Portfolio optimization

Portfolio optimization focuses on constructing a portfolio of assets that seeks to maximize returns and minimize risk. In this context, a portfolio refers to the distribution of an investor's assets—a weight vector—which can be optimized for risk tolerance, expected rate of return, cost minimization, and other objectives. This optimization can be performed regularly to reflect recent changes in market behavior.

In VBT, a portfolio is a collection of asset vectors combined into a larger array along the column axis. By default, each of these vectors is treated as a separate backtesting instance, but you can apply a grouping instruction to treat multiple assets as a single unit. Portfolio optimization then becomes the process of converting a set of pricing vectors (information as input) into a set of allocation vectors (actions as output), which can then be provided to any simulator.

Thanks to VBT's modular design (and in line with the key principles of data science), optimization and simulation are handled separately. This enables you to analyze and filter allocation vectors even before they are backtested. This approach is similar to the typical workflow for working with signals: 1) generate, 2) pre-analyze, 3) simulate, and 4) post-analyze. In this example, we will cover how to complete each of these steps for the highest informational yield.

Data

As always, we should begin by obtaining some data. Because portfolio optimization involves working with a group of assets, we need to fetch data for more than one symbol. Here, we will fetch one year of hourly data for 5 different cryptocurrencies:

from vectorbtpro import *

symbols = ["BTCUSDT", "ETHUSDT", "BNBUSDT", "XRPUSDT", "ADAUSDT"]
data = vbt.BinanceData.pull(
    symbols,
    start="2020-01-01 UTC",
    end="2021-01-01 UTC",
    timeframe="1h"
)

Let's save the data locally to avoid re-fetching it every time we start a new runtime:

data.to_hdf()

data = vbt.HDFData.pull("BinanceData.h5").select(symbols)  

Allocation

In simple terms, asset allocation is the process of deciding where to invest funds in the market—it is a horizontal vector composed of weights or amounts of assets at a specific timestamp. For example, to allocate 50% to BTCUSDT, 20% to ETHUSDT, and distribute the remainder equally among the other assets, the allocation vector would be [0.5, 0.2, 0.1, 0.1, 0.1]. Frequently, weight allocations sum to 1, ensuring the entire stake is continuously invested, but you can also choose to invest only a portion of your balance or specify a particular (continuous or discrete) number of assets instead of weights. Since we generally want to allocate periodically rather than hold positions indefinitely, we also need to decide on rebalancing timestamps.

Manually

Let's manually generate and simulate allocations to better understand how everything works together.

Index points

The first step is to decide when to re-allocate. This is straightforward using ArrayWrapper.get_index_points, which converts a human-readable query into a list of index positions (also called "index points" or "allocation points"). These positions are simple numeric indices, where 0 is the first row and len(index) - 1 is the last.

For example, let's convert the first day of each month into index points:

ms_points = data.wrapper.get_index_points(every="M")
ms_points

array([0, 744, 1434, 2177, 2895, 3639, 4356, 5100, 5844, 6564, 7308, 8027])

data.wrapper.index.get_indexer(
    pd.Series(index=data.wrapper.index).resample(vbt.offset("M")).asfreq().index,
    method="bfill"
)

array([0, 744, 1434, 2177, 2895, 3639, 4356, 5100, 5844, 6564, 7308, 8027])

We can also convert these index points back to timestamps:

data.wrapper.index[ms_points]

DatetimeIndex(['2020-01-01 00:00:00+00:00', '2020-02-01 00:00:00+00:00',
               '2020-03-01 00:00:00+00:00', '2020-04-01 00:00:00+00:00',
               '2020-05-01 00:00:00+00:00', '2020-06-01 00:00:00+00:00',
               '2020-07-01 00:00:00+00:00', '2020-08-01 00:00:00+00:00',
               '2020-09-01 00:00:00+00:00', '2020-10-01 00:00:00+00:00',
               '2020-11-01 00:00:00+00:00', '2020-12-01 00:00:00+00:00'],
              dtype='datetime64[ns, UTC]', name='Open time', freq=None)

These are our rebalancing timestamps!

The main advantage of this method is its flexibility. The every argument can be a string, an integer, a pd.Timedelta object, or a pd.DateOffset object: