FINS2624 Lecture Notes - Lecture 1: Spot Contract, Reinvestment Risk, Arbitrage

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16 May 2018
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FINS2624 Kristy
Lecture 1: Bond pricing
- Formal defn: borrow-lend contract: principal, maturity, IR
- Assumptions: no default risk, no transaction costs, constant interest rates, complete
markets (possibility to replicate assets)
- Fundamental pricing: S/D equilibrium, properties of an asset tell us what that price is
likely to be
- Arbitrage pricing: law of one price: replicate future CF of an asset with portfolio of
other assets (price of asset = MV of replicating portfolio)
- Arbitrage: trades that generate zero CF in fut but +ve, risk free CF today
a) Law of one price violation
b) By replicating portfolios/synthetic assets- mimic CF of other A
For there to be no arb, the $P of CF stream must be the same as $P of
replication
c) Increase demand for the asset and raises its price until no further arb trades
are possible (equilibrium)- ie arb free prices
YTM is constant discount rate
- YTM varies inversely w bond $P (decreasing rate which price changes related to
YTM)
a) Par: P = FV (YTM=CPNr)
b) Discount: P<FV (YTM>CPNr)
c) Premium: P>FV (YTM<CPNr)
d) Price is less sensitive to changes in YTM when YTM is high
- Realised holding period bond returns
a) YTM will change over time depending on market interest rates for all futures
horizons at each time
- Realised compound yield
a) Collect all CF at maturity of bond- annualised return by dividing by $P
b) Comparing two bonds when reinvestment rates (determined by the market
and realised in the future) differ from YTM (determined by E(IR) for all future
horizons)
Useful if YTM is different at different times
- We hae assets hose alue e dot ko- use bank deposit based portfolio to
generate same CF, price the bond, price the bonds lead to calculate YTM to compare
the bonds
Lecture 2: Term structure of
- T-period spot rate (y(t))
a) Interest rate today for a t-period investment
b) Zero rate: on zero CPN bonds/pure yield
c) T-period spot rate (y(t)) differs from YTM (y) of a t-period bond
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FINS2624 Kristy
- Det of term structure: term structure of IR means how IR differ over investment
horizons
Spot rates and thus TS are implied by market bond prices
iterative method = bootstrapping
- Iosistet ter struture ad aritrage ar geerate 0 CF t=, ut risk free π t=0
a) If prices of different bonds imply inconsistent spot rates, then arb op arises
b) Arbitrager can replicate bods future CF  portfolio of other ods hose
market value will differ from the price of this bond
c) Arb trades will remove any mispricing in equilib and impose some structure
on the term structure of interest rates
- Term structure and future interest rates
a) Replicating cash flows of LT bonds by reinvesting CF from ST bonds
- Term structure and forward rates
a) FR: IR on bond where date the commitment is made and date money is
loaned are different (sft- investment start s and end at t)
- Expectations hypothesis
a) The theory that market expectations on future interest rates determine the
spot rates over different horizons (and thus the terms structure)
b) sft = E(syt)
- Liquidity preference hypothesis: maturity mismatch
a) HPR = (P1 + c1)/P0
- Issuers prefer to issue LT bonds and thus have longer investment horizons than
investors
a) ST investors need to carry the liquidity risk of holding LT bonds
b) Liquidity premium offered to induce ST investors to hold LT bonds
c) Higher yields for LT bonds- upwards sloping
d) As long as bond issuers and investors have dif horizons (preferred habitats),
there should be premium offered to induce investors to hold bonds whose
aturit doest ath their horizo
e) When investors have long investm horizons than issuers, investors need to
carry reinvestment risk to hold ST investm- premium (inverse YC)
- Reinvestment risk
- Liquidity preference theory can be generalised as preferred habitat theory- explain
YC shape by premia offered to investors to hold investm whose maturities do not
match their preferred horizons
- If L = 0 then EH is true- assume risk averse
a) sft = E(syt) + L
- Term structure is the spot rates (over dif maturities) the market sets in equilib
- Term structure will depend on the expectations de fut IR and risk preferences of
market participants
Lecture 3: Duration
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Document Summary

Formal defn: borrow-lend contract: principal, maturity, ir. Assumptions: no default risk, no transaction costs, constant interest rates, complete markets (possibility to replicate assets) Fundamental pricing: s/d equilibrium, properties of an asset tell us what that price is likely to be. Arbitrage pricing: law of one price: replicate future cf of an asset with portfolio of other assets (price of asset = mv of replicating portfolio) Ytm varies inversely w bond (decreasing rate which price changes related to. Ytm: par: p = fv (ytm=cpnr, discount: pcpnr, premium: p>fv (ytm

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