bond-yield/exchange rate

Discussion in 'CA1' started by Nicholas.Campbell, Jul 12, 2015.

  1. Hello,

    I'm not sure I fully understand the bond-yield/exchange rate argument:

    UK return on gov bond= US return on gov + appreciation of $ relative to the £


    if n is small and the US puts interest rates up, would that not:
    - increase the return on short US bonds
    - strengthen the dollar over pound (due to greater attractiveness of US bonds)?

    How is the return on UK bonds (short-term) not changed using the above argument?


    Thanks,

    Nick
     
    Last edited by a moderator: Jul 12, 2015
  2. Oxymoron

    Oxymoron Ton up Member

    I think the equation assumes the spot price of dollar/pound will remain unchanged.

    If interest rate in US increases x%, futures price of $/pound also increases by about x% to keep interest rate parity - keeping returns in UK constant. The equation doesn't seem to consider the dynamic factors at play between different markets.

    Tutors, correct me if I am wrong.
     
  3. Steve Hales

    Steve Hales ActEd Tutor Staff Member

    I think the point is that when n is small, the dollar/pound spot price will change.

    Imagine that current equilibrium position is as follows:

    Return on n-year UK government bond : 5%
    Return on n-year US government bond : 4%
    Expected appreciation of $ against £ over n years : 1%​

    and so the equation in the Notes is satisfied. If n is small (ie we're considering only the short-term bonds), then the argument says that a rise in US interest rates rise is more likely to impact the exchange rate than it is UK interest rates. For example, a rise in US interest rates of 0.5% may not have an immediate impact on UK interest rates because the shock could be absorbed by the expected appreciation in the dollar. So the new position would be:

    Return on n-year UK government bond : 5%
    Return on n-year US government bond : 4.5%
    Expected appreciation of $ against £ over n years : 0.5%​

    Remember that this equation only holds when the market is in equilibrium - the shock of the interest rate change would tend to cause an immediate appreciation in the dollar, but this would reduce the expectation of any future appreciation.
     
  4. Oxymoron

    Oxymoron Ton up Member

    Thanks Steve!

    I'm afraid I'll have to bug you a bit more on this. Isn't expected appreciation of the dollar over £ here the same as % change in price of $/£ futures?

    Let's assume:
    Return on n-year UK government bond : 5%
    Return on n-year US government bond : 4%
    Spot price of US/UK = 1

    In this case, Fut Price = 1*1.04/1.05 = .990476 approx

    So if I borrow 1 £ now, convert it to $1 at spot price, invest it at 4% in US to earn $1.04, and convert it back to £ at .990476, my return will be 5% - the same as UK interest rate.

    Consider an alternative scenario:
    Return on n-year UK government bond : 5%
    Return on n-year US government bond : 4.5% (rise by .5%)
    Spot price of US/UK = .98 (assume US rises because of increase in int rate)
    => Fut = .975333

    Here, if I borrow 1 £ now, convert it to $.98 at spot price, invest it at 4.5% in US to earn $1.0241, and convert it back to £ at .975333, my return will also be 5% - the same as UK interest rate.

    Oh I see see how this works. Perfect! Never mind!
     
    Last edited: Jul 15, 2015
  5. Steve Hales

    Steve Hales ActEd Tutor Staff Member

    I'm glad it all worked out :)
     

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