Investment Math edited untitled.md  almost 8 years ago

Commit id: 5302f9c70e5e8c2d66e379360dab3a7c170777a4

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Before delving into the topic of discrete rebalancing, I describe the trading policy induced by cppi products. I stay within the context of the two assets model, i.e. cash (with zero interest rate) plus a risky asset. As usual, the risky asset is initialized with price \(p=1\).  Consider a portfolio which trades so as to keep the proportion of the risky asset at \(0 \lt \pi \lt 1\). A cppi overlay consists in protecting a certain level \(\underline{p}\) with I choose to set at \(1/2\) for illustration. I'll assume that the exposure to the risky asset is decreased linearly from \(\pi\) at \(p=1\) to zero at \(p=1/2\). This gives the following exposure to the portfolio:  \[\pi(p)=_pi-2(1-p),\, \[\pi(p)=\pi-2(1-p),\,  p \lt 1,\]