bonds to clarify you have no chance. how do you do you think you price anything in bonds? from what i can see r is quite fundamental to the whole set up.
there is strong evidence that a proof of the zeroes of an L function like reiman's over finite fields has almost no use for our purposes.
If someone asked you the same question but were instead, referencing index futures, would you have answered similarly? Yes, bond futures, just like index futures and many other products, have a basis between contract and cash that reflects interest rate differentials, coupon payments and when applicable, dividends. As such, depending upon if a futures contract is at positive or negative carry, it will converge with it's corresponding cash instrument as expiration nears. When trading most front month futures contracts, "carry" isn't much of an issue. But if you're trading "back month" fixed income or currency futures, basis spreads can be considerable. (Example: Dec Bonds are nearly 2pts less in price than June)
. Correct. No future pays interest. Embedded in the price of every future is the cost to carry the cash product until expiration. In the case of index futures, interest and dividend flows, but you do not get paid them. You can go out and buy a basket of stocks and short the future or the reverse if it lines up. The equity basket would, but not the future.
Thanks for all the help all. I was thinking more on this subject. In trying to lever bond exposure, it seems there would be a problem with the cost of carry. Please correct me if my logic is wrong. Lets say I wanted $3mm in bond exposure with $1mm in cash. If I bought $3mm worth of 30y bond futures, I would be getting the following total return in my portfolio(roughly). (return on cash) + (return on bond exposure) = (Rf x $1mm) + ((30y rate - Rf) x $3mm)) My point is that simply because I went long 3mm in long bonds futures, I will not be getting the same return as actually owning 3mm in long bonds because I have to pay the cost of carry on 3mm, whereas I am only earning the risk free rate on my cash. Is this correct?
$3mm in notional bond futures provides no return or interest. You are betting on the cost of the bond at the time the future expires. If you buy $3mm in bonds with $1mm cash and $2mm in loans, the loan rate of the $2mm will likely be higher than the interest you will receive. I can't find a benefit to this. It is not clear to me what you want to accomplish. Do you want a return on your investment or make a bet on future interest rates?
With regards to the bond basis, here is how it works in a nutshell. Bond futures are physically settled at expiration (roughly). That means that when you are short a bond futures, you are required to deliver a bond at expiration. The deliverable bond is selected from a basket of the eligible bonds that have the maturity within some window. Since these bonds might have somewhat different maturity, very different coupon and accrued interest (i.e. different dirty price), the exchange gives you a conversion factor for each bond. On the day when you deliver, you will get paid face value adjusted by that conversion factor. That delivery happens some time in the future which means the person that gets it will forego some coupon interest over that period. On the other hand, he/she will not have to pay financing for owning that bond in a leveraged form. Most of the difference of the futures price and the current bond price (adjusted for the conversion factor) is due to the financing and coupon. There is also a little bit (these days negligible) value in the ability to pick the cheapest bond out of the deliverable basket. In general, this implied value (financing, coupon and optionality) is expressed as "implied repo rate". Regular repo is the interest rate that you would pay/receive for a cash loan that uses a treasury bond as a collateral. By the same token, since you are able to "lend/borrow" the deliverable bond and buy it back, the implied rate can be backed out of the difference between bond price vs futures price and dividing it by the time to expiration. It's not as glamorous as you think it is. In real life at the current level of interest rates the convexity embedded into the bond futures basis is negligible (it maximizes when rates are around the coupon of the theoretical bond which is 6%). Most of the trickery that goes in the basis today has to do with financing.
Thanks Robert and sle. It appears you guys are saying two different things. Robert, you seem to be saying you will not capture any of the yield embedded in the 30yr bond, which doesn't seem right. If the majority of the cash/future basis is based on financing(risk free rate?) and the coupon, then you would certainly be capturing part of the 30yr yield assuming financing rate is less than the bond rate. Is this not correct? Also, I thought that leveraging bonds was how risk parity has worked so well over the years. If they are levering a stock and bond portfolio, they are actually getting the returns of equity and bonds minus the financing rate, right? And Robert, you said earlier in the thread, that you would not be charged interest on(in my example) 2mm as long as you has margin requirements you could buy the bond futures. If you are buying equity, I understand you would have to pay for that loan, but I thought futures was entirely different.
We are because sle is discussed how many use bond futures like owning the cash bond and shorting the future. I was responding to being long a future. The Future pays no interest. Yes, if you buy bonds on margin, your return to the expiration of the bond is based on the coupon/discount you earn over the financing rate. GS can make money doing this, you can't. That was a different example and not related to this. $2mm notional of 10-Year T-Note Futures = 20 futures. You need the margin for 20 futures.