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The existence of basis spreads leads to that e.g. a 6M forward rate has a different price than two after each other following 3M forward rates. This due to that the 6M forward rate has a higher credit and liquidity premium.

Can someone explain why? As I see it, the money is locked in 6 months in both contracts and therefore should have equal credit and liquidity risk. Is this because the demand and supply of 3M contracts is higher than the 6M?

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You are confusing the underlying index 3M Libor and a 6M loan that pays a compounded 3M interest. A 3M Libor is by definition the (average) rate on an interbank 3M loan. A 6M loan, regardless of its reference interest rate, is subject to counterparty risk up to 6M.

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  • $\begingroup$ Let me clarify: If we disregard LIBOR, and only consider two 3M rolling FRAs vs a 6M FRA. Equal cash flow amounts and timings. Why does the 6M contract have a higher yield? $\endgroup$ – karamell May 11 '17 at 14:42
  • $\begingroup$ Perhaps I misunderstood your question. how do you define the yield on an FRA ? $\endgroup$ – Antoine Conze May 11 '17 at 14:45
  • $\begingroup$ The return I would get if I invested some quantity of money in the contracts. So I claim that if I invested £1 in both contracts, I would get a higher return from the 6M FRA. $\endgroup$ – karamell May 11 '17 at 14:49
  • $\begingroup$ an FRA is worth zero when you enter into it and does not require an initial investment, it is just a swap between a reference index (Libor 3M, Libor 6M, ...) and a fixed rate. The actual return you would get is the difference between the realized Libor(s) and the fixed rate. The expected return is zero in both cases. $\endgroup$ – Antoine Conze May 11 '17 at 14:58
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    $\begingroup$ But I think I see where are you are confused. Consider the following strategies (a) you lend 1 to a BB rated bank at 6M Libor and after 6 months you get 1 + 6M Libor if the bank has not defaulted. (b) you lend 1 to a BB rated bank at 3M Libor and after 3 months you get 1 + 3M Libor if the bank has not defaulted. At this point you have the choice of not lending, lending again at 3M Libor to the same bank if its rating is unchanged, or lending at 3M Libor to another BB rated bank. (a) and (b) do not bear the same liquidity and counterparty risk, hence the difference in rates $\endgroup$ – Antoine Conze May 11 '17 at 16:17

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