This might be against the law of gravity, but I'll give a try 🙂
Is there a way to combine two financial products $p_1$ and $p_2$, into a single product $p_c$ that is more volatile than its components?
Mathematically, if the daily returns of the original products are:
$$r_1\sim \mathcal{N}(\mu,\,\sigma^{2})$$ $$r_2\sim \mathcal{N}(\mu,\,\sigma^{2})$$
Can I build a financial product whose daily returns are:
$$r_c\sim \mathcal{N}(\mu_c,\,\sigma_c^{2})$$ $$\sigma_c > \sigma$$
Careful:
I am not looking to increase volatility of absolute returns. (e.g. returns in USD). That is easy, just use leverage. But with leverage come proportionally higher transaction costs. So you don't have an extra edge in trading.
I am looking to increase volatility of relative returns (e.g. percentage returns). I want to obtain higher volatility, at stable transaction costs. That would be an extra hedge in trading.