FINS2624: PORTFOLIO
MANAGEMENT NOTES
Daniel Quinn
UNIVERSITY OF NEW SOUTH WALES
FinS2624: Portfolio Management Notes
Daniel Quinn
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
The Optimal Portfolio _____________________________________________________________ 13
Complete Portfolio ___________________________________________________________________ 13
Separation Theorem __________________________________________________________________ 13
Capital Asset Pricing Model _____________________________________________________________ 15
CAPM__________________________________________________________________________ 16
The Security Market Line _______________________________________________________________ 16
Chapter: Table of Contents
Portfolio Selection ____________________________________________________________________ 12
1
FinS2624: Portfolio Management Notes
Daniel Quinn
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
Chapter:
Delta Hedging _______________________________________________________________________ 27
2
FinS2624: Portfolio Management Notes
Daniel Quinn
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
Chapter: Bond Pricing

3
FinS2624: Portfolio Management Notes
Daniel Quinn
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, t2 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 (
Chapter: Bond Pricing


4