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Bonds

Let two U.S Treasury Bonds:
Long Term Bond (LTB) pays $1000 at the end of ten years.
Short Term Bond (STB) pays $1000 at the end of one year.

1) Effective interest rates are equal to 2% / year. Which bond will sell for a lower price?
\( LTB : \frac{1000}{(1+0,02)^{10}}= 820,35 \\ STB : \frac{1000}{(1+0,02)}= 980,39 \)
So it's LTB.

2) If there is a surprise interest rate cut of 0.5% for all, which bond will have a larger percentage price drop?

Why would the price drop? isn't it the other way around? I don't understand it

3) Would stock prices be affected by this surprise interest cut ? If yes, in which direction ?

Thanks in advance for your help !
 
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2 must be stated wrong given rates and prices move inversely to one another (except for things like MBS C-strips because rate cuts can increase prepayments which causes decrease in price). In any case, duration is an increasing function, in absolute value, of maturity, so all things the same the price change in absolute value of the LTB would be greater than that of the STB if rates change (either up or down). For 3, the rate cut pushes bond prices up and spurs more borrowing which would cause net inflow into stocks leading to higher stock prices (this is admittedly very simplified).
 
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