What Is The Sharpe Ratio?

The Sharpe ratio is a measure used to evaluate the risk-adjusted return of an investment or portfolio. It's named after William F. Sharpe, the Nobel laureate economist who developed it. The ratio helps investors understand the return of an investment relative to its risk.

Sharpe Formula

The formula used for calculating the Sharpe ratio is:

Sharpe Ratio = (𝑅𝑝−𝑅𝑓)/𝜎𝑝​​

Where:

• 𝑅𝑝​ is the expected return of the investment or portfolio
• 𝑅𝑓​ is the risk-free rate of return (such as the yield on government bonds)
• 𝜎𝑝​ is the standard deviation of the investment or portfolio's excess return

The expected return is the long-term, average rate of return. The standard deviation of the investment is the level of volatility

A higher Sharpe ratio indicates a better risk-adjusted return. In other words, it suggests that the investment has provided higher returns relative to the amount of risk taken. Investors often use the Sharpe ratio to compare the risk-adjusted returns of different investments or portfolios and to make more informed decisions about allocating their capital.

Examples

1. Investment A: Let's say you have an investment that has an expected return of 8% and a standard deviation of 10%. If the risk-free rate is 2%, then the Sharpe ratio would be (8%-2%)/10% = 0.6. This indicates that for every unit of risk taken, the investment provides a return of 0.6 units.
2. Investment B: Now, consider another investment with an expected return of 12% and a standard deviation of 15%. Using the same risk-free rate of 2%, the Sharpe ratio would be (12%-2%)/15% = 0.67. This investment has a higher Sharpe ratio compared to Investment A, indicating a better risk-adjusted return.

The Effect Of Bitcoin On The Sharpe Ratio

Bitcoin is a high-risk investment. It has huge volatility. In the course of a market cycle, it might increase 20-100x in value; it also regularly experiences 70-85% drawdowns.

And yet, adding to a portfolio in the right amounts actually improves the Sharpe Ratio.

The point is that bitcoin's returns tend to outweigh the risks of its volatility, so that over even a relatively short time frame, a portfolio with a small allocation of bitcoin outperforms.

Of course, past performance is no guarantee of future results, and just because a 5% allocation would have proven profitable over the last 10 years does not necessarily mean it will for the next decade.