Creating Arbitrage in Binomial Pricing Model > You have a stock in a 1-period binomial model such that $S_0 = 4$, $S_u=8$, and $S_d=2$, and $r = 1.5$ > > Show how to extract arbitrage by explicitly defining a portfolio $(X, > ∆)$ such that $X_0<0$ while $X_1≥ 0$. So I know that arbitrage is possible because the numbers given in the problem violate the rule $d < 1+r <u$ since $u=2$ and $d=0.5$. I think I could figure out how to create arbitrage if this was a call or put option but since it's just a stock I'm not sure how to create arbitrage.

Short 1 unit of stock at the current rate, so we hold -1 units of stock and $\$4.$ Put that $\$4$ into bonds.

After 1 period, cash out the bond at $\$10$ and buy 1 unit of stock at the then-current price. You will end up with either $\$2$ or $\$8.$