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Comment by bluedevil2k | Hacker News Reader

Risk is measured by volatility, and Bitcoin is currently 5x more volatile than Tesla stock. To me, that’s risky.

https://www.buybitcoinworldwide.com/volatility-index/

https://www.alphaquery.com/stock/TSLA/volatility-option-stat...

The word "risk" is overloaded in finance, unfortunately. Your usage is not affected by the price being near all time highs. The parent's use is affected.

"Risk is measured by volatility"

Consider a hypothetical security issued by the central bank. In one year's time, the security will be redeemed. An official will roll a pair of dice. Snake eyes means the holder gets $3600; otherwise, the holder gets $0.

How would the market value such a security? The expected value on the expiry date is $100, so let's say $98 today to account for the time value of money.

How volatile would the price of this security be over the next 1 month, next 3 months, next 6 months? Very low, right? The price would edge up slowly from $98 to $100, with maybe some small fluctuations due to changes in interest rate expectations.

This security has a greater than 90% chance that you lose 100% of your initial investment. If volatility is a good measure of risk, how can volatility be so low when there's such a high risk that you lose your shirt?

EDIT: Corrected the payoff: should have been $3600, not $1200.

I would say that this is a very low risk investment. The price, like you say will inch up slowly from 98 to 100. I can then sell this security at any point with very low but steady return. This is the hallmark of a low risk investment.

It's true that if I hold the security until maturity, I could lose my investment. This, however, is easily offset by buying many such securities and recognizing that many will fail but some will succeed, giving me my expected return on average. In fact, I might even decide to buy many of these and repackage them into a basket of securities and split them up into many pieces and sell them off as low risk tranches.

Now, if you claim that all the outcomes are correlated (i.e. there's only one pair of dice that is tossed once), then the price you're talking about ($98) is absolutely not the price it would trade for because of the inherent risk associated with the asset. Instead it would trade at a much lower price. Just imagine that you were given the option of buying this asset for $98 or something like a US bond for $98, both of which will yield $100 at maturity in expectation. Which one would you choose?

"then the price you're talking about ($98) is absolutely not the price it would trade for because of the inherent risk associated with the asset"

But the risk is not correlated with other assets in the universe. So, according to CAPM, the discount rate should be the risk-free rate. The logic being is that any risk within this one assets is diversified away at scale.

"Just imagine that you were given the option of buying this asset for $98 or something like a US bond for $98, both of which will yield $100 at maturity in expectation. Which one would you choose?"

I'd pay $97.99 at these odds. I wouldn't put all my money in it. But I'd look for as many risky-but-uncorrelated assets as I could with these. As long as I have enough of them, I have a very very high chance of being better off than if I had bought the 'safer' securities with known payoffs.

the true volatility of this security isn't zero, its the standard deviation between the two outcomes, zero and 1200, or about 848. This is exactly why high volatility is associated with higher risk - you can think of volatility as a spread between high and low values that this security can take on randomly. Just plug in those two outcomes, 0 and 1200 into excel stdev calculation. that's the volatility.

I do not have great math skills, but wouldn't the security have an expected value of $33.33 because of 1,200 * 1/6 * 1/6?

Sorry, you are correct. I updated my comment and replaced the $1200 with $3600. The math works now.

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