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\[\pi(p)=\pi-2(1-p),\, p \lt 1,\]  \[\pi(p)=\pi,\, p \geq 1.\]  I give the calculations below, but the next two graphs illustrate the results. As is clear from the graphs (and intuitively obvious), the trading policy is contrarian for \(p \geq 1\) and momentum for \(p \le 1\). Downside protection forces to sell the asset when its price has gone down, and to buy it when it has gone up.  This closes the illustrations. I'll now move on to investigate the way contrarian and momentum trading interact with discrete time rebalancing. In the context of discrete time rebalancing, price cycles hurt momentum trading while it benefits contrarian trading.  # Calculations  The value function is easily obtained by solving:  \[\frac{dV}{V}=\pi(p)\frac{dp}{p}.\]   This leads to: