Ship Investor 2: Continuous Edition

Keyboard Shortcuts

If you get tired of clicking and dragging with the mouse, there are a few keyboard shortcuts to help you out::

Spacebar: Advance to the next day with the current wealth allocation.
Number keys 1-9: Set Gibraltar fund allocation and immediately advance to the next day. So, for example, if you press 1 the Gibraltar fund gets 10 % of your wealth and a day passes. Press 2 for 20 %, and so on up to 90 %.

History

The year is 1781, and 60 years have passed since Ship Investor. You are the child of a rich person, and you want to put your inheritance to use.

Some things have changed in the last 60 years. The Bering Strait shipments went extinct when traders realised nobody lived north of the Bering Strait anyway. Institutional investors have made it hard for individuals to invest in single shipments, too.

However, you can still invest in shipments – indirectly. Investment funds were invented just a few years ago, and someone has already set up two for the type of shipments you are interested in: the Gibraltar fund and the Malacca fund. Shares in these funds are sold in a dark corner of the Amsterdam Stock Exchange. When you buy shares in these funds, they pool together the money from many people like you, and use it to invest in shipments of the corresponding route.

These funds want to make long-term commitments to the various trading companies, so you are not allowed to take money out of the market. You must reinvest all your winnings. You choose how much of your wealth to invest in each fund by dragging the corresponding slider.

When you drag the slider, you sell shares in one fund and the money is automatically used to buy shares in the other – or vice versa. There are no trading fees. When you are happy with your allocation, you press the Trade! button, and a day and a night passes, and your wealth grows or it doesn't, depending on what other speculators think of that fund.

You will have to consider two funds.

Malacca: Risky investment, but with potentially very good payoff. This is where you can both make and lose a lot of money in a short amount of time.
Gibraltar: Safer investment that doesn't change too much over time. If you think the Malacca fund is about to crash, it could be wise to put some of your money in the Gibraltar fund to keep it safe.

For each fund, you are presented with a curve showing how it's changed in value the last year. You can also read how many percent it changed the last year, the last month, the last week, and since yesterday.

Technical Details

You don't need to read this to play the game – it's here in case you are curious.

Optimal Non-Anticipatory Portfolio

This problem of asset allocation was not solved until the mid-to-late 1900s. The optimal non-anticipatory portfolio you can compare yourself to here is the Universal portfolio (Cover, 1991). The non-anticipatory part means that it uses no insider information when computing its asset allocation; it is only allowed to use the recent history (in this case, same as you: the last year) of the funds. Critically, it is not pre-programmed with any information about the statistical distribution of returns.

It is easy to outperform this portfolio in the short term: you just get lucky and then call it quits. This is probably an aggressive, unsustainable strategy, and the universal portfolio will, given enough time, catch up to your overbetting. The goal, in other words, is not to outperform the optimal portfolio; the goal is to not fall too much behind it.

Market Simulation

The market is simulated using a bivariate discrete time Markov-switching multifractal (Calvet & Fisher, 2004) with Bernoulli volatility components and normally distributed log-returns (without jump diffusions). This model was chosen because of its simplicity in implementation and that it yields somewhat satisfactory gameplay.

The Markov-switching multifractal is a random walk with a standard normal step size at its heart. What lends it the characteristic of market movements is that its volatility is governed by a Markov process that encodes both long-term and short run trends. At every step, each volatility component has some probability of changing, where the probability is high for short-run trends and low for longer term trends. The standard deviation of a step is the product of all volatility components.

The bivariate part means that the model generates two timeseries, which can depend on each other. In this specific case, they have strongly correlated volatility and weakly negatively correlated returns. (Sort of mimicking the common behaviour of equity and government bonds.)

I've been lazy with dependencies. Please wait while a gazillion HTTP requests are being performed under the hood.