The Model Thinker #26 - Multi Armed Bandit Problems

In my opinion, this chapter was not written very well and I had to google some Youtube videos to really understand the concepts this time round.

Imagine you have two choices when deciding on an investment strategy.

Each strategy would either give a 'good' outcome or a 'bad' outcome that may or may not be related to actual investment returns. This is because, in some cases, a strategy may return less but do so in a way that gives you more psychological comfort. You can also assume that each strategy spans an entire investment philosophy so you can only engage in one strategy at any one time.

Suppose you have already have a strategy that works and gives makes you feel good 60% of the time.

Now, suppose you attend an investment course and the instructor shows you a totally new investment strategy.

Do you switch strategies and adopt what the instructor proposes or you stick to status quo?

There are some ways to resolve this dilemma.

The sample and greedy approach would mean giving the new strategy a chance and try it, say, for 10 years. If a good outcome occurs more than 6 out of the 10 years, you then adopt the new strategy for good.

The adaptive exploration approach will try the new approach for 10 years, after which the proportion of good outcomes will be weighted to determine the proportion of old and new strategies to employ. So if the next 10 years produce 8 good outcomes. The subsequent 15 years will be split 6:8 ratio according to the good results arising from old and new strategies.

The most powerful approach would be to choose the strategy that provides a higher Gittens Index which is complicated mathematically ( as shown above ) but introduces a discounted element into consideration and addresses a historical record of good and bad outcomes. The Gittens Index is dynamic and based on the outcome of every subsequent year an investment strategy is being adopted.

While it would be clunky to use the Gittens Index on a blog, some qualitative insights are useful.

If you are a young investor with a much longer horizon, the Gitten's Index will give the future the benefit of the doubt and you are encouraged to try out a new investment idea for size. There is more room for exploration since you have more time to take advantage of compound interest. I would like to think that leveraged investing adoption will be more favourable to younger investors who have more time and less capital.

If you are an older investor and moving towards end of time horizon, perhaps you want to stick with an investment strategy that has worked for you all these years. Older investors are looking to refine their already mature investment strategies and will rather add one or two stocks into their portfolio rather than adopt your investment philosophy whole sale.