(Self-study) Futures, bonds, and arbitrage

Question

I'm currently self studying futures, so I'm sorry if this questions comes off a bit stupid. I'm currently reading a book by Walsh, J.B. Knowing the Odds: An Introduction to Probability.
I quote this part of the text:

I want to understand how the bond's worth at time $t$, $(P-S_0)e^{rt}$ came about. If I understood it right, in b) $S_0-P$ was invested, so how come at time $t$, the bond's worth is not $(S_0-P)e^{rt}$.
Sorry about the ignorant question.

Tosh · Answer

Let me just rephrase in less complex literature. 
So at $t=0$, you short the expensive side, $S_0$. 
Use proceed to buy the cheaper side, $P$. 
You will invest the difference, $(S_0 - P)$ at the risk free rate, where you multiply by $e^{rt}$ due to time value of money, which grows at time $t$.
Now at time $t=t$,
You close the position, i.e if you have gone short at $t = 0 $, you will go for long (liquid) position at $t = t$. Hence you should get a net of $(S_0 - P) + (P-S_0)$. This where you get this rissoles profit of $(P-S_0)e^{rt}$.
Hope this helps and good luck for your self study.

(Self-study) Futures, bonds, and arbitrage

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