Week 4 - Valuing government bonds Flashcards

1
Q

2 definitions of arbitrage

A
  1. 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
  2. 0 cash flows today & definitely no -ve CF in future, w/ at least 1 +ve CF in future
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2
Q

Spot rate, rt

A

Interest rate fixed today on a loan that is made TODAY

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3
Q

Macaulay duration, Dmac & its weight

A

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

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4
Q

Modified duration, Dmod (aka volatility)

Also try to derive it

A
  1. Duration is a measure based on computing the SLOPE/gradient of the price/yield relationship
  2. Use it to approximate the change in bond price when the yield changes
  3. Main disadvantage: it is a LINEAR APPROXIMATION to a CONVEX FUNCTION
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5
Q

How to make the approximation for changes in bond price using Dmod more accurate?

A

Dmod is a linear approximation to a convex function, thus only good for small changes in x.

Include a CONVEXITY TERM.

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6
Q

Why are prices of long term bonds more interest rate sensitive (and have higher Dmac and Dmod) than short term bonds?

A

CFs of long term bonds are farther in the future & are more heavily discounted

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7
Q

Forward rate, ft

A

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

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8
Q

Term structure & the 3 theories

A

A plot of spot rates against maturities (= shape of yield curve)

  1. (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
  2. 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
  3. 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
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9
Q

Conditions for bond trading at a premium & discount

A

YTM < coupon rate => premium
YTM > coupon rate => discount

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