Summer of Math Exposition

If this were twice as long, and took a bit of time with the definitions, it would be a perfect video

Please slow down. Both the animations and explanations went too fast. Spend some time explaining how your formulas are constructed and used.

The motivation was good, but as a pure mathematician who isn't knowledgeable about finance, there were a few aspects of the explanation that I found a little confusing and had to think about a little after watching the video. For one, in the last example, the asymmetry between the two assets struck me as odd. I think it would have helped to hear some clarification about what "causation" is going on here. For example, we could imagine a scenario where the price of the first asset is already fixed, and the second is some newly-created asset that we are considering investing in; we can determine a fair price via these "probabilities" which we can infer from the first price. Then if the first asset's price changes for some reason, the second must change accordingly. (It's still not clear to me what actually determines risk-neutral probabilities in real life--is it just people's beliefs about the real-life probabilities, or do the risk preferences of buyers and sellers play a role?) Second (and much less confusing for me), I'm used to seeing interest rates stated as rates *per unit time*, so for me it would have helped to hear some explicit statement about when the various assets pay out.

The visuals are very nice and kept to a minimum, so that they do not distract. I think the video could be a little bit longer. Personally I do not like to have to pause just for rereading and thinking about it, at some points I believe a little bit of extra time would suffice and make it easier for the viewer. An example is around the 1 minute mark, where the goal of the video is kind of set: We want to create a system with no arbitrage. There could be a higher focus on that, since that will be the result of the video (Something like: The goal is to create a *fair* system. In other words, a system that is free of arbitrage.). Maybe repeat it before the "Recap" at 1:40. Additionally in the practice step, I would like to see just the same values from the beginning plugged in again (with the new value of the second asset), so that I can *see*, that there is a probability of loss. From there on, one could do more examples, but that is not necessary. Overall a nice and concise video, which could be a bit longer and reduced in tempo.

The video was overall short, but sweet. The mathematics was quite well motivated and explained. The animations were really well made. I wish it were slightly longer and certain terms like shorting, for example (in your case, you just took the negative of the outcome, with no cost to take out the short?), were explained.

Very good video! but you talk too fast, and it was hard to understand because if that

Another good, short video. 20-minute videos have their place, but this one is a well-executed showcase of what to aim to do in <5 minutes.

I think to introduce risk neutral probabilities to people, the explanations of terms like arbitrage and probability measure needs to be simplified even further.

Bad explained. No explanation of model. How works interest rate, what do you mean by "short 5 assets"? How does it work? How do we calculate those numbers in example where you short 5 assets? Why do we calculate sime probabilities while our goal to calculate the price? What is connection? And finally: in the beginning, you asked about the price of one asset. Why do we calculate it's price from some other asset? Where does formula come from? I'm very good at maths, but I didn't get it after watching the video thrice.

blissfully short