I was going through paper "Learning to Trade via Direct Reinforcement" by Moody and Saffell. It explains additive profit as follows

Additive profits are appropriate to consider if each trade is for a fixed number of shares or contracts of security $z_t$. This is often the case, for example, when trading small stock or futures accounts or when trading standard US\$ FX contracts in dollar-denominated foreign currencies. We define $r_t=z_t-z_{t-1}$ and $r_t^f=z_t^f-z_{t-1}^f$ as the price returns of a risky (traded) asset and a risk-free asset (like T-Bills) respectively, and denote the transactions cost rate as $\delta$. The additive profit accumulated over $T$ time periods with trading position size $\mu > 0$ is then defined in term of the trading returns, $R_t$, as:
$P_T=\Sigma_{t=1}^TR_t$, where
$R_t\equiv\mu\{r_t^f+F_{t-1}(r_t-r_t^f)-\delta|F_t-F_{t-1}| \}$
with $P_0=0$ and typically $F_T=F_0=0$.

Earlier, paper explains $F_t$ as follows:

Our traders are assumed to take only long, neutral or short positions, $F_t\in \{1,0,—1\}$, of constant magnitude.

So $F_t$ is a decision function.

I have following doubts:

  1. Why to consider price returns of a risky and risk free assets separately? (May be this will also be answered by the answer to next question)

  2. I didnt get how the formula $R_t\equiv...$ is formed. Can someone please help me with this?

I guess miss some big understanding here...

PS: sorry if this sounds too basic. Am a noob (I guess). If you dont feel to answer, please at least give me some direction, may be by sharing related topic / content link.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.