Comment by aoeusnth1 | Hacker News Reader

Comment by aoeusnth1 | Hacker News Reader

This article only catches its stride halfway through. At first, I nearly pulled a muscle rolling my eyes at the “the standard deviation of total returns” argument. Of course the standard deviation of total returns will be higher for stocks than bonds, because the potential gains are so much larger! A (penny + a lottery ticket) has higher standard deviation in total returns than just a penny, but that doesn’t make its risk meaningfully higher. Risk aversion only really kicks in on the downside, so standard deviation of total returns is a useless measure.

Luckily, I kept reading, because the option pricing argument seems extremely solid to me. The common sense notion that your expected downside gets smaller over time is actually wrong according to options pricing - actually, longer-term put options are more expensive. I don’t see a way around that.

There is an interesting rebuttal to the option pricing argument by Zvi Bodie [1] (you can view a free copy via Google Scholar), which I don't claim to fully understand. Warren Buffett famously sold 15-year European puts in the S&P 500, FTSE, euro stoxx 50, Nikkei 225 and received premiums of $4.5B. To me, it feels like invoking Black-Scholes in this way, Bodie may be making the error of citing a mathematical formula without satisfying all of its assumptions. Perhaps Black-Scholes works for accurately pricing short-term options, but not for 15-year or higher time horizons that more closely match an average adult working career?

[1] On the risk of stocks in the long run: A note. R Taylor, DJ Brown. Financial Analysts Journal, 1996

It does seem that Black-Scholes cannot apply here. I think the main issue is timing the strike: for a normal option, if it is ever in the money, it will get exercised. For a "portfolio insurance" argument, it seems like we don't really care if the portfolio is down 99.9% for only a single day in the 20 year timespan. But neglecting that possibility would be ruinous to someone underwriting a normal option.

I know very little about finance but I did notice that the author specifically notes that the insurance is the same as an European put option (ie can only be exercised at expiry), to which Black-Scholes can be applied.

I knew that overlooking the word "European" which I did not understand would be a mistake. Thank you.

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