# Value in time of the bond in delta-hedging

I am trying to implement a simple delta-hedging strategy. The idea is that I want to verify that the covered position "1 option long + delta stocks short" is actually evolving as $$e^{rt}$$, the bond, as I see from the Black-Scholes model.

I am currently considering a stock starting from $$S_0=100$$, with $$\mu=0.1$$ and $$\sigma=0.2$$, and a European call with $$K=100$$ and $$r=0.05$$.

I actually see something much more random, even if the portfolio evolves in a large number of time steps, say $$10^5$$, nowhere close to an exponential, and that suddenly reaches 0 at the option expiration. Is there anything wrong?