I apologize in advance for my very simple question but I seem to be unable to wrap my head around this for some reason.Let P(t, T) the time t price of a pure discount bond paying $1 at time T. Assume that interest rates remain constant over time, i.e. at time t = 1 the bond P(1, 2) will be worth the same as today's P(0, 1).Consider the following strategy: At t = 0 go long P(0, 2) and finance this strategy by borrowing the price of this bond until T = 1.At time T = 1, the bond will be worth P(1, 2) = P(0, 1) and the loan will have accumulated to -P(0, 2) / P(0, 1).Since none of the components were stochastic and the strategy at T = 0 had zero cash flow, the portfolio value at T = 1 needs to be zero as well, meaning:P(0, 1) = P(0, 2) / P(0, 1) => P(0, 1) * P(0, 1) = P(0, 2).I do not think this should always hold and I have never seen this no-arbitrage condition, but I cannot seem to find my mistake.(Put differently: I noticed that the strategy of buying a credit-financed bond and holding it for short period of time resulted in a net change in value of the position even if the interest rates remained constant.)

A basic no-arb requirement is that P(0,1)*F(0,1,2)=P(0,2), where F(0,1,2) is the time 0 forward price for delivery at time 1 of a zero coupon bond maturing at time 2. In a world of deterministic interest rates you will have P(1,2)=F(0,1,2) to avoid a trivial arbitrage. Adding your specific assumption that not only are interest rates deterministic, they are also constant, we have F(0,1,2)=P(0,1), and it follows that P(0,1)*P(0,1)=P(0,2).

Thank you!