# Volatility of Bitcoin, Litecoin, Ether and Dash in comparison with some US large cap stocks

Volatility of an asset expresses the ‘wiggliness’ of its price curve, the width of the band in which the price moves up and down seemingly at random. Volatility can be quantified and is considered a key characteristic of an asset because to a large extent it measures uncertainty in future price and therefore relates directly to investment risk.

In its simplest mathematical form the volatility of an asset is the standard deviation of its daily results (as a percentage) over a recent time period of some arbitrary length, e.g. one year which is 252 trading days for stocks and 365 for cryptocoins. When the price of a (hypothetical) asset grows or shrinks exponentially, i.e. at a fixed percentage per day, volatility of that asset would be zero. Any deviation from mono-exponential growth or shrinkage causes volatility to go up.

The large-cap US stock market contains low-volatile assets, like MA (Mastercard) and high-volatile assets, like TSLA (Tesla). SPY, an ETF consisting of the 500 largest US companies weighted by market-cap, has a lower volatility than each of its member stocks separately.

For a series of assets considered as investment instruments, volatility is useful to compute for each asset upfront, because its relation to risk. Volatility is typically used in risk-adjusted-returns like the Sharpe ratio, where the absolute return (in %) of an asset is normalized by its volatility (in %). In risk-optimized portfolios, asset size is often chosen proportional to the inverse of the volatility of the constituents.

Cryptocurrencies are said to be highly volatile, which only has meaning when compared to other asset classes like stocks or ETFs. This post presents normalized price and volatility since 1 Jan 2016 of four cryptocurrencies out of the current top-ten ranked on market capitalization: BTC (Bitcoin), LTC (Litecoin), ETH (Ethereum) and DASH (Dash). For comparison, MA (Mastercard), TSLA (Tesla) and SPY (S&P 500 ETF) were added. Input data for TSLA, MA and SPY are EOD (End of Day) prices (generally 4:30 PM EST) as provided by Tiingo.com, input data for the cryptocurrencies are the prices at 12:00 PM UTC) as provided by coinmarketcap.com.

First, the price histories of these assets, indexed at 1 Jan 2016:

The huge gains in the cryptocurrencies relative to the stocks and ETF immediately stand out. The difference is even larger than visually perceived because of the logarithmic scaling.

Next, the dynamic volatilities of these assets:

Dash, Ethereum and Litecoin have almost identical current volatility of 7%/day, although having arrived there via different trajectories. Not so long ago Dash had the highest volatility, followed by Ethereum followed by Litecoin. Bitcoin’s current volatility of 4%/day is nearly half of the volatility of its newer competitors. Tesla’s is one of the higher-volatile large-cap stocks at 2.5%/day. Mastercard is half that of Tesla at 1.2%/day, while the S&P500 volatility is lowest of all at 0.72%/day.

This table shows daily, monthly and annual volatilities, based upon statistical independence assumptions (and thus obtained by multiplication of the daily volatility with the square root of the number of days). For the stocks and the ETF, the number of trading days in a month (20) and year (252) are used, for cryptocurrencies the total number of days in a month (30) and a year (365) because they are traded 24/7. One should not be surprised that where the price of Tesla easily fluctuates more than 11% up and down in a month, Bitcoin does this more than 20% and the other cryptos nearly 40%.

Price data is readily available from all major platforms, but volatility is not. For my personal investment decisions, volatility data adds quite a lot. For example: when building a mixed, risk optimised portfolio of these stocks and cryptocurrencies, the Weight column in the table gives the risk-optimised asset size (to a first degree, since only within-asset variances are used instead of all between-asset co-variances). The weight is proportional to the reciprocal volatility, and the sum of all weights is 100%. The portfolio portion in crypto vs. the portion in stocks/ETF is about 18% vs. 82%. This ratio could serve as a take home message from this post: for a risk balanced investment portfolio, size cryptocurrencies some four times lower than stocks. Because these asset classes are practically uncorrelated, the risk in both is then roughly equal.

*Practice due diligence before investing in any investment vehicle mentioned in this article.*