annual turnover metric

breaded-xyz · Feb 20, 2024 · d0e2da6 · d0e2da6
1 parent 79b6461
commit d0e2da6
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Showing 3 changed files with 38 additions and 20 deletions.
diff --git a/alphavec/backtest.py b/alphavec/backtest.py
@@ -198,7 +198,8 @@ def backtest(
     port_rets = strat_rets.sum(axis=1)
     port_cum = strat_cum.sum(axis=1)
 
-    port_ann_turnover = 1
+    # Aproximate the portfolio turnover as the weighted average sum of the asset-wise turnover
+    port_ann_turnover = (strat_ann_turnover * weights.mean().abs()).sum()
 
     port_perf = pd.DataFrame(
         {
@@ -319,9 +320,25 @@ def _turnover(
     weights: pd.DataFrame | pd.Series,
     rets: pd.DataFrame | pd.Series,
 ) -> pd.Series | float:
-    diff = weights.fillna(0).diff().abs()
-    port = (1 + rets).cumprod() - 1
-    turnover = diff.sum() / ((1 + port.iloc[-1]) / 2)
+    """Calculate the turnover for each position in the strategy."""
+    # Assume capital of 1000
+    capital = 1000
+    # Calculate the delta of the weight between each interval
+    # Buy will be +ve, sell will be -ve
+    diff = weights.fillna(0).diff()
+    # Capital is fixed (uncompounded) for each interval so we can calculate the trade volume
+    # Sum the volume of the buy and sell trades
+    buy_volume = (diff.where(diff > 0, 0).abs() * capital).sum()
+    sell_volume = (diff.where(diff < 0, 0).abs() * capital).sum()
+    # Trade volume is the minimum of the buy and sell volumes
+    # Wrap in Series in case of scalar volume sum (when weights is a Series)
+    trade_volume = pd.concat(
+        [pd.Series(buy_volume), pd.Series(sell_volume)], axis=1
+    ).min(axis=1)
+    # Calculate the uncompounded returns to get the average of the portfolio
+    # Finally take the ratio of trading volume to mean portfolio value
+    equity = capital + (capital * rets.cumsum())
+    turnover = trade_volume / equity.mean()
     return turnover
 
 

diff --git a/example.ipynb b/example.ipynb
@@ -607,7 +607,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -709,7 +709,7 @@
        "      <td>0.512587</td>\n",
        "      <td>1.616165</td>\n",
        "      <td>0.632456</td>\n",
-       "      <td>0.644781</td>\n",
+       "      <td>2.944701</td>\n",
        "      <td>1.000637</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -722,7 +722,7 @@
        "      <td>1.058797</td>\n",
        "      <td>0.699507</td>\n",
        "      <td>0.659074</td>\n",
-       "      <td>4.950039</td>\n",
+       "      <td>2.331747</td>\n",
        "      <td>1.000745</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -735,7 +735,7 @@
        "      <td>0.385551</td>\n",
        "      <td>0.233350</td>\n",
        "      <td>0.497637</td>\n",
-       "      <td>15.555918</td>\n",
+       "      <td>4.970033</td>\n",
        "      <td>1.000637</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -748,7 +748,7 @@
        "      <td>0.615083</td>\n",
        "      <td>0.081175</td>\n",
        "      <td>0.585446</td>\n",
-       "      <td>27.251474</td>\n",
+       "      <td>5.556876</td>\n",
        "      <td>1.000708</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -761,7 +761,7 @@
        "      <td>0.477024</td>\n",
        "      <td>0.174253</td>\n",
        "      <td>0.459495</td>\n",
-       "      <td>21.644242</td>\n",
+       "      <td>5.605835</td>\n",
        "      <td>1.001065</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -774,7 +774,7 @@
        "      <td>0.408337</td>\n",
        "      <td>-0.086424</td>\n",
        "      <td>0.659143</td>\n",
-       "      <td>59.531211</td>\n",
+       "      <td>8.762681</td>\n",
        "      <td>1.000637</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
@@ -805,12 +805,12 @@
        "                                          \n",
        "          annual_turnover trades_per_day  \n",
        "symbol                                    \n",
-       "BTCUSDT          0.644781       1.000637  \n",
-       "DOGEUSDT         4.950039       1.000745  \n",
-       "ETHUSDT         15.555918       1.000637  \n",
-       "MATICUSDT       27.251474       1.000708  \n",
-       "SOLUSDT         21.644242       1.001065  \n",
-       "XRPUSDT         59.531211       1.000637  "
+       "BTCUSDT          2.944701       1.000637  \n",
+       "DOGEUSDT         2.331747       1.000745  \n",
+       "ETHUSDT          4.970033       1.000637  \n",
+       "MATICUSDT        5.556876       1.000708  \n",
+       "SOLUSDT          5.605835       1.001065  \n",
+       "XRPUSDT          8.762681       1.000637  "
       ]
      },
      "metadata": {},
@@ -893,7 +893,7 @@
        "      <td>1.582458</td>\n",
        "      <td>2.094833</td>\n",
        "      <td>0.954154</td>\n",
-       "      <td>1</td>\n",
+       "      <td>1.287296</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
@@ -904,7 +904,7 @@
        "portfolio       1.425487           1.582458  2.094833      0.954154   \n",
        "\n",
        "           annual_turnover  \n",
-       "portfolio                1  "
+       "portfolio         1.287296  "
       ]
      },
      "metadata": {},

diff --git a/tests/test_backtest.py b/tests/test_backtest.py
@@ -93,7 +93,8 @@ def test_turnover():
     prices = pd.Series([10, 20, 40, 80, 40])
     returns = weights * prices.pct_change()
 
-    act = bt._ann_turnover(returns, weights)
+    act = bt._turnover(weights, returns).squeeze()
+    assert act == 0.48
     logging.info(act)