Smart Investment Strategies

Transcription

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2 Smrt Investment Strtegies Risk-Rewrd Rewrd Strtegy Quntifying Greed How to mke good Portfolio? Entrnce-Exit Exit Strtegy: When to buy? When to sell? 2

3 Risk vs.. Rewrd Strtegy here is certin mount of risk P nd certin mount of cpitl tht n investor is willing to tolerte/lose for certin mount of rewrd or return. As returns b ccumulte beyond the expected mount, the investors risk increses considerbly, nd investors should hve lower inclintion to tke such risks to ern bit more return. How to blnce Risk-Rewrd? Rewrd? he old Greeks might give us some insight on this (to be explined in person). 3

4 Risk vs.. Rewrd Strtegy Firness Prob.= p Rewrd b Risk = 50 % Investment 4

5 Risk vs.. Rewrd Strtegy : Cpitl being risked b : Return or rewrd (Greed) p : Firness of the underlying process P P : Probbility of Ruin (Risk) N : Durtion (how long it tkes) 1 p/ q 1 p/ q b b N Strtegy : Ply ( b, ) 5 b b b 1 p / q p q b 2p 1 2p 11 p / q b p q for risk = P 1 2

6 Risk nd Rewrd Strtegy Risk = 10 % Rewrd Investment 6

7 Risk nd Rewrd Strtegy Risk = 20 % Rewrd Investment 7

8 Risk nd Rewrd Strtegy Risk = 30 % Rewrd Investment 8

9 Risk nd Rewrd Strtegy Risk = 40 % Rewrd Investment 9

10 Risk nd Rewrd Strtegy Risk = 50 % Rewrd Investment 10

11 Risk nd Rewrd Strtegy Risk = 50 % Rewrd Investment 11

12 Risk nd Rewrd Strtegy Risk = 50 % Rewrd Investment 12

13 Risk nd Rewrd Strtegy Risk = 60 % Rewrd Investment 13

14 Risk nd Rewrd Strtegy Risk = 70 % Rewrd Investment 14

15 Risk nd Rewrd Strtegy Risk = 80 % Rewrd Investment 15

16 Risk nd Rewrd Strtegy Risk = 90 % Rewrd Investment 16

17 Risk nd Rewrd Strtegy p = 0.3 Rewrd Investment 17

18 Risk nd Rewrd Strtegy p = 0.4 Rewrd Investment 18

19 Risk nd Rewrd Strtegy p = 0.45 Rewrd Investment 19

20 Risk nd Rewrd Strtegy p = 0.48 Rewrd Investment 20

21 Risk nd Rewrd Strtegy = 5, b = 1 (20%) = 10, b = 1 (10%) Fvor Prob. Risk Durtion Fvor Prob. Risk Durtion p P N p P N = 5, b = 2 (40%) = 10, b = 2 (20%) Fvor Prob. Risk Durtion Fvor Prob. Risk Durtion p P N p P N

22 Risk nd Rewrd Strtegy = 10, b = 3 (30%) = 15, b = 3 (20%) Fvor Prob. Risk Durtion Fvor Prob. Risk Durtion p P N p P N = 15, b = 2 (13.33%) = 15, b = 5 (33.33%) Fvor Prob. Risk Durtion Fvor Prob. Risk Durtion p P N p P N

23 Investment Strtegy: How to Mke A Good Portfolio Portfolio Optimiztion Gol: Invest cpitl to mke more money (not to lose cpitl) 23

24 How to Mke A Good Portfolio Which industry sectors to invest? Which specific stocks to invest in ech sector? How mny shres of ech stock to buy? Mrkowitz s pproch to Risk Minimiztion New pproches bsed on Mtched Filter How long to hold Portfolio? When to buy? When to sell? 24

25 Wht Kinds of Stocks to Buy Difficult questions; Need both qulittive nd quntittive mrket grip nd reserch. Refer to others reserch Stocks in Dow, NASDAQ, nd S&P 500 industries re good strt. 25

26 Portfolio Fundmentls C 0 m s () t i i : Initil Cpitl : number of distinct stocks in the portfolio i th : stock price t time : the cpitl distribution fctor for stock i 0 m i1 i 1 Cpitl invested in stock = C 0 i i th t, i1,2, m i th n i C 0 i s (0) i = the number of shres purchsed for stock i th 26

27 Portfolio Fundmentls Portfolio vlue t time = t m i1 ns() t i i Portfolio return t time : t s () t s (0) P n s () t C C C r() t m m m i i i i 0 0 i 0 i i i1 i1 si (0) i1 i th Return from stock: r() t i si() t si(0) s (0) i 27

28 Portfolio Fundmentls Expected return of the stock: i th E r() t i i Expected return of the portfolio: m m G EP Eiri() t ii i1 i m [,,,, ] rt () [ r(), t r(), t r(), t, r()] t m E r() t [,,,, ] m 28

29 Portfolio Fundmentls Overll Risk of the Portfolio: 2 () () 2 P Vr P E P E P E r t r t () () E rt rt R Covrince Mtrix: R E r() t r() t 0 i i j j R cov r(), t r () t E r () t r () t i, j i j i, j i j 29

30 Portfolio Optimiztion: Wht Cn Fund Mnger Do? A fund mnger does not run ny compny. However, the fund mnger cn decide when to buy stocks, which stocks to buy, how mny stocks to buy, how mny shres of ech stock to buy, nd how long to hold etc. Mrkowitz Ide: Select portfolio such tht the overll risk of the whole combintion during the holding time is minimized. How to do it? Minimize the Risk 2 p Vr P 30

31 Mrkowitz s Strtegy: Minimize Risk min 2 P R R ( e1), subject to e 1 e [1,1,1,,1] 2R e 0 R 1 e Mrkowitz Solution 1 e R R 1 e e need not hve ll positive entries 31

32 Mrkowitz s Strtegy: Minimize Risk If short selling is not llowed, then ll cpitl distribution must be positive. he positivity of every entry of is not gurnteed by Mrkowitz Strtegy. Modified Mrkowitz Strtegy: min 2 P subject to: e 1 nd 0 he inequlity constrint requires the use of Qudrtic Progrmming. R 32

33 New Strtegy: Mtched filter Mximize Gin nd Minimize Risk Mtched filter mximizes SNR: Signl Power w s SNR Noise Power w Rw 2 Mximiztion of SNR strtegy is used in clssicl receiver design to mximize the output signl t the decision instnt while minimizing the output interference plus noise Mrkowitz pproch Minimiztion of Risk (noise power) Wht plys the role of signl in Portfolio? 33

34 New Strtegy: Mtched filter Mximize Gin nd Minimize Risk Portfolio Anlogy: Noise Power Risk Signl Portfolio Gin New Strtegy (Mtched Filter): Mximize expected gin nd simultneously minimize Risk mx G 2 2 P 2 R subject to e 1 34

35 New Strtegy: Mtched filter Mximize Gin nd Minimize Risk Schwrz inequlity 2 2 1/2-1/2 1 R R R R with equlity if 1 R R 1 R 1 kr R Mtched Filter Solution e R -1 R -1 need not hve ll positive entries 35

36 New Strtegy: Mtched filter Mximize Gin nd Minimize Risk 1 kr : Whitening following by Mtched Filtering 2 P min e R R , G opt e R R 1 1 Use constrined non-liner progrmming to gurntee positivity of every entry of. Modified Mtched Filter Strtegy: subject to: e 1 0 subject to: nd mx G 2 2 P 36

37 New Strtegy: Mtched filter Mximize Gin nd Minimize Risk Other vritions of the Mtched Filter strtegy re possible. hey led to the sme result mx G 2 2 P R or mx G 4 2 P R 4 leds to e R -1 R -1 37

38 Optiml Expected Utility Strtegy Money Utility: In investment, there is certin mount of risk tht n investor is willing to tolerte for certin mount of return. However, s return ccumultes, investors hve lower inclintion to tke risk to ern just bit more return. Expected utility predicts betting preferences with regrd to uncertin outcomes or how much n investor is stisfied with the mount of return received. Utility Function for Portfolio Investment: up ( ) 1e kp k risk version consnt 0, P portfolio gin 38

39 Optiml Expected Utility Strtegy k 0.1 k 10 risk-loving = increses return increses utility risk-verse = utility stgntes fter 40% return 39

40 Optiml Expected Utility Strtegy Proposition: Return vector rt () is Gussin distributed with men Deduced: Portfolio gin m P i1 r() t i i G E P Expected Utility 40 p Vr P R 2 1 PG 1 2 P kp E u( P) u P f P dp 1e e dp 2 1e k 2 kg P 2 is lso Gussin distributed P 2

41 Optiml Expected Utility Strtegy Mximiztion of the Expected Utility: k 2 kg P 2 mx ( ) 1 mx E u P e G k 2 2 P herefore, by qudrtic progrmming for no short selling. mx k R 2 subject to: e 1 0 subject to: nd 41

42 Exmple Stocks From Industry Sectors Bsic Mterils Cpitl Goods Finncil Services echnology Consumer Cyclicl Helth Cre GPK LPX UFS X DD PO GOLD MON CDE HMY ROCK CYD IRSN CHB KAI AAON MH ECUA GR C UBS BCS HBC WFC FFG RDN OKSB PMI HNBC FCZA MOVE RHD YBVA IP DIE CHUX S PSS GPI SMR AAPL LLL RIMM ILMN KYO DHR ENR BEC SOHU MIL SRI DORM BWS CB G HMX VC QSND KCP MOV JNJ PFE NVS LLY BAX CELG ACL EVA MRK WYE 42

43 Simultion: 3-month 3 Investment Period (Jnury 2003 to December 2008) 5 stocks 10 stocks 20 stocks 30 stocks 43

44 Simultion: 6-month 6 Investment Period (Jnury 2003 to December 2008) 5 stocks 10 stocks 20 stocks 30 stocks 44

45 Simultion: 12-month Investment Period (Jnury 2003 to December 2008) 5 stocks 10 stocks 20 stocks 30 stocks 45

46 Simultion: 24-month Investment Period (Jnury 2003 to December 2008) 5 stocks 10 stocks 20 stocks 30 stocks 46

47 How to Pick Stocks? Bsic Mterils Cpitl Goods Finncil Services echnology Consumer Cyclicl Helth Cre m Stocks m Stocks m Stocks m Stocks m Stocks m Stocks i 0 i R i 0 i R i 0 i R i 0 i R i 0 i R i 0 i R Select Portfolio with minimum risk i Portfolio i 0 47

48 Entrnce-Exit Exit Strtegy: When to Buy? When to Sell? Strtegy: Buy low; Sell high. How to do it? Entrnce Strtegy: Buy stocks, Portfolios when the probbility of hitting the lowest price is mximum so tht the probbility positive return is mximized. Estblish first observtion period, nd buy beyond it whenever the current price is lower thn the minimum during the first observtion period. (Rndom Buy instnt ). When to get out? Exit Strtegy: Strting t the buy instnt,, determine second observtion period nd sell beyond it whenever the price is higher thn the mximum during the second observtion period. he probbility of getting the highest possible return is mximized. (Otherwise quit t end). 48

49 Entrnce-Exit Exit Strtegy: When to Buy? When to Sell? Observtion ime to buy Observtion ime to sell Gin Buy Here Sell Here 49