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Quick summary: > To illustrate this concept, you could consider a simple coin-flip game where you make a 50% return on your money if the coin lands on heads, o

• curtisf 4y ago
  There's actually a little something here, but the blog loses it by being way too loose with "expectation". The interesting thing, which is confused by the blog, is that "expectation" is not that same thing as "expectation of log". The "expectation of log" is a simple and effective way to adjust for risk, so trading off between these two can be useful. In the simple betting case, you're multiplying your money by {e^k, e^-k}. In this case, k≈0.4, so you end up with Y = P * {0.66, 1.50} This has expectation of `1.08 * P`, and it has an expectation-of-log of `log P`. In the rebalancing case, you're multiplying your money by (1 + {e^k, e^-k})/2. You end up with Z = P * {0.83, 1.25} This has an expectation of `1.04 * P`, and it has an expectation-of-log of `log P + 0.0204`. So you actually have a smaller expectation, but a larger expectation-of-log. This could be helpful, depending on your goals, because it is a simple way to describe how "risky" the strategy is. For example, after 5 rounds of this, the first strategy has a median value of +8.5%, while the second strategy has a median of +13%. On the other hand, on average the first strategy has grown +49% while the second has grown only +23%.