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1 Part II : POTFOLIO THEOY o isk and eturn o Efficient Diversification o CPM and PT o Efficient Markets o Behavioral Finance and Technical nalysis 0

2 isk and eturn 1

3 eturn and isk Investment returns The rate of return on an investment can be calculated as follows: HP = Capital gain yield (Ending price-beginning price + Cash dividend) (HP: Holding period return) Beginning price Dividend yield initial price(p 0 ): $1,000, $1,100 after one year(p 1 ) and $100 dividend, the rate of return for this investment is: ($1,100 - $1,000+$100) / $1,000 = 0%.

4 eturn and isk Measuring returns over multiple periods Table 5.1 : Quarterly cash flows and rates of return of a mutual fund (unit: mil.) 1 st nd 3 rd 4 th ssets(beg.) HP.10.5 (.0).5 T (Before Net Flows) Net Inflows (0.8) 0.0 ssets(end)

5 eturn and isk Measuring returns over multiple periods rithmetic average r a = (r 1 + r + r r n ) / n r a = ( ) / 4 =.10 or 10% Geometric (time-weighted average return) average (1+r g ) n =[(1+r 1 ) (1+r )... (1+r n )] r g = {[(1.1) (1.5) (.8) (1.5)]} 1/4-1 = (1.5150) 1/4-1 =.089 = 8.9% 4

6 eturn and isk Money (dollar)-weighted average rate of return I for the portfolio, whennpv (1 i) 0 or PV(COF) PV(CIF) , i 3 4 (1 i ) (1 i ) (1 i ) 4.17% Time Outflows($mil.) Inflows($mil.) Net Cash Flows ($mil.) 0 1 (1) (0.1) (0.5) (0.8)

7 eturn and isk Case. Money (dollar)-weighted rate of return time Outlay 0 $00 to purchase the first share 1 $5 to purchase the second share Proceeds 1 $5 dividend received from the first share(not reinvested) $10 dividend ($5 per share * shares) $470 received from selling two shares at $35 per share $00 $5 $5 $470 $10, i (1 i) (1 i ) (1 i ) 9.39% Time Outflows($) Inflows($) eturn(%) (Div.) # 15[=(5-00+5)/00] 470(35*) + 10(Div. 5*) 6.67[=( )/450] # not reinvested rithmetic mean: 10.84% [=( )/] Geometric mean: 10.76% [=(1.15)(1.0667) 1] 6

8 eturn and isk Money (dollar)-weighted rate of return (cont d) I 9.39% vs. rithmetic mean 10.84% More weight given to the second year when more money was invested. ($00 vs. $450) Drawback as a tool for money managers performance measure Clients determine when and how much money is given. 7

9 eturn and isk Conventions of rate of return quotation Nominal rate (i NOM ) also called the contracted, quoted, stated rate or P (annual percentage rate). P=(periods in year) X (rate for period) P = 1 * 1% = 1% Periodic rate (i PE ) amount of interest charged each period, e.g. monthly or quarterly. i PE = i NOM / m, where m is the number of compounding periods per year. m = 4 for quarterly and m = 1 for monthly compounding. 8

10 eturn and isk Effective (or equivalent) annual rate (E): the annual rate of interest actually being earned. E=( 1+ i PE ) Periods per year - 1 =( 1 + i NOM / m ) m - 1 E for monthly return of 1% E = (1.01) 1-1 = 1.68% n investor would be indifferent between an investment offering a 1.68% annual return and one offering a 1% monthly compounding return. 9

11 eturn and isk Why is it important to consider E? n investment with monthly payments is different from one with quarterly payments. Must put each return on an E basis to compare rates of return. ㅇ Nominal rate of return (P) : 8% ㅇ Effective rate of return E annually : (1+0.08)-1=8.00% E semiannually : (1+0.08/) -1=8.16% E quarterly : (1+0.08/4) 4-1=8.4% E monthly : (1+0.08/1) 1-1=8.30% E continuously compounding : e =8.33% 10

12 eturn and isk ㅇ effective rate (cont d) Ex.) Which one has a higher effective interest rate? 3mo. T-bill selling at $97,645 (pure discount bond, face value : $100,000) vs. coupon bond selling at par and paying a 10% coupon semiannually. (100,000-97,645)/97,645=r 3 =0.041 E T =(1+r 3 ) 4-1=( ) 4-1= vs. E C =(1+r 6 ) -1=(1+0.1/) -1 =

13 eturn and isk eal vs. Nominal ates Nominal (eal) rate: growth rate of the money (purchasing power) Fisher effect: Exact (1+ 명목 )=(1+ 실질 )*(1+ 예상물가상승률 ) (1+)=(1+r)(1+i), r = ( - i) / (1 + i) r=(9%-6%) / (1.06) =.83% Fisher effect: pproximation nominal rate real rate + expected rate of inflation (Ex) = 9%, i = 6% = r + i, r = - i r= 9% - 6%=3% 1

14 eturn and isk Probability distributions listing of all possible outcomes, and the probability of each occurrence. Firm X Firm Y ate of eturn (%) Expected ate of eturn 13

15 eturn and isk Expected ate of eturn ^ k expected rate of return ^ k n i1 k i P i ^ k M (100%) (0.3) (15%) (0.4) (-70%) (0.3) 15.0% 14

16 eturn and isk Stand-lone isk: the standard deviation Standard deviation variance E ( k kˆ) E k Ek n i1 (k i ^ k) P i M ( ) (0.3) ( ) (0.3) ( ) (0.4) 1 =65.84% 15

17 eturn and isk Normal Distribution with Mean of 1% and St Dev of 0% 16

18 eturn and isk Comments on standard deviation as a measure of risk Standard deviation (σ i ) measures total, or stand-alone, risk. Larger σ i is associated with a wider probability distribution of returns. The larger σ i is, the lower the probability that actual returns will be close to expected returns. 17

19 eturn and isk Example of measuring Expected return and risk States (s) Prob. (p s ) eturns (,s ) E[ ] n s1 p n s1 s p s [, s, s E( 0.13 )] E E( )) E E (, s 18

20 Portfolio construction Portfolio return and risk : risky assets E ( p ) x E ( ) x B E ( B ) P x x B B x x B B x x B B x x B B B 예) 구분 E() σ S1 15% 15% S 30% 40% ρ1 0. x 40% 60% E(p)= 0.4, σp= * E(aX+bY)=a*E(X) + b*e(y), * Var(aX+bY)=a*Var(X) + b*var(y) + *a*b*cov(x,y) 19

21 Portfolio construction Portfolio return and risk : N risky assets E( ex) P p ) N N j1 N x i1 j1 j x E( i x j ij j ) E() σ x S1 15% 15% 30% S 30% 40% 50% S3 5% 30% 0% E(p)= 0.45; σ p = 0.65 < Variance-Covariance Matrix > 1 n 1 x 1 1 x x 1 1 x n x 1 n1 x 1 x 1 x x n x n N x 1 x n 1n x x n n x n n Ρ 1 S1 S S3 S S S3 1 0

22 Portfolio construction Portfolio risk ㅇ공분산 (Covariance) - 두확률변수 ( 수익률 ) 의공조성 (co-movement) - 수익률이체계적인관계없이움직이면 B 0 B p E ( 1 (,1 p n E( E( (, n )( B ))( E( E( B,1 E( ))( B B, n ) B )) E( p B ( )), E( ))( B, E( B )) p i j, i E( : i 상황이발생할확률 ( i 1,,, n) : i 상황에서주식 j의수익률 ( j j ) : 주식 j 의기대수익률, B) 1

23 Portfolio construction Portfolio risk ㅇ상관계수 (Correlation Coefficient) - 두수익률의표준화된공조성 B >0 : 양의상관관계 (rho) B =+1 : 완전양의상관관계 B <0 : 음의상관관계 B =-1 : 완전음의상관관계 B =0 : ( B =0) 수익률의움직임에체계적인관계가없음 B B B 1 1 B

24 Portfolio construction Portfolio risk ( 예 ) 공분산, 상관계수산출 상태 (s) 확률 (p s ) 수익률 (,s ) 수익률 ( B,s ) E( B B 1 (,1 p ) 0.9; E ( p B B n E( E( (, n E( )( ))( E( B B E( B,1 E( ))( B B, n ) ; ) B )) p E( B (, )) ; E( B ))( B, E( B )) 3

25 eturn and isk Investor attitude towards risk Investor s view of risk isk verse isk Neutral isk Seeking isk aversion assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. isk premium=exp. ate of ret. f isk-free rate: the rate you can earn from risk-free asset such as T-bills, MMF, etc. Excess return=ctual rate of return f isk premium = Expected excess return 4

26 eturn and isk isk Premium isky Inv. W 1 = 150 Profit = p =.4 W = 80 Profit = -0 isk Free T-bills (5%) Profit = 5 isk Premium = 17 [=0.6*50+0.4*(-0)-5] (compensation for the risk of the investment) 5

sset allocation 자산배분과증권선택 sset llocation (risky vs.

Security Selection (technical analysis) (portfolio

35 + iskless portfolio(0.4) B1: 0.7 CD: 0.

27 sset allocation 자산배분과증권선택 sset llocation (risky vs. riskless) Bottom-up Top-down (fundamental analysis) Security Selection (technical analysis) (portfolio analysis) isky portfolio (0.6) S1: 0.5 S: 0.4 S3: iskless portfolio(0.4) B1: 0.7 CD: 0.3 Complete portfolio S1: 0.15; S: 0.4; S3: 0.1; B1:0.8; CD:0.1 6

28 sset allocation 무위험자산 (isk-free sset) ㅇ가치가변하지않고일정하게유지되어미래에얻게될소득의크기가확실한자산 - 수익률의표준편차 rf = 0 - 채무불이행이없는 (default risk free) 자산 예 ) 미국 : T-Bill; 국내 : 재정증권, 통화안정증권 7

29 sset allocation 위험자산 ( p, p, ) 과무위험자산 ( f, rf, 1- ) 결합ㅇ포트폴리오기대수익률 E( c )= *E( p )+(1- )* f = f + [E( p )- f ] ㅇ포트폴리오수익률의위험도 c= * p + (1-) * f + **(1-)* pf = * p c = * p => = c / p 예 ) E( p )=15%, p = %, f =7% -> E( c )= *; -> c= 0. *, c = 0. * * E(aX+bY)=a*E(X) + b*e(y), * Var(aX+bY)=a *Var(X) + b *Var(Y) + *a*b*cov(x,y) 8

30 sset allocation 위험자산 ( p, p, ) 과무위험자산 ( f, rf, 1- ) 결합 ( 계속 ) ㅇ기대수익률과위험을두축으로한그래프 E() E( p )=0.15 f =0.07 p =0. 자본배분선 (CL: Capital llocation Line): 특정위험포트폴리오 P 와무위험자산을결합하여얻을수있는투자기회집합 (Investment Opportunity Set) - 기울기 : [E( p )- f ]/ p = ( )/0. = 위험보상률 (V: reward-to-volatility ratio). Sharp ratio 9

31 sset allocation 위험자산 ( p, p, ) 과무위험자산 ( f, rf, 1- ) 결합 ( 계속 ) ㅇ차입포트폴리오 (Levered Portfolio) - 투자자가무위험수익률 ( f rate) 로차입포트폴리오구성ㅇ무위험자산수익률로차입할수없는경우 E() 차입 E( p )= S(>1)=0.7 E( f )=0.07 S(1)=0.36 p =0. 30

32 Passive investment strategy and CML 소극적투자전략 (Passive Investment Strategy) - 시장평균성과이상의수익률을기대하기어렵다는전제 - 증권분석을하지않고포트폴리오결정 - 시장포트폴리오 (Market Portfolio) 선택 : 단순히증권시장을구성하는각자산의구성비에따라포트폴리오구성 - 현실적으로상장지수펀드 (ETF) 등지수연동자산에투자 => CML선상에서투자의사결정 : 무위험자산과시장포트폴리오에분산투자 31

33 Passive investment strategy and CML Optimal CL 최적 CL=CML E(c) efficient frontier CL k f Optimal risky portfolio =>Market portfolio minimum variance portfolio Global minimum variance Minimize subject to P E( w i P ) 1.0 w w i w E( i j ij i ) k ( k c : 상수) 3

34 Passive investment strategy and CML Capital Market Line (CML: 자본시장선 ) - 무위험자산과시장포트폴리오를연결하는직선으로가장효율적인포트폴리오의기대수익률과위험과의관계설명 E() E(m) f M CML Market portfolio - all the assets traded in the market - proportion :mkt cap.(i) /total market cap. m E( C ) f E( m ) m f C eward per unit of risk borne (Market price of risk) 현재소비의희생에대한시간보상 (reward for waiting) 33

제 출 문 국방부 장관 귀하 본 보고서를 국방부 군인연금과에서 당연구원에 의뢰한 군인연금기금 체 계적 관리방안 연구용역의 최종보고서로 제출합니다. 2009. 4 (주)한국채권연구원 대표이사 오 규 철

군인연금기금 체계적 관리방안 연구 2009. 04 (최종보고서) 제 출 문 국방부 장관 귀하 본 보고서를 국방부 군인연금과에서 당연구원에 의뢰한 군인연금기금 체 계적 관리방안 연구용역의 최종보고서로 제출합니다. 2009. 4 (주)한국채권연구원 대표이사 오 규 철 목 차 제1장 서론 1 1. 연구의 목적 1 2. 연구의 방법 및 내용 2 제2장 현황분석 (AS-IS