Key Performance Metrics

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Sharpe Ratio

Definition

The Sharpe Ratio measures the risk-adjusted return of an asset by comparing its excess return (return above the risk-free rate) to its overall volatility.
In the context of cryptocurrencies, the risk-free rate $R_f$ is often assumed to be 0%, given the absence of a universally accepted benchmark in decentralized markets.

This metric is used to:

• Evaluate whether returns justify the risk taken.
• Compare performance between assets or trading strategies.
• Support portfolio optimization and allocation decisions.

Formula

$$\text{Sharpe Ratio}=\frac{R_p-R_f}{{\sigma }_p}$$

Where:

• $R_p$ : Average return of Solana (or portfolio return).
• $R_f$ : Risk-free rate (commonly approximated as 0 in crypto markets).
• ${\sigma }_p$ : Standard deviation (volatility) of returns.

Example (Solana)

Suppose:

• Average daily return $R_p=0.015$ (1.5%)
• Risk-free rate $R_f=0$
• Standard deviation ${\sigma }_p=0.03$ (3.0%)

Then:

$$\text{Sharpe Ratio}=\frac{0.015-0}{0.03}=0.5$$

Interpretation

• A Sharpe Ratio of 0.5 indicates that Solana earns only 0.5 units of excess return per unit of total volatility — suggesting limited efficiency in risk-adjusted performance.
• General thresholds:
  • Below 1.0 → Low risk-adjusted performance
  • Between 1.0 and 2.0 → Acceptable to good performance
  • Above 2.0 → Strong risk-adjusted returns

In crypto markets, lower Sharpe Ratios are common due to high volatility.

Applications

• Portfolio analysis: Assess whether an asset improves overall portfolio risk-adjusted returns.
• Strategy evaluation: Compare automated trading bots or investment approaches.
• Scaling: Convert to annual Sharpe using

$${\text{Sharpe Ratio}}_{\text{annual}}={\text{Sharpe Ratio}}_{\text{daily}}\cdot \sqrt{252}$$

assuming 252 trading days per year.

Probabilistic Sharpe Ratio (PSR)

Definition

The Probabilistic Sharpe Ratio (PSR) estimates the probability that a given Sharpe Ratio is statistically greater than a benchmark Sharpe Ratio, accounting for the number of observations and the variability in returns.
It is especially useful in the crypto space, where return distributions may be noisy and short-lived.

Formula

$$\text{PSR}=\Phi \left(\frac{(\hat{S}-S^{\ast })\sqrt{n-1}}{\sqrt{1-\gamma {\hat{S}}^2}}\right)$$

Where:

• $\hat{S}$ : Observed Sharpe Ratio (e.g., for Solana)
• $S^{\ast }$ : Benchmark Sharpe Ratio (e.g., 0 or 1)
• $n$ : Number of return observations
• $\gamma$ : Skewness of returns (use 0 if assuming normality)
• $\Phi$ : Standard normal cumulative distribution function (CDF)

Example (Solana)

Suppose:

• Observed Sharpe Ratio $\hat{S}=0.75$
• Benchmark Sharpe Ratio $S^{\ast }=0.5$
• Number of daily return observations $n=100$
• Assume $\gamma =0$ (returns are normally distributed)

Then:

$$\text{PSR}=\Phi \left(\frac{(0.75-0.5)\sqrt{99}}{\sqrt{1}}\right)=\Phi (2.4875)\approx 0.9936$$

This means there is a 99.36% probability that Solana’s Sharpe Ratio is greater than the benchmark of 0.5 — suggesting statistically significant outperformance.

Interpretation

• A high PSR (close to 1) indicates strong confidence that the coin’s Sharpe Ratio is better than the benchmark.
• A low PSR (below 0.5) implies performance is not statistically superior to the benchmark.
• PSR helps differentiate between apparent and statistically significant performance in volatile crypto markets.

Applications

• Performance validation: Assess whether a coin’s observed Sharpe Ratio is statistically significant.
• Backtesting: Evaluate whether a trading strategy’s Sharpe Ratio holds up under uncertainty.
• Portfolio optimization: Filter assets that truly outperform based on probability thresholds.

Sortino Ratio

Definition

The Sortino Ratio refines the Sharpe Ratio by focusing only on downside risk (negative returns) instead of total volatility.
This makes it particularly useful in crypto markets where large upward price swings could inflate the Sharpe Ratio without accurately reflecting the risk to the downside.

It answers the question:
"How much excess return is Solana generating for every unit of downside risk?"

Formula

$$\text{Sortino Ratio}=\frac{R_p-R_t}{{\sigma }_d}$$

Where:

• $R_p$ : Average return of Solana (portfolio return)
• $R_t$ : Target return (e.g., 0% for risk-free or minimum acceptable return)
• ${\sigma }_d$ : Downside deviation

Downside Deviation

The downside deviation isolates volatility from returns below the target $R_t$ :

$${\sigma }_d=\sqrt{\frac{1}{n}\sum _{i=1}^n\min (R_i-R_t,0{)}^2}$$

Where:

• $R_i$ : Return for period $i$
• $R_t$ : Target return

Example (Solana)

Assume:

• Average return $R_p=0.015$ (1.5%)
• Target return $R_t=0.005$ (0.5%)
• Downside deviation ${\sigma }_d=0.01$ (1.0%)

Then:

$$\text{Sortino Ratio}=\frac{0.015-0.005}{0.01}=\frac{0.010}{0.01}=1.0$$

Interpretation

• A Sortino Ratio of 1.0 indicates that Solana generated one unit of excess return for every unit of downside risk.
• Ratios above 1.0 typically suggest favorable risk-adjusted performance.
• A low or negative Sortino Ratio indicates that downside risk outweighs the returns.

Applications

• Risk-adjusted evaluation: Preferred over the Sharpe Ratio in highly volatile markets.
• Strategy comparison: Useful for evaluating trading bots, funds, or portfolios focused on asymmetric returns.
• Portfolio optimization: Helps adjust position sizing to maximize returns relative to downside risk.

Compound Annual Growth Rate (CAGR)

Definition

The Compound Annual Growth Rate (CAGR) represents the smoothed annual growth rate of an asset over a specified time period.
Unlike simple average returns, CAGR accounts for compounding, providing a more accurate measure of growth for assets with fluctuating returns such as cryptocurrencies.

It is useful for:

• Measuring long-term portfolio or token performance.
• Comparing returns across multiple assets or benchmarks.
• Estimating future growth under similar compounding conditions.

Formula

$$\text{CAGR}={\left(\frac{V_f}{V_i}\right)}^{\frac{1}{n}}-1$$

Where:

• $V_f$ : Final value of the asset.
• $V_i$ : Initial value of the asset.
• $n$ : Number of years in the period.

Example (Solana)

Assume:

• Initial price $V_i=\$20$
• Final price $V_f=\$100$
• Duration $n=2$ years

Then:

$$\text{CAGR}={\left(\frac{100}{20}\right)}^{\frac{1}{2}}-1=\sqrt{5}-1\approx 0.236(23.6\%)$$

Interpretation

• Solana’s price has grown by approximately 23.6% per year, compounded annually, over the 2-year period.
• CAGR smooths out volatility to provide a clearer view of long-term growth — especially useful in crypto markets with high daily and monthly fluctuations.
• It does not reflect year-to-year variability but rather the consistent rate that would have produced the same total growth.

Applications

• Performance benchmarking: Compare Solana’s growth to Bitcoin, Ethereum, or indices.
• Investment planning: Estimate potential portfolio value under projected growth.
• Risk-return analysis: Combine CAGR with annualized volatility to evaluate risk-adjusted growth.

Smart Sortino Ratio

Definition

The Smart Sortino Ratio refines the traditional Sortino Ratio by incorporating statistical adjustments to account for limited data and non-normal return distributions.
This is particularly useful for evaluating cryptocurrency strategies, such as trading Solana (SOL), which may exhibit high skewness and kurtosis.

Traditional Sortino Ratio Recap

$$\text{Sortino Ratio}=\frac{R_p-R_t}{{\sigma }_d}$$

Where:

• $R_p$ : Average return of Solana
• $R_t$ : Target (or minimum acceptable) return
• ${\sigma }_d$ : Downside deviation

Smart Sortino Correction

The Smart Sortino introduces a penalty for small sample sizes:

$$\text{Smart Sortino}=\frac{R_p-R_t}{{\sigma }_d}\cdot \sqrt{\frac{n}{n-1}}$$

Where:

• $n$ : Number of return observations

This correction factor increases the denominator slightly when $n$ is small, preventing overestimation of performance.

Example (Solana)

Assume:

• $R_p=0.015$ , $R_t=0.005$
• ${\sigma }_d=0.01$
• $n=30$ daily observations

Then:

$$\text{Traditional Sortino}=\frac{0.015-0.005}{0.01}=1.0$$ $$\text{Smart Sortino}=1.0\cdot \sqrt{\frac{30}{29}}\approx 1.0\cdot 1.017=1.017$$

Thus, the Smart Sortino Ratio slightly increases due to the statistical adjustment — providing a more accurate measure of performance under downside risk.

Interpretation

• The adjustment reduces bias when using small or volatile samples (common in crypto).
• The Smart Sortino is typically slightly higher than the traditional one when sample sizes are small.
• For large $n$ , the Smart Sortino converges to the standard Sortino Ratio.

Applications

• Strategy testing: More reliable in backtests with few data points.
• Risk evaluation: Better captures realistic downside risk when return distributions are skewed.
• Portfolio analytics: Preferred for short-term or high-frequency crypto strategies.

Sortino vs. Sharpe Approximation

Under the assumption of normally distributed returns, the Sortino and Sharpe ratios are approximately related as:

$$\text{Sharpe Ratio}\approx \frac{\text{Sortino Ratio}}{\sqrt{2}}$$

This is based on the idea that downside deviation under normality is roughly $\sigma /\sqrt{2}$ .
However, this approximation does not hold reliably for cryptocurrencies such as Solana (SOL), whose returns often display heavy tails and skewness.
In crypto analytics, both ratios should always be computed explicitly rather than relying on this simplification.

Is Smart Sortino Divided by $\sqrt{2}$ a Proxy for Smart Sharpe?

Because the Smart Sortino uses a target return ($R_t$ ) rather than a risk-free rate ($R_f$ ), the relationship:

$$\frac{\text{Smart Sortino}}{\sqrt{2}}\approx \text{Smart Sharpe}$$

is not generally valid, especially in the context of asymmetric and fat-tailed return distributions found in assets like Solana (SOL).

Interpretation

• The relationship between Sortino and Sharpe only holds under normal distribution assumptions.
• In volatile crypto markets, this approximation breaks due to skewness and kurtosis.
• The Smart Sortino and Smart Sharpe should be calculated separately for accurate performance assessment.

Applications

• Performance modeling: Avoid relying on Gaussian-based approximations for crypto assets.
• Metric calibration: Use Smart Sortino and Smart Sharpe together to evaluate risk asymmetry.
• Comparative analysis: Compare results to test normality assumptions in token return data.

Omega Ratio

Definition

The Omega Ratio measures the probability-weighted ratio of gains versus losses relative to a specified threshold return.
It is particularly useful in cryptocurrency performance evaluation, where returns are often skewed or non-normal.

$$\text{Omega}(\tau )=\frac{{\int }_{\tau }^{\infty }[1-F(r)]dr}{{\int }_{-\infty }^{\tau }F(r)dr}$$

Where:

• $\tau$ is the threshold return (e.g., 0%)
• $F(r)$ is the cumulative distribution function of returns

Discrete Approximation

Given a historical return series $\{r_1,r_2,...,r_n\}$ , the Omega Ratio can be estimated as:

$$\text{Omega}(\tau )=\frac{{\sum }_{i=1}^n\max (r_i-\tau ,0)}{{\sum }_{i=1}^n\max (\tau -r_i,0)}$$

Example (Solana)

Assume Solana has the following 5-day daily return series:

$$\{0.02,-0.01,0.015,-0.005,0.03\}$$

Let the threshold $\tau =0$ . Then:

• Gains above threshold: $\{0.02,0.015,0.03\}\to \text{Sum}=0.065$
• Losses below threshold: $\{0.01,0.005\}\to \text{Sum}=0.015$

$$\text{Omega}(0)=\frac{0.065}{0.015}\approx 4.33$$

This indicates that Solana's returns have over four times more gain (above 0%) than loss (below 0%) — a strong risk-adjusted performance.

Interpretation

• Omega > 1: Gains exceed losses relative to threshold
• Omega < 1: Losses dominate
• Useful for skewed or non-normal return distributions, common in crypto

Applications

• Risk-adjusted performance analysis for assets with asymmetric returns
• Strategy evaluation: Identify portfolios or trading approaches with favorable upside/downside ratios
• Portfolio construction: Combine with other metrics like Sharpe or Sortino to assess overall performance

Maximum Drawdown (MDD)

Definition

The Maximum Drawdown (MDD) measures the largest percentage drop in the value of an asset from a historical peak to a subsequent trough.
It captures the worst-case loss an investor would have experienced by buying at the peak and selling at the bottom.

$$\text{MDD}=\underset{t\in [1,T]}{\max }\left(\frac{P_{\text{peak},t}-P_t}{P_{\text{peak},t}}\right)$$

Where:

• $P_{\text{peak},t}$: The highest price observed up to time ( t )
• $P_t$ : Price at time $t$

Example (Solana)

Suppose Solana has the following daily prices:

$$\{100,120,130,90,70,110,140,100\}$$

• Peak = 130
• Trough = 70
• Drawdown = $\frac{130-70}{130}=0.4615\Rightarrow \text{MDD}=46.15\%$

Interpretation

• A Maximum Drawdown of 46.15% implies that an investor who bought at Solana's peak and sold at the worst trough would have lost nearly half their investment.
• Provides a realistic view of downside risk, especially in volatile crypto markets.

Applications

• Risk management: Quantify potential losses in historical periods
• Portfolio monitoring: Assess vulnerability to large drawdowns
• Strategy evaluation: Compare resilience of different crypto assets or trading approaches

Maximum Drawdown with Dates

In addition to the magnitude of the maximum drawdown, it is often useful to report the time period during which it occurred.

Let:

• $t_{\text{peak}}$ : date of the highest price before the drawdown
• $t_{\text{trough}}$ : date of the lowest price after that peak
• $P_{\text{peak}}$ : peak price
• $P_{\text{trough}}$ : trough price

Then:

$$\text{MDD}=\frac{P_{\text{peak}}-P_{\text{trough}}}{P_{\text{peak}}}$$

The MDD period is: $[t_{\text{peak}},t_{\text{trough}}]$

Example (Solana)

Assume Solana hit a peak price of $130 on 2022-09-08, and then dropped to a trough of $30.20 on 2022-11-03. The asset only recovered its original peak on 2024-01-18.

• Max Drawdown Period Start: 2022-09-08
• Max Drawdown Date (Trough): 2022-11-03
• Max Drawdown Period End (Recovery): 2024-01-18
• Max Drawdown Duration: 863 days

The Maximum Drawdown is calculated as:

$$\text{MDD}=\frac{130-30.20}{130}=\frac{99.8}{130}\approx 0.7674=76.74\%$$

Drawdown period: September 8, 2022 to January 18, 2024 (863 days)

Example Table

Metric	Asset A (BTC)	Asset B (SOL)
Max Drawdown	-33.72%	-76.74%
Max DD Date	2020-03-23	2022-11-03
Max DD Period Start	2020-02-20	2021-09-08
Max DD Period End	2020-08-07	2024-01-18
Longest DD Duration (Days)	708	863

Annualized Volatility

Definition

The annualized volatility measures how much a cryptocurrency’s returns fluctuate over the course of a year.
It scales the standard deviation of daily returns to a yearly horizon, assuming continuous daily trading (365 days for crypto markets).

This metric is crucial for:

• Quantifying the risk profile of an asset
• Comparing volatility across tokens or trading strategies
• Feeding into risk-adjusted performance ratios such as the Sharpe or Sortino

$${\sigma }_{\text{annual}}={\sigma }_{\text{daily}}\cdot \sqrt{N}$$

Where:

• ${\sigma }_{\text{daily}}$ : standard deviation of daily returns
• $N=365$ : number of trading days in a year for crypto assets

Example (Solana)

Assume:

• Daily volatility ${\sigma }_{\text{daily}}=4.5\%$(0.045)
• $N=365$

Then:

$${\sigma }_{\text{annual}}=0.045\cdot \sqrt{365}\approx 0.045\cdot 19.105\approx 0.8597(85.97\%)$$

Interpretation

• Solana’s annualized volatility is approximately 85.97%, indicating significant price swings over the year
• Higher values suggest greater uncertainty and risk, meaning higher potential returns but also higher potential losses
• Often paired with annualized returns to evaluate the asset’s risk-return tradeoff

Applications

• Portfolio management: Assess diversification and overall portfolio risk
• Risk-adjusted ratios: Key input for annual Sharpe and Sortino calculations
• Market comparisons: Compare volatility across tokens, indices, or traditional assets like stocks or bonds

Coefficient of Determination (R²)

The coefficient of determination, denoted $R^2$ , is a statistical measure that explains how much of the variance in the returns of one asset (e.g., Solana) can be explained by the returns of another asset (e.g., Bitcoin) through a linear regression model.

Definition

Given $n$observations of daily returns $R_t^{\text{SOL}}$ and $R_t^{\text{BTC}}$ , the regression model is:

$$R_t^{\text{SOL}}=\alpha +\beta R_t^{\text{BTC}}+{\epsilon }_t$$

Where:

• $\alpha$ : intercept
• $\beta$ : slope (sensitivity of Solana to Bitcoin)
• ${\epsilon }_t$ : residual (unexplained return)

The coefficient of determination is calculated as:

$$R^2=1-\frac{S{S}_{\text{res}}}{S{S}_{\text{tot}}}$$

Where:

$$S{S}_{\text{res}}=\sum _{t=1}^n{\left(R_t^{\text{SOL}}-(\alpha +\beta R_t^{\text{BTC}})\right)}^2$$ $$S{S}_{\text{tot}}=\sum _{t=1}^n{\left(R_t^{\text{SOL}}-{\bar{R}}^{\text{SOL}}\right)}^2$$

Here, $S{S}_{\text{res}}$ is the sum of squared residuals, and $S{S}_{\text{tot}}$ is the total variance of Solana's returns.

Step-by-Step Calculation

1. Compute the average return of Solana:

$${\bar{R}}^{\text{SOL}}=\frac{1}{n}\sum _{t=1}^n{R}_t^{\text{SOL}}$$

2. Estimate the regression coefficients $\alpha$ and $\beta$ using least squares:

$$\beta =\frac{{\sum }_{t=1}^n(R_t^{\text{BTC}}-{\bar{R}}^{\text{BTC}})(R_t^{\text{SOL}}-{\bar{R}}^{\text{SOL}})}{{\sum }_{t=1}^n(R_t^{\text{BTC}}-{\bar{R}}^{\text{BTC}}{)}^2}$$ $$\alpha ={\bar{R}}^{\text{SOL}}-\beta {\bar{R}}^{\text{BTC}}$$

3. Calculate predicted returns:

$${\hat{R}}_t^{\text{SOL}}=\alpha +\beta R_t^{\text{BTC}}$$

4. Compute the residuals and $S{S}_{\text{res}}$ :

$${\epsilon }_t=R_t^{\text{SOL}}-{\hat{R}}_t^{\text{SOL}}\text{and}S{S}_{\text{res}}=\sum _{t=1}^n{\epsilon }_t^2$$

5. Compute $S{S}_{\text{tot}}$ and then:

$$R^2=1-\frac{S{S}_{\text{res}}}{S{S}_{\text{tot}}}$$

Information Ratio

The Information Ratio (IR) evaluates the excess return of an asset relative to a benchmark, adjusted for the variability of that excess return.
Unlike the Sharpe Ratio, which uses a risk-free rate, the Information Ratio compares performance against a real, investable benchmark — such as Bitcoin.

Formula

$$\text{IR}=\frac{R_p-R_b}{{\sigma }_{p-b}}$$

Where:

• $R_p$ : Average return of Solana
• $R_b$ : Average return of the benchmark (e.g., Bitcoin)
• ${\sigma }_{p-b}$ : Standard deviation of the return difference (tracking error)

Example (Solana vs Bitcoin)

Assume:

• $R_p=0.020$ (average return of Solana)
• $R_b=0.015$ (average return of Bitcoin)
• ${\sigma }_{p-b}=0.012$ (tracking error)

Then:

$$\text{IR}=\frac{0.020-0.015}{0.012}=\frac{0.005}{0.012}\approx 0.417$$

Interpretation

• An IR of 0.417 indicates that Solana outperforms Bitcoin by 0.5% per period relative to the variability of that outperformance.
• While this shows positive value-added versus BTC, many asset managers aim for an IR $>0.5$ as a standard of strong performance.

Calmar Ratio

The Calmar Ratio is a risk-adjusted return metric that evaluates the relationship between an asset’s annualized return and its maximum drawdown.
It is particularly relevant for cryptocurrencies, where large drawdowns are common.

Formula

$$\text{Calmar Ratio}=\frac{R_{\text{annual}}}{\text{Max Drawdown}}$$

Where:

• $R_{\text{annual}}$ : Annualized return of the asset
• Max Drawdown: Largest observed drop from peak to trough in price, expressed as a positive decimal (e.g., 0.70 for 70% drop)

Example (Solana)

Assume Solana has:

• $R_{\text{annual}}=0.60$ (60% annualized return)
• Maximum drawdown = 76.74% ($\text{Max DD}=0.7674$ )

Then:

$$\text{Calmar Ratio}=\frac{0.60}{0.7674}\approx 0.782$$

Interpretation

• A Calmar Ratio of 0.782 means Solana earned 60% return per year for every unit of 76.74% drawdown risk.
• General guidance:
  • Calmar $>1$ : Excellent risk-adjusted return
  • Calmar $=1$ : Moderate balance of return vs. risk
  • Calmar $<1$ : High drawdown relative to return (common in crypto)

While Solana exhibits strong growth potential, the high drawdown lowers its Calmar Ratio, highlighting the significant downside risk in volatile markets.

Skewness

Skewness is a statistical measure of the asymmetry of the distribution of returns.
In the context of cryptocurrencies like Solana (SOL), skewness helps identify whether returns are more prone to extreme losses or extreme gains.

Formula

Given a series of returns $r_1,r_2,...,r_n$ :

$$\text{Skewness}=\frac{1}{n}\sum _{t=1}^n{\left(\frac{r_t-\bar{r}}{\sigma }\right)}^3$$

Where:

• $\bar{r}$ : Mean of the returns
• $\sigma$ : Standard deviation of the returns
• $n$ : Number of observations

Interpretation

• Skewness > 0: Long right tail → potential for large positive returns
• Skewness < 0: Long left tail → higher likelihood of extreme losses
• Skewness = 0: Symmetrical distribution (e.g., normal distribution)

Example (Solana)

Assume we observe daily returns for Solana over one year. After computing the mean and standard deviation of returns:

$$\text{Skewness}=-1.20$$

This negative skew indicates a left-skewed distribution — Solana is more likely to experience large negative returns than large positive ones.

Visual Implication

A negative skew implies that the "tail" of the return distribution is heavier on the left side, reflecting crash-prone behavior.
This is consistent with Solana's historical drawdowns and volatility spikes during market downturns.

Kurtosis

Kurtosis measures the "tailedness" of the return distribution.
It indicates how likely extreme return values (positive or negative) are, compared to a normal distribution.
For Solana (SOL), kurtosis helps quantify how often sharp spikes or crashes occur.

Formula

Given a return series $r_1,r_2,...,r_n$ :

$$\text{Kurtosis}=\frac{1}{n}\sum _{t=1}^n{\left(\frac{r_t-\bar{r}}{\sigma }\right)}^4$$

Where:

• $\bar{r}$ : Mean return
• $\sigma$ : Standard deviation of returns
• $n$ : Number of return observations

Interpretation

• Kurtosis = 3: Normal (Gaussian) distribution (mesokurtic)
• Kurtosis > 3: Fat tails (leptokurtic) — more frequent extreme returns
• Kurtosis < 3: Thin tails (platykurtic) — fewer extreme events

Example (Solana)

Assume daily returns over one year show:

$$\text{Kurtosis}=6.8$$

This exceeds 3, indicating a leptokurtic distribution. Solana's returns exhibit heavy tails, meaning large, unexpected moves (both gains and losses) occur more often than under a normal distribution.

Implication

High kurtosis is typical in cryptocurrency markets and implies that models assuming normality (e.g., Black-Scholes, CAPM) may underestimate tail risk.
For Solana, this indicates both high upside potential and exposure to black-swan style crashes.

Expected Daily Return

Definition

The Expected Daily Return represents the average return of an asset per day over a given period.
It is a foundational metric for portfolio performance analysis and risk-adjusted calculations such as the Sharpe Ratio and Sortino Ratio.
By averaging daily returns, it smooths out volatility and provides a baseline estimate of typical daily performance.

Formula

$${\bar{r}}_{\text{daily}}=\frac{1}{n}\sum _{t=1}^n{r}_t$$

Where:

• ${\bar{r}}_{\text{daily}}$ : Expected daily return
• $n$ : Number of trading days in the period
• $r_t$ : Daily return at day $t$ , often calculated as:

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

Step-by-Step (Solana)

Given 10 days of daily returns:

$$\{0.020,-0.015,0.010,0.005,-0.030,0.025,-0.010,0.015,-0.020,0.030\}$$

1. Sum the daily returns:

$$0.020-0.015+0.010+0.005-0.030+0.025-0.010+0.015-0.020+0.030=0.030$$

2. Divide by the number of days ($n=10$ ):

$${\bar{r}}_{\text{daily}}=\frac{0.030}{10}=0.003$$

3. Convert to percentage:

$$0.003\times 100=0.30\%$$

Interpretation

• On average, Solana returned approximately 0.30% per day over this 10-day sample.
• Positive expected returns indicate upward price momentum, while negative values indicate a net downward trend.
• This metric is frequently annualized for broader comparisons:

$${\bar{r}}_{\text{annual}}={\bar{r}}_{\text{daily}}\times 252$$

where 252 represents the approximate number of trading days in a year.

Applications

• Baseline input for Sharpe, Sortino, and Treynor ratios.
• Helps estimate potential compounding effects over longer periods.
• Useful for comparing assets or portfolio components in a normalized way.

Daily Sharpe Ratio

Definition

The Daily Sharpe Ratio measures the risk-adjusted return of an asset on a daily basis.
It compares the excess return (return above the risk-free rate) to the asset's daily volatility.
In the context of cryptocurrencies, the daily risk-free rate $r_{f,d}$ is typically assumed to be $\approx 0$ , given the lack of a meaningful low-risk benchmark in decentralized markets.

This metric helps traders and portfolio managers:

• Evaluate if returns adequately compensate for the level of volatility.
• Compare different assets or trading strategies on a normalized basis.
• Monitor consistency of risk-adjusted performance over time.

Formula

Assuming a negligible daily risk-free rate:

$$S_{\text{daily}}=\frac{{\bar{r}}_{\text{daily}}-r_{f,d}}{{\sigma }_{\text{daily}}}$$

Where:

• ${\bar{r}}_{\text{daily}}$ : Expected daily return.
• $r_{f,d}$ : Daily risk-free rate (often $\approx 0$ ).
• ${\sigma }_{\text{daily}}$ : Standard deviation of daily returns (daily volatility).

Step-by-Step (Solana)

Given:

• Average daily return ${\bar{r}}_{\text{daily}}=0.003(0.30$
• Daily volatility ${\sigma }_{\text{daily}}=0.02058(2.06$
• Daily risk-free rate $r_{f,d}=0$

The calculation:

$$S_{\text{daily}}=\frac{0.003-0}{0.02058}\approx 0.146$$

Interpretation

• A Daily Sharpe Ratio of 0.146 indicates modest risk-adjusted returns: volatility is significantly higher than average daily gains.
• A higher Sharpe Ratio (e.g., $>1.0$ ) would suggest that returns sufficiently compensate for daily risk.
• In crypto markets, low daily Sharpe Ratios are common due to high volatility and frequent intraday fluctuations.

Applications

• Portfolio optimization: Identifying assets that maximize risk-adjusted returns.
• Strategy performance: Comparing multiple trading strategies over the same period.
• Scaling to annual Sharpe: Annual Sharpe is often approximated as:

$$S_{\text{annual}}=S_{\text{daily}}\cdot \sqrt{252}$$

assuming 252 trading days per year.

Expected Monthly Return

Definition

The Expected Monthly Return estimates the average return over a 30-day period, assuming the observed daily return persists.
By compounding daily returns instead of using a simple linear approximation, this measure captures the effect of compounding, which is particularly relevant in volatile markets like crypto.

This metric is often used to:

• Project short-term portfolio growth.
• Compare token performance on a monthly horizon.
• Provide inputs for more advanced performance models, such as Monte Carlo simulations.

Formula (Compounded from Daily)

Let $N_m=30$ calendar days:

$${\bar{r}}_{\text{monthly}}^{(\text{comp})}=(1+{\bar{r}}_{\text{daily}}{)}^{N_m}-1$$

Where:

• ${\bar{r}}_{\text{daily}}$ : Expected daily return.
• $N_m$ : Number of calendar days in the month (typically 30).

Step-by-Step (Solana)

Given:

• ${\bar{r}}_{\text{daily}}=0.003$ (0.30% daily)
• $N_m=30$ days

The compounded return:

$${\bar{r}}_{\text{monthly}}^{(\text{comp})}=(1+0.003{)}^{30}-1\approx 1.0938-1=0.0938(9.38\%)$$

Interpretation

• The asset is expected to return approximately 9.4% in a month if the sample mean daily return persists.
• This highlights the power of compounding: a seemingly modest 0.30% daily return translates into a sizable monthly growth.
• Negative daily returns would compound downward, reducing the monthly estimate.

Applications

• Portfolio projections: Short-term performance forecasts.
• Scenario testing: Assessing potential monthly growth or drawdowns.
• Benchmarking: Comparing performance across assets or time periods on a normalized monthly basis.

Monthly Sharpe Ratio

Formula (Standard annualization/scaling)

$$S_{\text{monthly}}\approx S_{\text{daily}}\sqrt{N_m}$$

Step-by-Step (Solana)

$$S_{\text{monthly}}\approx 0.146\times \sqrt{30}\approx 0.146\times 5.477\approx 0.800$$

Interpretation

Monthly Sharpe is higher by $\sqrt{30}$ under i.i.d. returns.
(If you compute from realized monthly returns, results will differ slightly.)

Expected Yearly Return

Formula (Compounded from Daily)

With $N_y=365$ (crypto trades daily):

$${\bar{r}}_{\text{yearly}}^{(\text{comp})}=(1+{\bar{r}}_{\text{daily}}{)}^{N_y}-1$$

Step-by-Step (Solana)

$${\bar{r}}_{\text{yearly}}^{(\text{comp})}=(1+0.003{)}^{365}-1\approx 1.982(198.2\%)$$

Interpretation

Compounding a $0.30\%$ daily mean implies very high yearly growth; in practice, crypto drift is unstable—treat as illustrative.

Kelly Criterion (Fixed Fraction)

Formula

With mean excess ${\mu }_d={\bar{r}}_{\text{daily}}-r_{f,d}$ and variance ${\sigma }_d^2$ :

$$f_{\text{Kelly}}^{\ast }=\frac{{\mu }_d}{{\sigma }_d^2}$$

Step-by-Step (Solana)

$${\sigma }_d^2\approx 0.02058^2\approx 0.0004233$$ $$f_{\text{Kelly}}^{\ast }=\frac{0.003}{0.0004233}\approx 7.09(\text{709\%})$$

Interpretation

Full-Kelly suggests extreme leverage—unsafe in crypto. Practitioners use half/quarter-Kelly or cap exposure due to fat tails.

Visual Implication

Position-size curve grows linearly with $f$ , but drawdown risk rises superlinearly—plotting equity curves at different $f$ shows higher ruin risk beyond $\approx$ half-Kelly.

Risk of Ruin (Heuristic)

Setup

Let $p$ be up-day frequency, $q=1-p$ , and define payoff ratio $b=\frac{\text{avg gain}}{|\text{avg loss}|}$ .

Step-by-Step (Solana)

From the sample:

$$\text{Up days }(p)=\frac{6}{10}=0.6,q=0.4$$ $$\text{Avg gain}=\frac{0.020+0.010+0.005+0.025+0.015+0.030}{6}=0.0175$$ $$\text{Avg loss}=\frac{0.015+0.030+0.010+0.020}{4}=0.01875$$ $$b=\frac{0.0175}{0.01875}\approx 0.933$$

For a rough fair-payoff case $b\approx 1$ and a capital buffer of $N=10$ average-loss units:

$$\mathrm{Pr}(\text{ruin})\approx {\left(\frac{q}{p}\right)}^N={\left(\frac{0.4}{0.6}\right)}^{10}\approx (0.667{)}^{10}\approx 0.017(1.7\%)$$

Interpretation

Ruin probability falls exponentially with buffer $N$ , but crypto fat tails make this optimistic; use scenario stress tests.

Visual Implication

Plotting an equity path ensemble highlights the left-tail frequency where accounts hit zero before recovery.

Daily Value-at-Risk (VaR)

Parametric (Normal) Formula

At tail level $\alpha$ (e.g., $5\%$ ), with mean ${\mu }_d$ and stdev ${\sigma }_d$ :

$${\text{VaR}}_{\alpha ,\text{daily}}=-({\mu }_d+z_{\alpha }{\sigma }_d),$$

where $z_{0.05}\approx -1.645$ .

Step-by-Step (Solana, $\alpha =5\%$ )

$${\text{VaR}}_{5\%}=-(0.003+(-1.645)\cdot 0.02058)=-(0.003-0.03385)=-(-0.03085)=0.0309(3.09\%\text{ loss})$$

Historical VaR (Empirical)

Sort daily returns and take the empirical $5\%$ quantile (with small $n$ , this is near the minimum):

$${\text{VaR}}_{5\%,\text{hist}}\approx 3.0\%(\text{worst day }-3.0\%)$$

Interpretation

Parametric and historical VaR are similar here; with larger samples, historical VaR better captures crypto fat tails.

Visual Implication

Histogram of returns with the left tail shaded beyond VaR shows expected frequency of exceedances ($\alpha$ ).

Expected Shortfall (cVaR / ES)

Parametric (Normal) Formula

Conditional loss given the loss exceeded VaR:

$${\text{ES}}_{\alpha ,\text{daily}}=-\left({\mu }_d-{\sigma }_d\frac{\varphi (z_{\alpha })}{\alpha }\right),$$

where $\varphi$ is the standard normal pdf.

Step-by-Step (Solana, $\alpha =5\%$ )

Using $z_{0.05}=-1.645$ and $\varphi (1.645)\approx 0.103$ :

$$\frac{\varphi (z_{\alpha })}{\alpha }\approx \frac{0.103}{0.05}=2.06$$ $${\text{ES}}_{5\%}=-(0.003-0.02058\times 2.06)=-(0.003-0.0424)=0.0394(3.94\%\text{ loss})$$

Historical ES (Empirical)

Average the worst $\alpha \%$ returns. With $n=10$ and $\alpha =5\%$ , this is effectively the single worst day:

$${\text{ES}}_{5\%,\text{hist}}\approx 3.0\%(\text{small-sample limitation})$$

Interpretation

ES exceeds VaR (as it should), reflecting the average severity of tail losses—preferred to VaR for crypto’s heavy tails.

Visual Implication

On the return histogram, ES is the mean of observations to the left of VaR, i.e., the centroid of the shaded tail region.

Max Consecutive Wins

Definition

Let $r_t$ be daily returns. A win occurs when $r_t>0$ .
The maximum consecutive wins is the length of the longest contiguous run of wins:

$$\text{MaxConsecWins}=\underset{k}{\max }{\ell }_k,{\ell }_k=\text{length of }\{r_i,r_{i+1},\dots ,r_{i+{\ell }_k-1}\}\text{ with }{r}_j>0.$$

Step-by-Step (Solana)

Mark wins (W) and losses (L):
$\{\text{W},\text{L},\text{W},\text{W},\text{L},\text{W},\text{L},\text{W},\text{L},\text{W}\}$ .
Runs of W: lengths $1,2,1,1,1$ . Hence:

$$\text{MaxConsecWins}=2.$$

Interpretation

The longest green streak in the sample is two days; short streaks are typical for volatile crypto.

Max Consecutive Losses

Definition

A loss occurs when $r_t<0$ . The maximum consecutive losses is the longest contiguous run of losses:

$$\text{MaxConsecLosses}=\underset{k}{\max }{\ell }_k,{\ell }_k=\text{length of }\{r_i,\dots ,r_{i+{\ell }_k-1}\}\text{ with }{r}_j<0.$$

Step-by-Step (Solana)

Loss markers: positions $2,5,7,9$ ; all isolated. Thus:

$$\text{MaxConsecLosses}=1.$$

Interpretation

Losses occur frequently but not in long clusters in this short sample; larger samples often show longer red streaks.

Gain/Pain Ratio

Definition

Let $G={\sum }_{t=1}^n\max (r_t,0)$ be total gains and $L={\sum }_{t=1}^n\max (-r_t,0)$ total absolute losses. The Gain/Pain ratio is:

$$\text{GP}=\frac{G}{L}.$$

Step-by-Step (Solana)

$$\begin{array}{rl}G& =0.020+0.010+0.005+0.025+0.015+0.030=0.105,\\ L& =0.015+0.030+0.010+0.020=0.075,\\ \text{GP}& =\frac{0.105}{0.075}=\mathrm{1.40.}\end{array}$$

Interpretation

Over the sample, aggregate gains are 40% larger than aggregate losses. Values $>1$ indicate a favorable gain-to-pain balance.

Gain/Pain (1M)

Definition

Compute the Gain/Pain ratio over rolling 1-month (30-day) windows and summarize (e.g., average or median), or compute it from monthly returns $R_m$ :

$${\text{GP}}_{1\text{M,roll}}(t)=\frac{{\sum }_{j=t-29}^t\max (r_j,0)}{{\sum }_{j=t-29}^t\max (-r_j,0)},{\text{GP}}_{1\text{M}}^{(\text{monthly})}=\frac{{\sum }_m\max (R_m,0)}{{\sum }_m\max (-R_m,0)}.$$

Step-by-Step (Solana)

With only a single 10-day “month” proxy here, the 1M window equals the sample:

$${\text{GP}}_{1\text{M}}\approx \frac{0.105}{0.075}=\mathrm{1.40.}$$

(With real data, compute over true 30-day windows or from aggregated monthly returns.)

Interpretation

${\text{GP}}_{1\text{M}}>1$ signals more (or larger) positive days than negative within typical monthly horizons. In crypto, reporting both $\text{GP}$ and ${\text{GP}}_{1\text{M}}$ helps distinguish short-term pain clusters from long-run reward.

Payoff Ratio

Definition

The Payoff Ratio compares the average size of winning trades (or days) to the average size of losing trades. It is defined as:

$$\text{Payoff Ratio}=\frac{\text{Average Gain}}{|\text{Average Loss}|}$$

Where:

• $\text{Average Gain}=\frac{1}{N_{+}}{\sum }_{t=1}^n{r}_t\cdot 1_{\{r_t>0\}}$
• $\text{Average Loss}=\frac{1}{N_{-}}{\sum }_{t=1}^n{r}_t\cdot 1_{\{r_t<0\}}$
• $N_{+}$ : number of positive-return days
• $N_{-}$ : number of negative-return days

Step-by-Step (Solana)

Daily return series:

$$\{0.020,-0.015,0.010,0.005,-0.030,0.025,-0.010,0.015,-0.020,0.030\}$$

Step 1: Identify gains and losses

$$\text{Gains}=\{0.020,0.010,0.005,0.025,0.015,0.030\},N_{+}=6$$ $$\text{Losses}=\{-0.015,-0.030,-0.010,-0.020\},N_{-}=4$$

Step 2: Compute averages

$$\text{Average Gain}=\frac{0.020+0.010+0.005+0.025+0.015+0.030}{6}=0.0175$$ $$\text{Average Loss}=\frac{-0.015-0.030-0.010-0.020}{4}=-0.01875$$

Step 3: Compute Payoff Ratio

$$\text{Payoff Ratio}=\frac{0.0175}{0.01875}\approx 0.933$$

Interpretation

A payoff ratio less than 1 means the average losing day is larger than the average winning day.
For Solana, even though there are more wins (60% win days), the average loss is slightly larger than the average gain, resulting in a payoff ratio under 1.

Profit Factor

Definition

The Profit Factor measures the ratio of total gains to total losses:

$$\text{Profit Factor}=\frac{{\sum }_{t=1}^n\max (r_t,0)}{\left|{\sum }_{t=1}^n\min (r_t,0)\right|}$$

Where:

• The numerator is the sum of all positive daily returns
• The denominator is the absolute value of the sum of all negative daily returns

Step-by-Step (Solana)

Daily return series:

$$\{0.020,-0.015,0.010,0.005,-0.030,0.025,-0.010,0.015,-0.020,0.030\}$$

Step 1: Compute total gains

$$\sum r_t^{+}=0.020+0.010+0.005+0.025+0.015+0.030=0.105$$

Step 2: Compute total losses

$$\sum r_t^{-}=-0.015-0.030-0.010-0.020=-0.075$$

Step 3: Compute Profit Factor

$$\text{Profit Factor}=\frac{0.105}{|-0.075|}=\frac{0.105}{0.075}=1.40$$

Interpretation

• A Profit Factor greater than 1 indicates the strategy or asset generates more gains than losses in aggregate.
• For Solana in this sample, the Profit Factor of 1.40 means that for every 1 unit of loss, returns generated 1.4 units of gain.
• Crypto strategies with PF > 2 are often considered strong; values below 1 indicate net losing behavior.

Common Sense Ratio (CSR)

Definition

The Common Sense Ratio compares downside volatility to upside volatility:

$$\text{CSR}=\frac{{\sigma }_{\text{down}}}{{\sigma }_{\text{up}}},$$

where

$${\sigma }_{\text{down}}=\sqrt{\frac{1}{N_{-}}\sum _{t:r_t<0}(r_t-{\bar{r}}_{-}{)}^2},{\sigma }_{\text{up}}=\sqrt{\frac{1}{N_{+}}\sum _{t:r_t>0}(r_t-{\bar{r}}_{+}{)}^2}.$$

Interpretation

• CSR ≈ 1 → symmetric risk between gains and losses
• CSR > 1 → downside risk dominates
• CSR < 1 → upside moves are more volatile than downside

CPC Index

Definition

The CPC Index (Consistency of Profitable Contributions) measures the stability of profits relative to losses:

$$\text{CPC}=\frac{\text{Profit Factor}}{\text{Payoff Ratio}}$$

Interpretation

Higher CPC values indicate that profits are consistently achieved relative to losses. Low CPC reflects fragile profitability.

Tail Ratio

Definition

The Tail Ratio compares the magnitude of large upside moves to large downside moves:

$$\text{Tail Ratio}=\frac{\text{95th Percentile of }{r}_t}{|\text{5th Percentile of }{r}_t|}$$

Step-by-Step (Solana Example)

Suppose:

$$\text{95th Percentile}=0.030,\text{5th Percentile}=-0.030$$

Then:

$$\text{Tail Ratio}=\frac{0.030}{|-0.030|}=1.0$$

Interpretation

A tail ratio close to 1 means extreme gains and extreme losses are balanced. Values below 1 mean crashes are more severe than rallies.

Outlier Win Ratio

Definition

The Outlier Win Ratio measures how extreme positive outliers compare to average gains:

$$\text{Outlier Win Ratio}=\frac{\max (r_t)}{\text{Average Gain}}$$

Step-by-Step (Solana)

$$\max (r_t)=0.030,\text{Average Gain}=0.0175$$ $$\text{Outlier Win Ratio}=\frac{0.030}{0.0175}\approx 1.71$$

Interpretation

Solana’s largest daily win was about 1.7 times bigger than the average winning day.

Outlier Loss Ratio

Definition

The Outlier Loss Ratio measures how extreme negative outliers compare to average losses:

$$\text{Outlier Loss Ratio}=\frac{|\min (r_t)|}{|\text{Average Loss}|}$$

Step-by-Step (Solana)

$$\min (r_t)=-0.030,\text{Average Loss}=-0.01875$$ $$\text{Outlier Loss Ratio}=\frac{0.030}{0.01875}\approx 1.60$$

Interpretation

The worst Solana daily loss was 1.6 times greater than the average losing day, reflecting fat-tail downside risk.

Month-to-Date (MTD) Return

Definition

Measures cumulative return from the start of the current month to date.

Formula

$$R_{\text{MTD}}=\prod _{t=1}^n(1+r_t)-1$$

where $n$ = number of trading days this month.

Example (Solana)

If cumulative growth = $1.0093$ :

$$R_{\text{MTD}}=1.0093-1=0.93\%$$

Interpretation

Captures short-term monthly momentum. Solana gained mildly (+0.93%).

3-Month (Quarterly) Return

Definition

Performance over the trailing 90 days.

Formula

$$R_{3M}=\prod _{t=1}^{90}(1+r_t)-1$$

Example (Solana)

$\prod (1+r_t)=1.1923⟹R_{3M}=19.23\%$

Interpretation

Reflects recent quarter’s strength. Solana rallied +19.23%.

6-Month Return

Definition

Measures cumulative return over the last 180 days.

Formula

$$R_{6M}=\prod _{t=1}^{180}(1+r_t)-1$$

Example (Solana)

$R_{6M}=8.07\%$

Interpretation

Shows medium-term trend. Solana grew moderately.

Year-to-Date (YTD)

Definition

Tracks performance from January 1 to the present date.

Formula

$$R_{\text{YTD}}=\prod _{t=1}^n(1+r_t)-1$$

Example (Solana)

$R_{\text{YTD}}=7.04\%$

Interpretation

Indicates 2025 progress. Solana gained +7.04%.

1-Year Return

Definition

Cumulative return over the past 365 days.

Formula

$$R_{1Y}=\prod _{t=1}^{365}(1+r_t)-1$$

Example (Solana)

$R_{1Y}=12.48\%$

Interpretation

Full trailing year performance. Solana returned +12.48%.

3-Year Annualized Return

Definition

Average compounded annual return across 3 years.

Formula

$$R_{3Y,ann}={\left(\prod _{t=1}^{3Y}(1+r_t)\right)}^{\frac{1}{3}}-1$$

Example (Solana)

$R_{3Y,ann}=10.91\%$

Interpretation

Indicates Solana compounded +10.91% annually.

5-Year Annualized Return

Definition

Average compounded annual growth across 5 years.

Formula

$$R_{5Y,ann}={\left(\prod _{t=1}^{5Y}(1+r_t)\right)}^{\frac{1}{5}}-1$$

Example (Solana)

$R_{5Y,ann}=10.19\%$

Interpretation

Shows steady long-term return. Solana averaged +10.19% per year.

10-Year Annualized Return

Definition

Annualized return over a decade.

Formula

$$R_{10Y,ann}={\left(\prod _{t=1}^{10Y}(1+r_t)\right)}^{\frac{1}{10}}-1$$

Example (Solana)

$R_{10Y,ann}=9.06\%$

Interpretation

Decade-long performance smoothing. Solana held +9.06% yearly.

All-Time Annualized Return

Definition

Compounded annual growth since inception.

Formula

$$R_{\text{all-time, ann}}={\left(\prod _{t=1}^T(1+r_t)\right)}^{\frac{252}{T}}-1$$

where $T$ = number of trading days since launch.

Example (Solana)

$R_{\text{all-time, ann}}=9.06\%$

Interpretation

Reflects enduring long-term growth rate since Solana’s inception.

Best Day

Definition

The best day is the maximum single-day return of the asset.

Formula

$$R_{\text{best day}}=\max (r_t),t\in \text{trading days}$$

Example (Solana)

If Solana’s maximum daily return was $10.5\%$ on March 15, 2023:

$$R_{\text{best day}}=10.5\%$$

Interpretation

Shows the strongest daily upside potential observed.

Worst Day

Definition

The worst day is the minimum single-day return.

Formula

$$R_{\text{worst day}}=\min (r_t),t\in \text{trading days}$$

Example (Solana)

Worst daily return was $-10.94\%$ .

Interpretation

Indicates maximum single-day downside risk.

Best/Worst Month

Definition

The best (worst) month is the highest (lowest) monthly compounded return.

Formula

$$R_{\text{best month}}=\max (R_m),R_{\text{worst month}}=\min (R_m)$$

Example (Solana)

$$R_{\text{best month}}=12.7\%,R_{\text{worst month}}=-12.49\%$$

Interpretation

Shows how volatile performance can be on a monthly scale.

Best/Worst Year

Definition

The best (worst) year is the maximum (minimum) annual return.

Formula

$$R_{\text{best year}}=\max (R_y),R_{\text{worst year}}=\min (R_y)$$

Example (Solana)

$$R_{\text{best year}}=31.22\%,R_{\text{worst year}}=-18.18\%$$

Interpretation

Summarizes long-term variability in returns.

Average Drawdown

Definition

The mean of all drawdown episodes.

Formula

$$\overline{DD}=\frac{1}{N}\sum _{i=1}^{N}D{D}_i$$

Example (Solana)

$\overline{DD}=-1.69\%$

Interpretation

Shows the typical peak-to-trough decline.

Average Drawdown Days

Definition

Average duration of drawdown periods (in days).

Formula

$$\overline{D}=\frac{1}{N}\sum _{i=1}^N{D}_i$$

Example (Solana)

$\overline{D}=18\text{ days}$

Interpretation

Measures how long investors usually wait for recovery.

Recovery Factor

Definition

Ratio of cumulative return to maximum drawdown.

Formula

$$\text{Recovery Factor}=\frac{\text{Cumulative Return}}{|\text{Max Drawdown}|}$$

Example (Solana)

If cumulative return = $+142\%$ , max drawdown = $-33.7\%$ :

$$\text{Recovery Factor}=\frac{1.42}{0.337}\approx 4.22$$

Interpretation

High values mean strong recovery ability.

Ulcer Index

Definition

A risk measure that penalizes depth and duration of drawdowns.

Formula

$$UI=\sqrt{\frac{1}{N}\sum _{t=1}^N(D{D}_t^2)}$$

Example (Solana)

$UI=0.07$

Interpretation

Low values indicate smoother performance.

Serenity Index

Definition

A risk-adjusted return metric based on CAGR and Ulcer Index.

Formula

$$\text{Serenity Index}=\frac{\text{CAGR}}{UI}$$

Example (Solana)

If CAGR = $10.91\%$ , $UI=0.07$ :

$$\text{Serenity Index}\approx 1.61$$

Interpretation

Higher values mean more stable growth.

Average Up/Down Month

Definition

The mean return of positive vs negative months.

Formula

$$\overline{R_{up}}=\frac{1}{N_{up}}\sum R_{up},\overline{R_{down}}=\frac{1}{N_{down}}\sum R_{down}$$

Example (Solana)

$\overline{R_{up}}=3.68\%,\overline{R_{down}}=-4.6\%$

Interpretation

Shows asymmetry between gains and losses.

Win Ratios

Definition

Percentage of periods ending with positive returns.

Formula

$$\text{Win Days}=\frac{\#\{r_t>0\}}{\text{Total Days}},\text{etc.}$$

Example (Solana)

Win Days = $55.13\%$ , Win Months = $68.6\%$ , Win Years = $72.73\%$

Interpretation

Indicates the consistency of profitability.

Beta

Definition

Sensitivity of asset returns to the benchmark.

Formula

$$\beta =\frac{\text{Cov}(r,r_m)}{{\sigma }_m^2}$$

Example (Solana)

$\beta =1.3$

Interpretation

Solana moves more than the market (amplified risk).

Alpha

Definition

Excess return relative to CAPM expectation.

Formula

$$\alpha =R_p-\left[R_f+\beta (R_m-R_f)\right]$$

Example (Solana)

$\alpha =0.1$

Interpretation

Positive alpha means outperformance beyond risk exposure.

Correlation

Definition

Measures co-movement with the benchmark.

Formula

$$\rho =\frac{\text{Cov}(r,r_m)}{{\sigma }_r{\sigma }_m}$$

Example (Solana)

$\rho =62.11\%$

Interpretation

Moderate correlation with crypto market index.

Treynor Ratio

Definition

Return per unit of systematic risk (beta).

Formula

$$\text{Treynor}=\frac{R_p-R_f}{\beta }$$

Example (Solana)

If excess return = $0.703$ , $\beta =1.3$ :

$$\text{Treynor}\approx 540.48\%$$

Interpretation

High ratio = efficient compensation for market risk.

Average Holding Period

Definition

The Average Holding Period measures how long, on average, a trader holds an asset before selling it.

Formula

$$\text{Average Holding Period}=\frac{{\sum }_{i=1}^N{H}_i}{N}$$

Example (Solana - SOL)

Trades:

• Jan 1–Jan 10 → 9 days
• Feb 5–Feb 8 → 3 days
• Feb 20–Feb 25 → 5 days

$$\text{Average Holding Period}=\frac{9+3+5}{3}\approx 5.67\text{ days}$$

Implication

• Short period → active trading (scalping/day-trading)
• Long period → buy-and-hold strategy
• Useful for comparing trader discipline with stated strategy.

Average Holding Period When You Win

Definition

Average holding time of profitable trades.

Formula

$$\text{Average Holding Period When You Win}=\frac{{\sum }_{i=1}^{N_{win}}{H}_i}{N_{win}}$$

Example (Solana - SOL)

Winning trades:

• Jan 1–Jan 5 → 4 days
• Jan 10–Jan 20 → 10 days

$$\text{Average Holding Period When You Win}=\frac{4+10}{2}=7\text{ days}$$

Implication

• Short → quick profit-taking
• Long → letting winners run
• Comparing with overall holding period reveals behavioral biases.

Average Holding Period When You Lose

Definition

Average holding time of losing trades.

Formula

$$\text{Average Holding Period When You Lose}=\frac{{\sum }_{j=1}^{N_{loss}}{H}_j}{N_{loss}}$$

Example (Ethereum - ETH)

Losing trades:

• Jan 1–Jan 3 → 2 days
• Jan 15–Jan 25 → 10 days

$$\text{Average Holding Period When You Lose}=\frac{2+10}{2}=6\text{ days}$$

Implication

• Short → cutting losses quickly
• Long → “holding and hoping”
• Compare with winning trades to detect behavioral biases.

Average Market Cap When You Buy a Coin

Definition

Average market capitalization of assets at purchase.

Formula

$$\text{Average Market Cap When You Buy a Coin}=\frac{{\sum }_{i=1}^{N_{buy}}M{C}_i}{N_{buy}}$$

Example (BTC, ETH, SOL)

• Ethereum: 200B
• Solana: 40B
• Bitcoin: 800B

$$\frac{200+40+800}{3}\approx 346.7\text{ B}$$

Implication

• Higher → prefers established assets
• Lower → trades smaller, riskier coins
• Profiles risk appetite and strategy.

Win %

Definition

Proportion of profitable trades.

Formula

$$\text{Win \%}=\frac{N_{win}}{N_{total}}\times 100$$

Example (BTC, ETH, SOL)

• Total trades = 10
• Wins = 6
• Losses = 4

$$\text{Win \%}=60\%$$

Implication

• Higher → consistent profitable trades
• Lower → difficulty predicting profitable trades
• Alone, does not indicate net profitability.