12.  - Rf의 확인 :

  13. (2) Impact of the Number of Securities (Diversification Effects)  - ex) A, B, and introducing sec C w/ E( )=30, Var( )=2500

  14. ◦ 위험분산효과

  15. [분산투자와 포트폴리오의 위험] 위험 고유위험 (비체계적위험) 시장위험 (체계적위험) 구성주식수

  16. - 위험의 분류 : 체계적 위험 (시장위험, 분산불가능 위험) 비체계적 위험 (기업특유위험, 분산가능위험) - 특정 증권이 Pfo의 위험에 미치는 영향은 특정증권의 위험(분산)의 크기가 아닌 타 증권의 분산(혹은 ρ)에 달려 있다. • 따라서 투자위험에의 적절한 보상은 분산불가능위험 • 인 체계적위험으로 한정해야 한다. - 도해적이해

  17. ◦투자기회집합 ◦Pfo Frontier the set of all the possible combinations of expected return and standard deviations by pooling securities   - By varying the fraction invested in each security, we can create an alternative number of combinations. - Frontier Pfo : A pfo which has minimum variance among pfos that have the same expected return - Pfo Frontier : the set of frontier pfos • 효율적 투자선(efficient frontier)의 도출

  18. (1)w/ risky assets only

  19. [위험자산만으로 구성된 효율적 투자선] Y

  20. (2) w/ riskless asset let ω be the fraction invested in risky asset

  21. 무위험자산의 추가로 인해 새로이 형성된 효율적 투자선

  22. ◦ Efficient Set ( Capital Allocation Line )   - Efficient pfo : A pfo which dominate other pfos in the sense that given variance, it has a higher expected return and  given expected return, it has a lower variance.   - Dominance principle   - Efficient Set : a set of efficient pfos (1) w/ risky assets only  : upper segment of hyperbola

  23. ⑵ w/ riskless asset  - riskless lending and borrowing - tangent pfo : the pfo where the efficient set for the risky asset and the straight line emanating from the risk-free asset are tangent.  - CAL : all feasible risk-return combinations using a risky and riskless asset : CAL의 기울기 = 위험보상비율(위험의 시장가격)  → 위험 1단위 증가시 pfo 기대수익률의 증가분

  24. 최적 포트폴리오의 선택 ⑴ w/ risky assets only   - Optimal pfo is a pfo where an IC is tangent to the efficient set.   - different risky pfos depending on the degree of risk averse(different preference or IC)

  25. [무위험자산이 존재하지 않는 경우의 최적pfo]

  26. ⑵ w/ risk-free asset   - If people have the same expectations about security payoffs (homogeneous expectations), they will hold the same risky pfo(tangent pfo) regardless of their preferences.   - two steps of decision making i) Finding out the best combination(tangent pfo) of risky securities ;     → investment decision regardless risk preference ii) Finding out the best combination of risk-free asset and the risky pfo such that they maximize their utilities.     → financing decision on considering risk preference     ⇒ pfo separation (= Tobin's separation theorem)

  27. [무위험자산이 존재하는 경우의 최적pfo] M

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