Why do the SP6 notes make a "no arbitrage" argument in the context of expectations?

[M Willis]

Suppose we deposit F_0 e^{-rT} in cash at time 0 and also enter into a long position on a future with maturity at time T . The cash will grow to F_0 by time T , which is just enough to pay the futures price at maturity and take delivery of the asset worth S_T , which we assume is sold immediately.
If we assume that there are no arbitrage opportunities, the present value of these cashflows (ie the initial outlay plus the proceeds) must be zero, so that (ignoring margining):
-F_0 e^{-rT} + E[S_T]e^{-kT} = 0
or
F_0 = E[S_T]e^{(r-k)T}

The above is from the 2026 notes for SP6. Can anyone help my to understand why a "no arbitrage" argument is being made in the context of expectations?

I was under the impression that "no arbitrage" meant a guaranteed profit without the risk of loss, rather than an *expected* profit with the potential for loss.

This is from chapter 2, so presumably the expectation is real world (risk neutral has not been introduced at this stage in the course).

 

[John Potter]

Hi M Willis,

This section is about comparing. We're thinking about how do futures prices compare with the market's expected spot prices? and the whole thing is about examining whether we are going to end up in a contango market or normal backwardation.

You are 100% correct that the E[ST] should NOT feature in a no arbitrage argument to derive the value of F0 - it doesn't.

And, yes, these probabilities are actual - the market's actual expected spot prices,

John