FINS2624: PORTFOLIO MANAGEMENT NOTES

Transcription

1 FINS2624: PORTFOLIO MANAGEMENT NOTES UNIVERSITY OF NEW SOUTH WALES

2 Chapter: Table of Contents TABLE OF CONTENTS Bond Pricing 3 Bonds 3 Arbitrage Pricing 3 YTM and Bond prices 4 Realized Compound Yield 4 Term Structure of Interest Rates 5 What is the Term Structure? 5 Inferring the Term Structure 5 Exploiting Mispricing with Three Bonds (Example) 5 Reinvestment Risk 6 Forward Rates 6 Liquidity Risk 6 Market Expectations 7 Duration 8 Macaulay s Duration: Measure of Maturity (D) 8 Modified Duration: Measure of Yield Sensitivity (D*) 8 Portfolio Duration 10 Immunization 10 Rebalancing 10 Markowitz Portfolio Theory 11 Utility 11 Statistics 11 Portfolio Variance 11 Diversification 12 Portfolio Selection 12 The Optimal Portfolio 13 Complete Portfolio 13 Separation Theorem 13 Capital Asset Pricing Model 15 CAPM 16 The Security Market Line 16 1

3 Chapter: Unsystematic Risk 16 Systematic Risk 17 The SML and the CAL 17 Portfolio Beta 17 Assumptions of CAPM 17 Using the CAPM 17 Portfolio Management in Practice 18 Criticisms of CAPM 18 The Single Index Model 18 Exploiting Mispricing 18 Factor Models 19 Behavioural finance and Market Efficiency 20 Efficient Market Hypothesis 20 Behavioural Finance 20 Performance Measures 21 Active Investments: Risk Adjusted Performance Measures 21 Passive Investments 22 Practical Considerations 22 Sources of Performance 22 Performance attribution 23 Options Strategies 24 Value of Options 24 Options Strategies 24 Black-Scholes Formula 27 Assumptions 27 Greeks 27 Delta Hedging 27 2

4 Chapter: Bond Pricing BOND PRICING BONDS A claim on fixed future cash flows Typically a large cash flow (face value) at maturity (FV) May be series of smaller cash flows before maturity (coupons) Sum of annual coupons are expressed as fraction of FV (coupon rate) Bond s current yield = Assumptions in the pricing model: o No default risk o No transaction costs o Constant interest rates o Complete markets ARBITRAGE PRICING Arbitrage: set of trades that generate zero cash flows in the future, but a positive, risk free cash flow today Arbitrage pricing: constructing replicating portfolios using assets with known prices to exactly mimic the cash flows of some other asset For example price a bond with coupon rate 5%, FV $100, 2 year maturity, when interest rate is 8% for both lending and borrowing Exploiting mispricing: Buy cheaper instrument, sell expensive instrument riskless profit o T = 0 will result in riskless profit, every other period will have 0 net cash flow Arbitraging increases demand for bond, increases price until no further arbitrage is possible arbitrage free price 3

5 Chapter: Bond Pricing PRICING FORMULA Replicate: o One coupon stream of c from 1 to T o One large payment of FV at T PV(FC) = ( ) PV(Coupon stream) = PV(perpetuity starting at time 1) PV(perpetuity starting at time T+1) In practice, interest rates are not constant We take P as given and define Y as a yield to maturity (YTM) Holding period return = ( ) YTM AND BOND PRICES Bond price decreases with YTM Price is less sensitive to changes in YTM when YTM is high When YTM = C, P = FV o C = YTM P = FV bond trades at par o C < YTM P < FV bond trades at a discount o C > YTM P > FV bond trades at a premium REALIZED COMPOUND YIELD If bond A and B have the same YTM, t 2 cash flows will differ However if coupon in B can be reinvested at an interest rate that equals YTM, time two cash flows will be equal Realized compound yield solves for the annualized return useful when reinvestment rate is different from YTM o Collect all cash flows at maturity of bond o Divide by price and solve for annualised return o ( ) 4