Hello! Glad to meet you. I'm currently a student at Columbia University studying Financial Engineering, and want to give an overview of the projects I'm working on!
To start things off, Columbia has been hosting a trading competition that myself and another partner are competing in. I'm including a notebook of the algorithm that we're using, just to give a simple overview of a miniature algorithm.
Our algorithm uses a basic momentum strategy: in the given list of potential portfolios, pick the stocks that have been performing well in the past 30 days. Then, optimize for return subject to the drawdown being below a specific level. We didn't include the Sharpe ratio as a constraint, mostly because we were a bit late entering the competition.
**UPDATE 12/5/2015**: Now that the competition has ended, I wanted to update how the algorithm performed. Unfortunately, it didn't do very well. I'm planning to make some tweaks over the coming weeks, and do another forward test in January.
**Goal: Max return given maximum Sharpe and Drawdown**
```python
from IPython.display import display
import Quandl
from datetime import datetime, timedelta
tickers = ['XOM', 'CVX', 'CLB', 'OXY', 'SLB']
market_ticker = 'GOOG/NYSE_VOO'
lookback = 30
d_col = 'Close'
data = {tick: Quandl.get('YAHOO/{}'.format(tick))[-lookback:] for tick in tickers}
market = Quandl.get(market_ticker)
```
## Calculating the Return
We first want to know how much each ticker returned over the prior period.
```python
returns = {tick: data[tick][d_col].pct_change() for tick in tickers}
display({tick: returns[tick].mean() for tick in tickers})
```
```
{'CLB': -0.0016320202164526894,
'CVX': 0.0010319531629488911,
'OXY': 0.00093418904454400551,
'SLB': 0.00098431254720448159,
'XOM': 0.00044165797556096868}
```
## Calculating the Sharpe ratio
Sharpe: ${R - R_M \over \sigma}$
We use the average return over the lookback period, minus the market average return, over the ticker standard deviation to calculate the Sharpe. Shorting a stock turns a negative Sharpe positive.
sharpes = {tick: sharpe(returns[tick]) for tick in tickers}
display(sharpes)
```
```
{'CLB': -0.10578734457846127,
'CVX': 0.027303529817677398,
'OXY': 0.022622210057414487,
'SLB': 0.026950946344858676,
'XOM': -0.0053519259698605499}
```
## Calculating the drawdown
This one is easy - what is the maximum daily change over the lookback period? That is, because we will allow short positions, we are not concerned strictly with maximum downturn, but in general, what is the largest 1-day change?
```python
drawdown = lambda ret: ret.abs().max()
drawdowns = {tick: drawdown(returns[tick]) for tick in tickers}
display(drawdowns)
```
```
{'CLB': 0.043551495607375035,
'CVX': 0.044894389686214398,
'OXY': 0.051424517867144637,
'SLB': 0.034774627850375328,
'XOM': 0.035851524605672758}
```
# Performing the optimization
$$
\begin{align*}
max\ \ & \mu \cdot \omega\\
s.t.\ \ & \vec{1} \omega = 1\\
& \vec{S} \omega \ge s\\
& \vec{D} \cdot | \omega | \le d\\
& \left|\omega\right| \le l\\
\end{align*}
$$
We want to maximize average return subject to having a full portfolio, Sharpe above a specific level, drawdown below a level, and leverage not too high - that is, don't have huge long/short positions.
```python
import numpy as np
from scipy.optimize import minimize
#sharpe_limit = .1
drawdown_limit = .05
leverage = 250
# Use the map so we can guarantee we maintain the correct order
