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enter image description hereI have only government bond yields with different maturities. How can I obtain sythetic future prices on bonds? After obtained the future prices, I am supposed to compute the return and carry returns.

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  • $\begingroup$ May be a duplicate question quant.stackexchange.com/questions/25368/… $\endgroup$ – noob2 Apr 21 '16 at 20:59
  • $\begingroup$ That question has now been automatically deleted. However like before please provide more detail, can you please define what you mean by synthetic futures? I would expect that derivatives are involved but you don't mention them. $\endgroup$ – Bob Jansen Apr 22 '16 at 5:40
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    $\begingroup$ Do you know what "carry" is? It is a simple estimate of future 1-Year returns based on the assumption that "the prices currently in the market remain the same". For example assume I buy a US 2-year bond now, collect the income, and can sell it one year from now for the price the market currently believes 1-year bond will be worth one year from now. That hypothetical number is the one year carry on a 2 year bond. Of course your return will be different because market pricing is always changing. Carry is only an estimator of future returns, and a rather simplistic one. You understand this part? $\endgroup$ – noob2 Apr 22 '16 at 12:12
  • $\begingroup$ In an international context (i.e. with bonds of different countries) you will also need exchange rates to bring the returns to a common currency. So you need at a minimum: bond yields, short term rates and currency rates. And as haginile said below, you can only compute an approximation subject to many assumptions. $\endgroup$ – noob2 Apr 22 '16 at 14:17
  • $\begingroup$ This paper "Carry" by Pedersen et. al uses Zero Coupon yields, not regular bond yields. papers.ssrn.com/sol3/papers.cfm?abstract_id=2298565 $\endgroup$ – Alex C Apr 22 '16 at 22:10
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This is pretty much impossible to do, but if you must, you'll have to make some assumptions.

You can assume that the yields given are par yields. In other words, they represent both the yield AND the coupon rates of bonds trading at par. And assuming you also have short-term interest rates, you can compute forward price on this hypothetical par bond and use that as the basis for futures price (you won't need to worry about delivery option, but you still have to account for the conversion factor). Carry is simply the difference between spot price (assumed to be 100) and forward price.

To compute returns, you take this bond and reprice at at the next period (i.e., holding coupon rate constant and reducing time to maturity, you reprice it at the new yield). That allows you to compute returns.

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  • $\begingroup$ Thank you for the reply. I have zero coupon bond yields as attached in the picture above. So you would say that the F and S are the formulas for the synthetic prices? And based on these prices I should obtain the carry, right. The point is I do not have the interest rate, and the literature does not provide any information on these. I always thought that the government bond is the interest rate, so this is different now. I hope Bloomberg has those interest rates. For returns, I am going to compute a time series of future prices. So this would be easy solved if my future pricing is correct $\endgroup$ – user20280 Apr 23 '16 at 22:09

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