Wednesday, July 29, 2009

why does yield follow libor rates?

Q: When interest rates (libor or T or others) rises, why does yield rise?

I used to think yield reflects credit quality. I think that's still correct, but that's a static "snapshot" view -- explaining different yields of 2 bonds at a point in time.

For now, focus on one particular bond. When interests rise, yield does rise but why? Remember yield is a discounting device, so why do traders discount the future payouts more deeply? Here's my answer.

First, ignore credit risk and look at a $1000 T zero maturing in 12 months. Say we used to discount the payout by 201bp but now interest rate is higher for similar maturities in Libor and Treasury markets. Sellers of this zero would each discount the payout at 222bp. If you stick to 201bp, then you create arbitrage opportuniuty within this particular market alone. Therefore all sellers of this zero all advertize at very similar prices.

Q: What if there are only 3 big sellers in the market and we collude to keep our price high at 201bp? Crucially, to avoid arbitrage, bid yield has to be slightly higher at 202bp.

%%A: arbitrager can BUY 12-month libor (==a zero bond) at a higher yield of 300bp, and hit our bids at 202bp. There's an arbitrage linkd between them.

%%A: arbitrager can BUY a mix of Treasuries of 6-month and 2-year, both of which have higher yields above 250bp and hit out bids at 202bp. There's a arbitrage link across the maturities.

Effectively inflation is rising meaning future payouts getting "cheaper". If you don't discount future payouts, then people will see you are pricing your cash flow unfairly.

In the end, it's a matter of valuation. If you still discount your coupon payouts at the old 201bp then you over-value your bond. Consequence is arbitrage. If competing sellers undersell, then you can't sell. If you monopolize this market and also bid around that 201bp, then your bid will get hit due to arbitrage using similar instruments.

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