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fix rate names in readme
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gianlucadetommaso authored Dec 8, 2020
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Expand Up @@ -86,10 +86,10 @@ Given these estimates, Volatile provides a rating for each stock by introducing
where <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;y_{T,i}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;y_{T,i}" title="y_{T,i}" /></a> is the last available log-price, <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\hat&space;y_{T&plus;5,i}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\hat&space;y_{T&plus;5,i}" title="\hat y_{T+5,i}" /></a> is its prediction in 5 trading days (usually, that corresponds to the log-price in one week) and <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\hat\sigma_{T&plus;5,i}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\inline&space;\hat\sigma_{T&plus;5,i}" title="\hat\sigma_{T+5,i}" /></a> is the estimated standard deviation of the prediction. If the future prediction is larger than the current price, the score will be positive; the larger the difference and the more confident we are about the prediction (or equivalently, the smaller the standard deviation is), the more positive will be the score. We can reason similarly if the score is negative. In other words, a large positive score indicates that the current price is undervalued with respect to its stock trend, therefore an opportunity to buy; a large negative score indicates, vice versa, that the current price is overvalued with respect to its stock trend, therefore a moment to sell.

Then, stocks are rated according to the following criteria:
- STRONG BUY if <a href="https://www.codecogs.com/eqnedit.php?latex=\text{score}_i>3" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\text{score}_i>3" title="\text{score}_i>3" /></a>;
- BUY if <a href="https://www.codecogs.com/eqnedit.php?latex=2<\text{score}_i<=3" target="_blank"><img src="https://latex.codecogs.com/gif.latex?2<\text{score}_i<=3" title="2<\text{score}_i<=3" /></a>;
- NEUTRAL if <a href="https://www.codecogs.com/eqnedit.php?latex=-2<\text{score}_i<=2" target="_blank"><img src="https://latex.codecogs.com/gif.latex?-2<\text{score}_i<=2" title="-2<\text{score}_i<=2" /></a>;
- SELL if <a href="https://www.codecogs.com/eqnedit.php?latex=-3<\text{score}_i<=-2" target="_blank"><img src="https://latex.codecogs.com/gif.latex?-3<\text{score}_i<=-2" title="-3<\text{score}_i<=-2" /></a>;
- STRONG SELL if <a href="https://www.codecogs.com/eqnedit.php?latex=\text{score}_i<=-3" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\text{score}_i<=-3" title="\text{score}_i<=-3" /></a>.
- HIGHLY BELOW TREND if <a href="https://www.codecogs.com/eqnedit.php?latex=\text{score}_i>3" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\text{score}_i>3" title="\text{score}_i>3" /></a>;
- BELOW TREND if <a href="https://www.codecogs.com/eqnedit.php?latex=2<\text{score}_i<=3" target="_blank"><img src="https://latex.codecogs.com/gif.latex?2<\text{score}_i<=3" title="2<\text{score}_i<=3" /></a>;
- ALONG TREND if <a href="https://www.codecogs.com/eqnedit.php?latex=-2<\text{score}_i<=2" target="_blank"><img src="https://latex.codecogs.com/gif.latex?-2<\text{score}_i<=2" title="-2<\text{score}_i<=2" /></a>;
- ABOVE TREND if <a href="https://www.codecogs.com/eqnedit.php?latex=-3<\text{score}_i<=-2" target="_blank"><img src="https://latex.codecogs.com/gif.latex?-3<\text{score}_i<=-2" title="-3<\text{score}_i<=-2" /></a>;
- HIGHLY ABOVE TREND if <a href="https://www.codecogs.com/eqnedit.php?latex=\text{score}_i<=-3" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\text{score}_i<=-3" title="\text{score}_i<=-3" /></a>.

Because we model log-prices as a Gaussian, the distribution of prices is a log-Normal distribution, whose mean and standard deviation can be derived in closed form from the estimators <a href="https://www.codecogs.com/eqnedit.php?latex=\hat&space;y_{t,i}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat&space;y_{t,i}" title="\hat y_{t,i}" /></a> and <a href="https://www.codecogs.com/eqnedit.php?latex=\hat\sigma_{t,i}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat\sigma_{t,i}" title="\hat\sigma_{t,i}" /></a>. We use log-Normal distribution statistics at times <a href="https://www.codecogs.com/eqnedit.php?latex=t=1\dots,T" target="_blank"><img src="https://latex.codecogs.com/gif.latex?t=1\dots,T" title="t=1\dots,T" /></a> to produce the stock estimation plot and at time <a href="https://www.codecogs.com/eqnedit.php?latex=T&plus;1" target="_blank"><img src="https://latex.codecogs.com/gif.latex?T&plus;1" title="T+1" /></a> to fill the prediction table. In order to produce the sector estimation plot, we proceed analogously but with sector-level estimators <a href="https://www.codecogs.com/eqnedit.php?latex=\hat&space;y^s_{t,k}=\sum_{j=0}^{D}\hat\phi^s_{k,j}\,\tau_t^j" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat&space;y^s_{t,k}=\sum_{j=0}^{D}\hat\phi^s_{k,j}\,\tau_t^j" title="\hat y^s_{t,k}=\sum_{j=0}^{D}\hat\phi^s_{k,j}\,\tau_t^j" /></a> and <a href="https://www.codecogs.com/eqnedit.php?latex=\hat\sigma^s_{t,k}=\log(1&plus;e^{\hat\psi^s_k&plus;|1-\tau_t|})" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\hat\sigma^s_{t,k}=\log(1&plus;e^{\hat\psi^s_k&plus;|1-\tau_t|})" title="\hat\sigma^s_{t,k}=\log(1+e^{\hat\psi^s_k+|1-\tau_t|})" />.

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