Absolute Profit & Expected ROI

Edge per share and return on money invested are both useful, but they answer different questions. A low-priced contract can have modest cents of edge and a large percentage ROI because little capital buys one share.

One share and many shares #

For one YES share,

$$EV_{share}=q-p.$$

For $N$ shares,

$$EV_{position}=N(q-p), \qquad Capital=Np.$$

Expected return on invested capital is

$$ROI_{expected}=\frac{q-p}{p}.$$

This is not annualized and ignores time, costs, and opportunity cost.

Fixed shares versus fixed budget #

With a fixed 100 shares, expected profit is $100(q-p)$ and settlement notional is always 100. With fixed budget $B$, share count is $B/p$ and

$$EV_B=\frac{B}{p}(q-p)=B\frac{q-p}{p}.$$

At $q=0.65$, $p=0.50$ has EV +0.15 per share and ROI 30%; $p=0.60$ has EV +0.05 and ROI 8.33%. A $60 budget buys 120 shares at 0.50 but 100 shares at 0.60, creating different settlement exposure.

Life example #

Earning 10 on a 20 purchase is 50% ROI; earning 30 on a 300 purchase is only 10% ROI but more absolute money. Neither percentage alone tells portfolio risk or capacity.

Application to no-hedge #

Compare no-hedge opportunities on net expected profit, net ROI, capital lock-up, and settlement exposure. A cheap contract may show spectacular percentage ROI while concentrating enormous share count on one uncertain outcome.