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Term spread is the difference of long term and short term yield. If the spread is positive, the difference indicates the extra yield received on long term bond.

Forward rate is the future yield on a bond. It is calculated using the yield curve. For a yearly compounded bond, $$(1+r_1)^{t1}(1+f)^{tf-t1}=(1+r_{total})^{tf}$$

Although the mathematical expressions of term spread and spread are different, both values are obtained from the yield curve and somehow having the same economic meaning (the difference of yield).

Do I have any misunderstanding?

Many thanks

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    $\begingroup$ A term spread is the simple difference between 2 current interest rates (involving lending money starting today, for 2 different periods, say 2 vs 10 years). A forward is an interest rate applicable to lending money starting at some point in the future, i.e. not today. The spread and the forward will not be exactly equal due to mathematical quirks (for ex $r_2-r_1\ne (1+r_2)/(1+r_1)-1$) and are in any case conceptually distinct. $\endgroup$ – Alex C Apr 25 '18 at 14:33

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