Contango/Backwardation And Basis Relationship

[Rohit]

Hi David,

I am trying to relate the 2 concepts here and getting a little confused -
So-Fo = Basis where;
So<Fo = Weak Basis, Contango and model is Cash and Carry

at time = 0 if So<Fo ex. 4 and 4.2 i.e basis = -0.2 weak basis here
at time = t if St<Ft ex. 4.2 and 4.3 then basis = -0.1 weak basis here
but relative basis strengthens (-0.2 to -0.1)

is the model here Cash and Carry or Reverse ?

 

[David Harper CFA FRM]

Hi @Rohit You might need three numbers to reconcile these concepts: S(0), observed or traded F(0), and the theoretical futures price given by the cost of carry model, let's call it COC_F(0); please note we do not here need a fourth variable which is also different, E[S(t)], the unobserved expected future stock price which we do not expect to equal either F(0) nor COC_F(0). So, let's just say that:

• observed S(0) = $4.00
• traded one-year future price F(0) is aka F(0,1) = 4.20
• Say the risless rate is 1.0% and storage cost is 3.0% and zero convenience such that COC_F(0) = $4.00 * exp(1%+3%) = $4.16

The basis is S(0) - traded F(0) = 4.00 - 4.20 = -0.20. This negative basis does imply a contango because F(0) > S(0); ie, contango is natural result of positive cost of carry. But it does not tell us whether there a carry arbitrage. The carry arbitrage occurs when F(0) <> COC_F(0); i.e., when the traded price differs from the theoretical price. In this case, because trading 4.20 > theoretical 4.16 , the (actual) futures contract is "trading rich" (relative to it's theoretical COC price) such that we'd conduct a "cash and carry" which entails shorting the rich asset (futures contract) and buying the cheap asset (the spot commodity). If, for example, trading F(0) $4.09 < theoretical 4.16, then "reverse cash and carry" is advised, where we short the expensive spot commodity and buy (take a long position in) the trading cheap futures contract. I hope that helps!

 

[Rohit]

Thanks @David Harper CFA FRM this makes it a lot clearer !