The textbook gave an example where the spread between Japanese and French bond is 300bps( or 75bps per quarter)The duration of Japanese bond is 7. 7*W=.75% Solving for w My question is left hand side of equation is change in price, but right hand side is spread, aren’t these two things in different units? How can they be equal? Thanks.
Change in price is also percent. Spread is also in percent.
The spread is like a return that you earn , and it will be wiped out when rates rise by W%
For the same investment value, the 75 bps advantage represents 0.75% additional return on investment.
The relative price change will be the duration (7) times the change in spread (say one market’s rates are fixed and the other experiences all of the movement).
You want the relative price change to equal the excess percent return. 7 * W is the percent change in price, and 0.75% is the current excess percent of price.
Solving for W provides the change in spread that will eliminate the excess returns. If the spread increases by 10.71 bps (or whatever it is, something close to that), the price of the Japanese bond will fall by 0.75%, so it will now equal the French bond.
I think there is some approximation in both breakeven analysis and hedge/not-to-hedge question. 1, “The spread of the two bonds” is used to determine the relative value. (Bond 1 over Bond 2, or Bond 2 over Bond 1?)
2, “Domestic currency appreciates by a%” is assumed to be the same as “Foreign currency depreciate by a%”. (Not exactly the same).
I will practice these problems again in May…
Breakeven problems are generally set up like this:
Bond A domestic: lower yield
Bond B foreign: higher yield
The question is how much do rates need to increase in the foreign market (assuming domestic rates are constant) to decrease the price of Bond B so that the higher yield advantage is offset.
To do that, you look what the spread is between the yields and say that the price needs to decline by that much to offset the yield advantage. You can then estimate the number of bps the the yield curve would need to move, given the duration.
That is the bridge between yield spread and price, and hopefully the example now makes more sense.
1, Both yields are given in domestic currency.
2, In an extreme case, the lower-yield bond is a “Treasury”.