Sharpe Ratio

If you want a single number that answers “how much return did I get for the risk I took?”, Sharpe is the classic starting point. It uses price volatility as a measure of risk, which is easy to measure and useful in many situations (though not all).

In plain English, Sharpe is excess return per unit of volatility. “Excess” means “above the risk‑free rate”, and “volatility” is the standard deviation of returns.

The formula

$$\text{Sharpe} = \frac{E[r] - r_f}{\sigma}$$

Where $r$ is the return series (we use daily simple returns from close-to-close), $E[r]$ is the average daily simple return annualized (not CAGR), $r_f$ is the risk‑free rate, and $\sigma$ is return volatility.

How we calculate Sharpe at Gale Finance

While it seemingly appears like a simple calculation, there are a lot of implementation choices that matter in practice. Here’s how we do it:

1. Returns: we use daily simple returns:

$$r_t = \frac{P_t}{P_{t-1}} - 1$$

We don’t “fill” missing dates. For an ETF, weekends and exchange holidays just aren’t in the dataset. Monday’s return is the change from Friday’s close to Monday’s close — which matches what you actually held through.

2. No forward-filling (no invented prices): when a metric needs shared dates (like correlation), we take the intersection of timestamps and drop everything else. Forward-filling would quietly invent “flat” returns on days that didn’t trade.

3. Annualization uses the asset’s calendar: Sharpe is a unitless number, but you only get comparable Sharpe ratios if you put both the mean and volatility on the same time scale.

• For crypto and stablecoins, we annualize using 365 because these markets trade 24×7 and weekends are often volatile.
• For equities/ETFs/metals, we annualize using ~252 trading days (or infer the effective frequency when needed).

This is not cosmetic. If you force a 24×7 asset onto a 252‑day calendar, you’re smoothing away weekend moves and changing the metric. This is especially important for an asset like Bitcoin and other crypto assets because historically these assets often show increased volatility on weekends.

4. Expected return input: we annualize expected return using the arithmetic mean of daily returns:

• E[r_annual] = mean(r_t) × N
• σ_annual = std(r_t) × sqrt(N)

This is a standard Sharpe convention. It’s also why we’re careful with language: this “expected annual return” is not CAGR.

5. Risk‑free rate: we use the average 3‑month Treasury rate over the analysis window (FRED series DGS3MO). If we can’t fetch it, we fall back to a configured default risk‑free rate.

How to read it (and where it breaks)

Sharpe is most useful when returns are “well-behaved” - roughly stable volatility, not too much skew, and tails that aren’t doing anything wild.

Two big caveats:

• Fat tails: If an asset has occasional huge moves (common in crypto), the standard deviation doesn’t fully describe risk. Sharpe can look fine right up until it doesn’t.
• Volatility clustering: Volatility isn’t constant; it comes in regimes. A single Sharpe number is an average over a period, not a promise about next month.

If you care more about downside risk than “wiggles in both directions,” take a look at the Sortino ratio next.