CryptoPortfolio - Simple trick to increase returns by 8% per year - Part 3: How much can I make?steemCreated with Sketch.

in cryptocurrency •  2 years ago  (edited)

Summary

Cryptocurrencies are extremely volatile. This creates an interesting opportunity to extract extra returns from rebalancing a portfolio and extract a “diversification dividend”.

Part 1


In Part 1: Geometric and Arithmetic Returns, I explored the difference b/w geometric and arithmetic returns and linked risk and returns for an investment. Normally these effects are tiny (for standard, less volatile investments) and hence are exploited only by the very large pension funds and sovereign wealth funds. But given the high volatility of cryptocurrencies I believe they may be interesting for all crypto-investors.

Part 2


In Part 2: Portfolio Risk and Diversification, I formalise the effect of diversification and what it means for a portfolio in terms of reduction of volatility and improvement to returns

How much can I make

From Part 2, the reduction in portfolio variance is:

(n-1)/n * ss^2 * (1 - corr)

Were:

  • ss^2 is the average variance of the cryptocurrencies (which I assume equal for simplicity)
  • S^2 is the variance of the portfolio of cryptocurrencies
  • n is the number of assets in the portfolio
  • corr is the average correlation among the assets (which I assume equal or simplicity)

From Part 1 the returns are

Rg = Ra - 1/2 * s^2

Now s^2 is reduced and hence a value of 1/2 * (n-1)/n * ss^2 * (1 - corr) is created.

Normally this is relatively small: the annualised volatility of equity is between 12% - 30%, thus their variance (ss^2) is between 1.4% and 9%, correlation among standard asset classes is relatively high, etc. This basically means that the effect, even if still present, is not interesting for most investors and is exploited only by large pension and sovereign wealth funds.

For crypto instead the volatility is very high 40% - 80% for bitcoin and more than 100% for smaller cryptocurrencies. Furthermore while they are very correlated in normal markets, they tend to have very idiosyncratic shocks (that affect one or a small group of coins rather than all) so when the volatility is at its peak they are also relatively low correlated.

So for a portfolio of 10 cryptos with say 80% volatility (and hence 64% variance) and a correlation of say 70%, the formula above becomes:

0.5 * 0.9 * 0.64 * 0.3 = 8.6%

Which is an interesting return considering it comes "for free": diversification is one of the only free lunches out there.

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hmmmm, interesting....

Thank you @constantius !

Interesting! Definitely check out this website for more data on volatility: https://www.sifrdata.com/cryptocurrency-volatility-index/

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Interesting🙄
Your diversification free lunch seems inversely proportional to the "correlation".
Thus to diversify we need crypto in different business spheres? Gaming,money,gambling,communcation etc?

To spread out in the highly correlated top 5 for example seems mathematically unsound?

Yes?
Thanks again.