Review. Prof. Ian Giddy

Transcription

1 Portfolio Management/1 New York University Stern School of Business Review Prof. Ian Giddy New York University Topics The Financial Markets Time Value of Money and Yields Money and Bond Markets Risk and Return Risk and Diversification Valuation and Asset Pricing (CAPM) Equity Valuation International Financial Markets Cash, Futures, FRAs and Swaps Options & Applications Portfolio Management and Performance Evaluation Copyright 2002 Ian H. Giddy Review 2

2 Portfolio Management/2 Managing a Portfolio Capital Allocation Risk-Free Asset Risky Assets Asset Allocation Bonds Real Estate Stocks Commodities FX Security Selection ConEd Viacom Chase Siemens Copyright 2002 Ian H. Giddy Review 3 Stocktrak Portfolio: Buy Kellogg? Conclusion: Benchmarks are needed because performance is is relative Copyright 2002 Ian H. Giddy Review 4

3 Portfolio Management/3 The Players, such as Institutional Investors and Money Managers Institutional Investors Money Managers Mutual Funds Insurance Companies Money Money managers managers Pension Funds Hedge funds, Central banks, etc. Stocks and bonds Copyright 2002 Ian H. Giddy Review 6 The Instruments What Investments? Treasury Bills? (risk-free) Stocks and Bonds? (risky) Copyright 2002 Ian H. Giddy Review 7

4 Portfolio Management/4 Fixed-Income Securities US Treasury Bonds Municipal Bonds Mortgage-Backed Securities Corporate Bonds Foreign Bonds Private Placements Euro$bonds Euroyen Bonds, etc. Copyright 2002 Ian H. Giddy Review 8 Prices and Yields of Treasurys Issue Coupon Maturity Yield Price Issue Coupon Maturity Yield Price T-NOTE /15/ T-BOND C T-BOND C T-NOTE /15/ T-NOTE /15/ T-BOND T-NOTE /15/ T-NOTE (OLD 10YR) 5 2/15/ T-NOTE /15/ T-BOND C T-BOND C T-NOTE (10YR) 5 8/15/ T-NOTE 5.5 2/15/ T-BOND T-NOTE /15/ T-BOND T-BOND C T-BOND C T-BOND C T-BOND T-BOND C T-BOND T-NOTE 5.5 5/15/ T-BOND T-NOTE 6 8/15/ T-BOND /15/ T-BOND C T-BOND /15/ T-BOND C T-BOND /15/ T-NOTE 6.5 2/15/ T-BOND /15/ October 11, 2001 Copyright 2002 Ian H. Giddy Review 9

5 Portfolio Management/5 The Yield Curve bondsonline.com Copyright 2002 Ian H. Giddy Review 10 Time Value Future Value of One Dollar ($) 20% 1.00 Periods 15% 5% 0% Copyright 2002 Ian H. Giddy Review 11

6 Portfolio Management/6 Future Values: Summary Single amount: the amount times the future value of interest factor, or FVIFk,n : FVr, n = PVxFVIFr, n = PVx( 1 + r ) Annuity: the periodic payment times the future value of annuity factor, or FVIFAr,n : ( 1+ r) 1 FVAr, n = PMTxFVIFAr, n = PMTx r n n Copyright 2002 Ian H. Giddy Review 12 Present Value (Example: J&J Mexico) If J&J s new pharmaceuticals facility in Mexico can produce the following dollar profits for the next four years, at a discount rate of 6%, what is the present value of the cash flow stream? Year Cash Flow $100 $400 $1000 $300 $100 $400 $1,000 $ $ (PVIF 6%,1 ) = (PVIF 6%,2 ) = (PVIF 6%,3 ) = (PVIF 6%,4 ) =.792 $1, = Present Value of cash flow stream (HP:1,519.24) Copyright 2002 Ian H. Giddy Review 13

7 Portfolio Management/7 Present Values: Summary Single amount: the amount times the present value of interest factor, or PVIFr,n : 1 PV, = FVxPVIF, = FVx ( 1 + r ) r n r n n Annuity: the periodic payment times the present value of annuity factor, or PVIFAr,n : 1 1/( 1+ r) PVAr, n = PMTxPVIFAr, n = PMTx r Copyright 2002 Ian H. Giddy Review 14 n Future Values: Summary Single amount: the amount times the future value of interest factor, or FVIFk,n : FVr, n = PVxFVIFr, n = PVx( 1 + r ) Annuity: the periodic payment times the future value of annuity factor, or FVIFAr,n : ( 1+ r) 1 FVAr, n = PMTxFVIFAr, n = PMTx r n n Copyright 2002 Ian H. Giddy Review 15

8 Portfolio Management/8 Present Values: Summary Single amount: the amount times the present value of interest factor, or PVIFr,n : 1 PV, = FVxPVIF, = FVx ( 1 + r ) r n r n n Annuity: the periodic payment times the present value of annuity factor, or PVIFAr,n : 1 1/( 1+ r) PVAr, n = PMTxPVIFAr, n = PMTx r Copyright 2002 Ian H. Giddy Review 16 n Present Value Of A Perpetuity PV = PMT r A perpetuity is an annuity that goes on forever... and (1/r) is the present value interest factor for a perpetuity, PVIFAr, = 1 r Copyright 2002 Ian H. Giddy Review 17

9 Portfolio Management/9 A Growing Annuity A growing annuity is one that pays a regular amount that grows at a constant rate each year. A common application is dividends n 1 (1 + g) /( 1+ r) PVGA= PMT(1 + g) r g n Example: Gold mine s value Copyright 2002 Ian H. Giddy Review 18 A Growing Perpetuity A growing perpetuity is one that pays a regular amount that grows at a constant rate each year. A common application is dividends PVGP= PMT(1 + g) r g Example: Mature company value Copyright 2002 Ian H. Giddy Review 19

10 Portfolio Management/10 Loan Amortization Example J&J leases $12,000 of computer equipment from Hewlett- Packard. How much would its annual end-of-year payments have to be at a 15% interest rate if the cost must be fully repaid in 3 years? PVA 3 = $12,000; r = 15%; n = 3 PVA 3 = PMT x PVIFA 15%,3 PMT = PVA 3 /PVIFA 15%,3 = $12,000/2.283 = $5, Loan Amortization Schedule - A schedule of equal payments to repay a loan. It shows the allocation of each loan payment to interest and principal. Copyright 2002 Ian H. Giddy Review 20 Basic Bond Valuation B = Ix( PVIFA ) + Mx( PVIF ) 0 B 0 = n t = r, n I M + t 1( 1 + r ) ( 1 + r ) WHERE: B o = value of the bond at time zero I = annual bond interest in dollars (interest payment) M = par value of the bond r t = required rate of return n = number of years to maturity n n Copyright 2002 Ian H. Giddy Review 21

11 Portfolio Management/11 The Zero Approach Use zero-coupon rates to value each cash flow - then add them! B 0 = C C M ( 1+ z ) ( 1+ z ) ( 1 + ) 1 2 z n n Where can we get the z s? One place is from the Treasury strip market. Copyright 2002 Ian H. Giddy Review 22 Bond Lego A Treasury Note as quoted in the Wall Street Journal Monday, July 24, 1995 Rate 6 Maturity, Mo/Yr Dec 97 Bid Asked 99:29 99:31 Ask Yld To value this bond, break it up into its component cash flows - e.g. 1st coupon of (5 3/4)/2 in Feb 1996, and so on... Then use zero s to see what each is worth, and add the total. In general, breaking up a security into its component parts is an excellent path to valuation. Copyright 2002 Ian H. Giddy Review 23

12 Portfolio Management/12 Forward Interest Rates EURODOLLAR INTEREST RATES The rate that can be locked in is the implied forward rate that equates long term rates with short term rates 0 3 mo 6 mo 9 mo 1 yr 15 mo 18 mo Copyright 2002 Ian H. Giddy Review 24 Calculating Implied Forward Rates I can buy a 2-year note or buy a 1-year note and reinvest it at some "forward" rate f: (1+y 2 ) 2 =(1+y 1 )(1+f) Find f! Copyright 2002 Ian H. Giddy Review 25

13 Portfolio Management/13 Theories of Term Structure Expectations Liquidity Preference Upward bias over expectations Market Segmentation Preferred Habitat Copyright 2002 Ian H. Giddy Review 26 Identifying Undervalued Securities Bonds Spot Rates Correct pricing Compare with actual Copyright 2002 Ian H. Giddy Review 27

14 Portfolio Management/14 A $1 Investment in Different Types of Portfolios: Index ($) Small Company Stocks $4, $1, Long-Term Government Bonds Large Company Stocks $33.73 $13.54 $ Treasury Bills Inflation Year-End Copyright 2002 Ian H. Giddy Review 28 Bond Price Changes: Actual vs. Duration-Based There s an error in duration-based estimation, because duration is linear. PRICE 100 Actual 9% Error Duration YIELD Copyright 2002 Ian H. Giddy Review 30

15 Portfolio Management/15 Calculating Duration: MacCauley and Modified D MAC tcft n t (1 + r) = P t= 1 D MOD = % P = dp P D = (1 + r / m) Copyright 2002 Ian H. Giddy Review 31 Portfolio Duration Assets (each $10m): 1-year E$ deposit 5-year, 6% T-note Duration=4.3 9-year Strip Fixed liabilities: $10m 3 years $15m 5 years $5m 7 years Asset Duration =.33(1)+.33(4.3)+.33(9) Liab Duration =.33(3)+.50(5)+.17(7) Net duration is = 0.10 Copyright 2002 Ian H. Giddy Review 32

16 Portfolio Management/16 Returns, Standard Deviations, and Frequency Distributions: Average Standard Series Annual Return Deviation Distribution Large Company Stocks 12.7% 20.3% Small Company Stocks Long-Term Corporate Bonds Long-Term Government Bonds U.S. Treasury Bills Inflation % 0% + 90% Source: Stocks, Bonds, Bills, and Inflation 1997 Yearbook, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. Copyright 2002 Ian H. Giddy Review 33 The Normal Distribution Probability 68% 95% % % 1 7.6% > 99% % % % % Return on large company stocks Copyright 2002 Ian H. Giddy Review 34

17 Portfolio Management/17 Credit Risk versus Market Risk Copyright 2002 Ian H. Giddy Review 35 Portfolio Optimization E(r) Efficient frontier Individual assets Global minimumvariance portfolio σ Copyright 2002 Ian H. Giddy Review 36

18 Portfolio Management/18 Measuring Portfolio Return and Risk The portfolio return E(R p ) is: E(R p) = (w 1 k 1 )+(w 2 k 2 )+... (w n k n ) = Σ w j k j where w j = weight of asset j, k j = return on asset j The variance of a 2-asset portfolio is: = w + w + 2w w σ P Aσ 2 2 A Bσ B A Bρ AB σ Aσ B where w A and w B are the weights of A and B in the portfolio. Copyright 2002 Ian H. Giddy Review 37 Case Study: A Portfolio Weight E(R) Std Dev GPU Teledyne Kodak Thai Fund Merck ATT TOTAL 1 Copyright 2002 Ian H. Giddy Review 38

19 Portfolio Management/19 Portfolio Risk Computation CORRELATION MATRIX STD DEV GPU TeledyKodakThai FMerck ATT GPU Teledyne Kodak Thai Fund Merck ATT Portfolio Variance 3.48% Portfolio Std Deviation 18.66% Copyright 2002 Ian H. Giddy Review 39 Plotting the Efficient Frontier THAI FUND 0.15 ORIGINAL 0.1 ATT Copyright 2002 Ian H. Giddy Review 40

20 Portfolio Management/20 Finding the Optimal Portfolio: Computations Given the Risk-Free rate is: 5.00% OPTIMAL PORTFOLIOS Risk Ratio Return Std. Dev. Premium RP/SD GPU 11.26% % % % % % % % MIN RISK 12.83% % % % % % % % % % % % % % % % THAI 20.75% % That's the one! Copyright 2002 Ian H. Giddy Review 41 Equity Risk and Return Investors diversify, because you get a better return for a given risk. There is a fully-diversified market portfolio that we should all choose The risk of an individual asset can be measured by how much risk it adds to the market portfolio. Copyright 2002 Ian H. Giddy Review 42

21 Portfolio Management/21 Types of Risk P or t f o li o R is k s kp TOTAL RISK DIVERSIFIABLE RISK { } } Number of Securities (Assets) in Portfolio NONDIVERSIFIABLE RISK Copyright 2002 Ian H. Giddy Review 43 Optimal Overall Portfolio E(r) Indifference curve OPTIMAL RISKY PORTFOLIO CAL P Opportunity set Optimal complete portfolio (one example) σ Copyright 2002 Ian H. Giddy Review 44

22 Portfolio Management/22 Security Market Line Required 17 Return, k(%) k z = k m = R F = Nondiversifiable Risk, β β R F β m β z SML Z s Risk }Market Risk Premium: 6% Premium: 4%}Asset Copyright 2002 Ian H. Giddy Review 45 The Equation for the CAPM k j = R F + β j (k m - R F ) where: k j = Required return on asset j; R F = Risk-free rate of return β j = Beta Coefficient for asset j; k m = Market return The term [β j (k m - R F )] is called the risk premium and (k m -R F ) is called the market risk premium Copyright 2002 Ian H. Giddy Review 46

23 Portfolio Management/23 Diversification and Asset Pricing: Summary Investors diversify, because you get a better return for a given risk. There is a fully-diversified market portfolio that we should all choose The risk of an individual asset can be measured by how much risk it adds to the market portfolio The CAPM tells us how the required return relates to the relevant risk. Copyright 2002 Ian H. Giddy Review 47 Value is Not Price What is Intrinsic Value? Self assigned Value Variety of models are used for estimation Market Price What stock can be sold for or bought at Trading Signal IV > MP Buy IV < MP Sell or Short Sell IV = MP Hold or Fairly Priced More, less, or same as market portfolio? Copyright 2002 Ian H. Giddy Review 48

24 Portfolio Management/24 Equity Valuation: From the Balance Sheet Value of Assets Book Liquidation Replacement Value of Liabilities Book Market Value of Equity Valuation approach depends on the purpose: Liquidation/breakup? Going independent concern Takeover/change in control? Copyright 2002 Ian H. Giddy Review 49 The Balance Sheet Total Value of Assets Total Value of Liabilities and Shareholders Equity Current Assets Net Working Capital Current Liabilities Long-Term Debt Fixed Assets 1. Tangible fixed assets 2. Intangible fixed assets Shareholders Equity Copyright 2002 Ian H. Giddy Review 50

25 Portfolio Management/25 Dividend Discount Model V 0 D D D + N P ( 1+ k) ( 1+ k) ( 1+ k) 1 2 = N N P N = the expected sales price for the stock at time N N = the specified number of years the stock is expected to be held Copyright 2002 Ian H. Giddy Review 51 No Growth Model: Example V o = D k E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33 Copyright 2002 Ian H. Giddy Review 52

26 Portfolio Management/26 Constant Growth Model: Example Vo = Do( 1+ g) k g E 1 = $5.00 b = 40% k = 15% (1-b) = 60% D 1 = $3.00 g = 8% V 0 = 3.00 / ( ) = $42.86 Copyright 2002 Ian H. Giddy Review 53 Shifting Growth Rate Model: Example D 0 = $2.00 g 1 = 20% g 2 = 5% k = 15% T = 3 D 1 = 2.40 D 2 = 2.88 D 3 = 3.46 D 4 = 3.63 V 0 = D 1 /(1.15) + D 2 /(1.15) 2 + D 3 /(1.15) 3 + D 4 / ( ) ( (1.15) 3 V 0 = = $30.40 Copyright 2002 Ian H. Giddy Review 54

27 Portfolio Management/27 Ratios May Have Meaning P Gordon Growth Model: 0 = DPS 1 r g n Dividing both sides by the earnings, P 0 = PE= Payout Ratio* (1 + g n ) EPS 0 r-g n Dividing both sides by the book value of equity, P 0 = PBV = ROE * Payout Ratio* (1 + g n ) BV 0 r-g n If the return on equity is written in terms of the retention ratio and the expected growth rate P 0 BV 0 = PBV = ROE - g n r -g n Dividing by the Sales per share, P 0 = PS = Profit Margin* Payout Ratio* (1 + g n ) Sales 0 r -g n Copyright 2002 Ian H. Giddy Review 55 Valuing a Firm with DCF: An Illustration Historical financial results Adjust for nonrecurring aspects Gauge future growth Projected sales and operating profits Adjust for noncash items Projected free cash flows to the firm (FCFF) Year 1 FCFF Year 2 FCFF Year 3 FCFF Year 4 FCFF Discount to present using weighted average cost of capital (WACC) Terminal year FCFF Stable growth model or P/E comparable Present value of free cash flows + cash, securities & excess assets - Market value of debt Value of shareholders equity Copyright 2002 Ian H. Giddy Review 56

28 Portfolio Management/28 Valuation in Acquisitions Rationale: Firm A should merge with Firm B if [Value of AB > Value of A + Value of B + Cost of transaction] Synergy Top-line Bottom-line Control Divestitures Financial restructuring Copyright 2002 Ian H. Giddy Review 57 The Gains From an Acquisition Gains from merger Synergies Control Top line Bottom line Financial Business restructuring Restructuring (M&A) Copyright 2002 Ian H. Giddy Review 58

29 Portfolio Management/29 Optika WACC: ReE/(D+E)+RdD/(D+E) Value: FCFF/(WACC-growth rate) Equity Value: Firm Value - Debt Value = = 2430 Optika Growth 5% Tax rate 35% Initial Revenues 3125 COGS 89% WC 10% Equity Market Value 1300 Debt Market Value 250 Beta 1 Treasury bond rate 7% Debt spread 1.5% Market risk premium 5.50% T+1 Revenues COGS Depreciation 74 =EBIT 287 EBIT(1-Tax) 187 -Change in WC 16 =Free Cash Flow to Firm 171 Cost of Equity (from CAPM) 12.50% Cost of Debt (after tax) 5.53% WACC 11.38% Firm Value CAPM: 7%+1(5.50%) Debt cost (7%+1.5%)(1-.35) Copyright 2002 Ian H. Giddy Review 59 Optika-Schirnding with Synergy Schirnding-Optika Optika Schirnding Combined Synergy Growth 5% 5% 5% 5% Tax rate 35% 35% 35% 35% Initial Revenues COGS 89% 87.50% 86.00% WC 10% 10% 10% 10% Equity Market Value Debt Market Value Beta Treasury bond rate 7% 7% 7% 7% Debt spread 1.5% 1.5% 1.5% 1.5% Market risk premium 5.50% 5.50% 5.50% 5.50% T+1 T+1 T+1 Revenues COGS Depreciation =EBIT EBIT(1-Tax) Change in WC =Free Cash Flow to Firm Cost of Equity (from CAPM) 12.50% 12.50% 12.50% 12.50% Cost of Debt (after tax) 5.53% 5.53% 5.53% 5.53% WACC 11.38% 11.98% 11.73% 11.73% Firm Value Increase 1620 Copyright 2002 Ian H. Giddy Review 60

30 Portfolio Management/30 What s a Company Worth? Alternative Models The options approach Option to expand Option to abandon Creation of key resources that another company would pay for Patents or trademarks Teams of employees Customers Examples? Lycos Messageclick.com Copyright 2002 Ian H. Giddy Review 61 International Exchange Rate Risk is the risk arising from fluctuating exchange rates between two currencies Copyright 2002 Ian H. Giddy Review 62

31 Portfolio Management/31 Foreign Exchange Quotations Spot Forward points Copyright 2002 Ian H. Giddy Review 63 Exchange Rates How Currency quoted British US$ pounds per (GBP) GBP Japanese Yen per yen (JPY) US$ Spot (2 business Forward days) (90 days) Copyright 2002 Ian H. Giddy Review 64

32 Portfolio Management/32 A Typical Forward Contract We agree today to pay a certain price for a currency in the future JPY Sony Sony B of of A Copyright 2002 Ian H. Giddy Review 65 Interest-Rate Parity $1 (1 + / E$ ) = ($1/ S t )(1 + / EBP ) F n t where S t is the spot exchange rate (dollars per British Pound) and F n t is the forward rate. to a close approximation, (/ E$ - / EBP ) = [(Ft n - S t )/S t ] (365/n) 100 Interest-rate differential = forward premium or discount Copyright 2002 Ian H. Giddy Review 66

33 Portfolio Management/33 Returns with FX (1 + r US ) = (1 + r FM ) (1 + r FX ) r US = return on the foreign investment in US Dollars r FM = return on the foreign market in local currency r FX = return on the foreign exchange Copyright 2002 Ian H. Giddy Review 67 Hedging International Equity Investments Buy foreign equity and hedge the anticipated future value, P+E(r)? Use short-term, value-adjusted, roll-over hedges? Do nothing, because equities bear no currency sign? Initial Initial Anticipated Actual Actual Copyright 2002 Ian H. Giddy Review 68

34 Portfolio Management/34 Commodities: Spot and Forward How can Coke s canners cap their can costs? ALUMINUM PRICE per tonne $ $ SPOT 3 MONTHS 6 MONTHS Copyright 2002 Ian H. Giddy Review 69 Swaps 8% Fixed GE Chase Ongoing short-term funding 3-mo Libor, floating Copyright 2002 Ian H. Giddy Review 70

35 Portfolio Management/35 Cost-of-Carry Theory Applied to Stock Futures Stock that pays no cash dividend no storage costs no seasonal patterns in prices Strategy 1: Buy the stock now and hold it until time T Strategy 2: Put funds aside today to perform on a futures contract for delivery at time T that is acquired today Copyright 2002 Ian H. Giddy Review 71 Options Payoff Call Option 0 Stock Price Copyright 2002 Ian H. Giddy Review 72

36 Portfolio Management/36 Payoff Profiles for Calls Payoff Call Holder 0 Call Writer Stock Price Copyright 2002 Ian H. Giddy Review 73 Arbitrage & Put Call Parity Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S 0 - X / (1 + r f ) T If the prices are not equal arbitrage will be possible Copyright 2002 Ian H. Giddy Review 74

37 Portfolio Management/37 Option Pricing Option Price Time value depends on on Time Volatility Distance from the strike price Option Price = Intrinsic value + Time value Underlying Price Copyright 2002 Ian H. Giddy Review 75 Trading Options: Delta Hedging Hedged with 40% short futures We ve written a put option Delta Copyright 2002 Ian H. Giddy Review 76

38 Portfolio Management/38 Goal: Understand Options Sensitivity An option trader has a portfolio of options with different deltas, gammas, etc. The goal is to discover the sensitivities of the portfolio to changes in rates, time, volatility, etc, and to neutralize them. Greek Measures D Delta Sensitivity of portfolio value to change in price of the underlying asset G Gamma Sensitivity of delta to change in price of underlying asset q Theta Sensitivity of portfolio value to change in time L Lambda (Vega) Sensitivity of portfolio value to change in volatility R Rho Sensitivity of portfolio to change in interest rate Copyright 2002 Ian H. Giddy Review 77 Option Applications Cap: Agreement to compensate buyer when interest rate exceeds a specified ceiling. Floor: Agreement to compensate buyer when interest rate falls below a specified floor. Collar: A simultaneous purchase of a cap and sale of a floor. Net cost is the price of the cap less the value of the floor. Example: If LIBOR > 12% cap, bank pays borrower the difference If LIBOR < 4% floor, borrower pays bank the difference Swaption: Option on a swap. Copyright 2002 Ian H. Giddy Review 78

39 Portfolio Management/39 Factors Influencing Cap Prices Length Steepness of yield curve Volatility Cap Forward Rates Yield Curve (Zero rates) Volatility Curve Copyright 2002 Ian H. Giddy Review 79 Convertibles, Warrants, and Other Hybrids Convertible Securities Stock-Purchase Warrants Structured Notes General principle: security can be valued as a portfolio of two or more instruments Copyright 2002 Ian H. Giddy Review 80

40 Portfolio Management/40 Breaking Down a Convertible: Kodak At the end of 2001, Kodak (EK) had a 5.25% convertible bond, coming due in 2009, trading at $1300. The face value was $1000. It also had straight bonds, with the same maturity, trading in December 2001 at a yield of 8.4%. What s the straight bond component worth? What s the convertible option worth? Assume the conversion ratio is 24, and Kodak stock is priced at $51. How would you determine whether the investor is overpaying? Copyright 2002 Ian H. Giddy Review 81 Breaking Up is Easy to Do Breaking a Convertible Bond Down Coupon rate on Convertible Bond = 5.25% Market Interest Rate on Straight Bond of same Risk = 8.40% Price of Convertible Bond = 1300 Maturity of Convertible Bond = 8 Value of Straight Bond Portion = $ Value of Conversion Option = $ Conversion ratio 24 Stock price 51 Intrinsic value 1224 Time value $ Value of option depends on volatility Copyright 2002 Ian H. Giddy Review 82

41 Portfolio Management/41 Capital Allocation Capital Allocation Risk-Free Asset Risky Assets Asset Allocation Bonds Real Estate Stocks Commodities FX Security Selection ConEd Viacom Chase Siemens Copyright 2002 Ian H. Giddy Review 83 Portfolio Performance Evaluation How well did the portfolio do? How do we adjust for risk, to compare different managers? Why? Risk Timing Asset allocation Security selection Copyright 2002 Ian H. Giddy Review 84

42 Portfolio Management/42 Performance Evaluation Measures Sharpe s measure The portfolio s average excess return per unit of total risk Treynor s measure The portfolio s average excess return per unit of systematic risk Jensen s measure The excess of the portfolio s return over that predicted by the CAPM Appraisal ratio Portfolio s abnormal return per unit of risk that could be diversified by holding a market index portfolio Copyright 2002 Ian H. Giddy Review 85 Performance Attribution Asset allocation choices Broad market allocations: equity, bonds, etc. Industry choices Security selection Evaluation: compare the portfolio returns at each level with returns on the appropriate index (benchmark portfolio or passive strategy) Copyright 2002 Ian H. Giddy Review 86

43 Portfolio Management/43 Active Portfolio Management Stock-picking and active portfolio management must pay, else the market would not be efficient! The optimal risky portfolio maximizes the reward-to-variability ratio; the slope of the CAL: E(r p ) ACTIVE CAPITAL ALLOCATON LINE PASSIVE CAPITAL ALLOCATON LINE Copyright 2002 Ian H. Giddy Review 87 σ Conclusion: Hold Three Things Risk-free asset Passive portfolio Active portfolio Copyright 2002 Ian H. Giddy Review 88

44 Portfolio Management/44 Ian Giddy NYU Stern School of Business 44 West 4 th St, NY 10012, USA Tel ; Fax ian.giddy@nyu.edu Copyright 2002 Ian H. Giddy Review 93