Week 4 - Valuing government bonds Flashcards
2 definitions of arbitrage
- A strategy where one side you go long and another side you go short. Get cash inflow today and 0 CFs in future. No negative CFs / no cash outflow in the future [usually use this definition 1]
> same as 0 CF today & guaranteed +ve CF in the future - 0 cash flows today & definitely no -ve CF in future, w/ at least 1 +ve CF in future
Spot rate, rt
Interest rate fixed today on a loan that is made TODAY
Macaulay duration, Dmac & its weight
A weighted average of the years in which the bond pays its cash flows
weight = PV of cash flow as a % of the PV bond price
Modified duration, Dmod (aka volatility)
Also try to derive it
- Duration is a measure based on computing the SLOPE/gradient of the price/yield relationship
- Use it to approximate the change in bond price when the yield changes
- Main disadvantage: it is a LINEAR APPROXIMATION to a CONVEX FUNCTION
How to make the approximation for changes in bond price using Dmod more accurate?
Dmod is a linear approximation to a convex function, thus only good for small changes in x.
Include a CONVEXITY TERM.
Why are prices of long term bonds more interest rate sensitive (and have higher Dmac and Dmod) than short term bonds?
CFs of long term bonds are farther in the future & are more heavily discounted
Forward rate, ft
Interest rate fixed today on a loan to be made in the FUTURE over a specified future period agreed today. Quoted on an annual basis
Term structure & the 3 theories
A plot of spot rates against maturities (= shape of yield curve)
- (unbiased) Expectations theory
- Our best guess of the expected 1-year spot rate in 1 year’s time is equal to the forward rate 1f1
(1+r2)^2 = (1+r1)(1+ E(1r1) ) then 1r1 = 1f1
> flat term structure, increasing, upward sloping, downward structures - Liquidity premium theory
- same as above + Savers have a preference for short term securities over long term ones
ie. investors have a preference for liquidity
- need to reward investors for long-term deposits through TERM PREMIUM - Market segmentation theory
- Diff. clientele of investors don’t trade across short and long term securities, thus short- and long-term rates are set separately
Conditions for bond trading at a premium & discount
YTM < coupon rate => premium
YTM > coupon rate => discount