Spread Question

Hey guys, I’m in book 4 (2006) and I am having trouble figuring this arb. spread question. Let me know what you think. "You predict the yield btw the 4 and 10 year T-Bill will diverge. 4-year has mod dur. of 2.5 and YTM of 3.00% and 10. of 6.25. and YTM of 5.00%. A. What short and long arb. position would take advatange of this? B. If both YTM rise, what would be your capital gain? YTM fall, capital loss?

Nothing like those 10-yr T-bills (there is no such thing). So you think the yield on the 10-yr will incease relative to the yield on the 4-yr. That means you think the price of the 10yr will decrease “relative” (in some kind of way) to the 4yr. So you are long the 4 yr and short the 10 yr… But you need to make a duration neutral position so short 6.25 of the 4’s for every 2.5 of the 10’s. If you’re duration neutral, the cap gains/losses are due to convexity and we only kinda have enough info to figure that out and I’m too lazy.

Just to make sure I’m following. The reason we think the 10yr will decrease “relative” to the 4 yr is due to the higher duration reflected in the 10 yr compared to the 4 yr, correct?

“You predict the yield btw the 4 and 10 year T-Bill will diverge” is a more exact way of saying that the prices will diverge. We only think this will happen because they tell us we think that.