Overview
Smart beta has a broad meaning, but we can say in practice that when we use the universe of stocks from an index, and then apply some weighting scheme other than market cap weighting, it can be considered a type of smart beta fund.
- Building a smart beta portfolio and calculating its tracking error against a benchmark stock index in order to see how well it performs.
- Using quadratic programming to optimize the portfolio’s weights.
- Rebalancing this portfolio and then calculating turnover in order to evaluate performance and determine optimal rebalancing frequency.
- The dataset is a set of end-of-day stock prices that comes from Quotemedia.
Concepts
- Using Pandas/NumPy to calculate portfolio weights based on dollar volume, as well as weights based on dividend returns.
- Writing methods that compute returns, weighted returns, cumulative returns, and tracking error.
- Solving convex optimization problems (quadratic programming) with the CVXPY Python library.
- Implementing methods that rebalance portfolio weights at any desired frequency and return the cost, or annualized turnover, of doing so.
Tracking Error
In order to check the performance of the smart beta portfolio, we can calculate the annualized tracking error against the index. Implement tracking_error to return the tracking error between the ETF and benchmark.
For reference, we’ll be using the following annualized tracking error function: \(TE = \sqrt{252} * SampleStdev(r_p - r_b)\) Where $ r_p $ is the portfolio/ETF returns and $ r_b $ is the benchmark returns.
Note: When calculating the sample standard deviation, the delta degrees of freedom is 1, which is the also the default value.
Portfolio Turnover
With the portfolio rebalanced, we need to use a metric to measure the cost of rebalancing the portfolio. Implement get_portfolio_turnover to calculate the annual portfolio turnover. We’ll be using the formulas used in the classroom:
\(SumTotalTurnover =\sum_{t,n}{\left | x_{t,n} - x_{t+1,n} \right |}\) Where $ x_{t,n} $ are the weights at time $ t $ for equity $ n $.
| $ SumTotalTurnover $ is just a different way of writing $ \sum \left | x_{t_1,n} - x_{t_2,n} \right | $ |
