💹 Managing a Trading Portfolio
Managing a trading portfolio begins with measuring and controlling trading risk. Several tools are available to help traders assess and manage their risk. However, before introducing key portfolio management ratios, it is important to highlight three fundamental investment concepts relevant to managing any portfolio:
👉 Risk-Free Rate
The risk-free rate represents the annual return an investor can earn without taking any market risk. It is typically based on the yield of a 3-month treasury bill.
👉 Standard Deviation (SD)
Standard deviation is a statistical measure that estimates the degree of variation in a set of values.
👉 MaxDrawdown
MaxDrawdown measures the maximum historical loss of a trading portfolio in relation to its highest recorded dollar value.
📊 Portfolio Management
Portfolio management is the process of aiming to achieve the highest return with the lowest possible risk. If return and risk are the two key variables that determine the effectiveness of money management, then combining them into a single metric can simplify the evaluation process. This combination is known as the risk-adjusted portfolio return.
Below are some of the most important measures of a portfolio's risk-adjusted return:
- Sharpe Ratio
- Treynor Ratio
- Sortino Ratio
- Jensen Measure or Jensen's Alpha
- MAR Ratio
- Calmar Ratio
- Information Ratio
- Omega Ratio
Below is a detailed explanation of each ratio individually.
The Sharpe ratio, developed in 1966 by William F. Sharpe, is one of the most widely used tools in investment portfolio management. It evaluates management effectiveness by considering both performance and diversification. The return used in the ratio is calculated by subtracting the risk-free rate from the expected return, while the risk is measured using the standard deviation.
Here is the Sharpe calculation formula:
■ Sharpe Ratio = {(P - RFR) / SD(P)}
Where:
□ P = Expected portfolio return
□ RFR = Risk-Free Rate (the risk-free rate, analyzed initially)
□ SD(P) = Standard deviation of portfolio return
If the Sharpe ratio exceeds one (>1) over a long period, the portfolio management is considered strong. Conversely, if the ratio falls well below one, the management is viewed as poor. It is noted that maintaining a Sharpe ratio above one for more than a decade indicates particularly satisfactory portfolio management.
The Treynor Ratio is another valuable tool for evaluating a portfolio’s performance. Its main difference from the Sharpe ratio is that it uses relative volatility (beta) in the denominator instead of standard deviation.
Here is Treynor's calculation formula:
■ Treynor = (P - RFR) / b
Where:
□ P = Portfolio performance
□ RFR = Risk-Free Rate
□ β = The beta coefficient (Greek β), which measures the volatility of a portfolio relative to the general market (e.g. S&P500)
The Sortino ratio is similar to the Sharpe ratio, but it specifically penalizes annual returns that fall below a predetermined target. Unlike Sharpe, it uses downside deviation in the denominator instead of standard deviation. The Sortino ratio is especially useful for investors seeking low-risk portfolios.
Sortino evaluates portfolio performance based on a set target return.
Here is the formula for calculating the Sortino ratio:
■ Sortino Ratio = (P - T) / SD(dP)
Where:
□ P = Average annual return of a portfolio
□ T = Targeted-return
□ SD(dP) = Standard deviation of negative annual returns
Evaluation of the indications of the Sortino index
A negative Sortino ratio indicates that a portfolio’s annual return fails to exceed the targeted return. Based on the index indicators, here are some conclusions:
- Below 0, the indicator indicates an unacceptable investment
- Below 1, the reading is considered low
- Between 1 and 2, the indication is considered satisfactory
- Between 2 and 3, the indication is considered very satisfactory
- Above 3, the indication is considered excellent
(4) Jensen's Alpha or Jensen's Measure
Jensen’s Alpha, like the Treynor ratio, is designed to evaluate only well-diversified portfolios, as it excludes portfolio variance (unsystematic risk).
Jensen’s Alpha measures a portfolio’s ability to generate returns above the market average by incorporating the CAPM (Capital Asset Pricing Model). The CAPM is widely used in financial analysis due to its simplicity and its ability to facilitate comparisons across different investment options.
Here is the calculation formula for the CAPM model:
■ Expected Return = RFR + β * (P(m) – RFR)
Where:
□ RFR = Risk-Free Rate
□ β = Beta coefficient (measures volatility relative to the market)
□ P(m) = The market return
Then follows the formula for calculating Jensen's Alpha:
■ Jensen's Alpha = P - {RFR + β * (P(m) - RFR)}
Where:
□ P = The return on the portfolio
□ RFR = Risk-Free Rate
□ β = Beta coefficient
□ P(m) = The market return
The MAR ratio is designed to evaluate the risk-adjusted returns of an investment strategy or hedge fund. Higher MAR values indicate better-quality portfolio returns. This ratio incorporates the compound annual growth rate (CAGR), assuming all earnings are reinvested at the end of each period.
Here is the general formula for calculating the MAR ratio:
■ MAR Ratio = CAGR / MaxDrawdown
Where:
□ CAGR = Compound Annual Growth Rate refers to the compound annual growth rate of an investment and is based on the reinvestment of all profits
□ MaxDrawdown = The maximum loss of a portfolio from its maximum value (analyzed initially)
The Calmar Ratio is designed to evaluate the risk-adjusted performance of an individual portfolio or investment fund.
The return is calculated by subtracting the risk-free rate from the average annual return. The risk is measured using the maximum loss from the peak, known as the MaxDrawdown. The analysis period should cover at least three years.
The Calmar Ratio is calculated as follows:
■ Calmar Ratio = (P - RFR) / MaxDrawdown
Where:
□ P = Average annual portfolio return (minimum 3 years)
□ RFR = Risk-Free Rate
□ MaxDrawdown = The difference of the maximum loss from the maximum value of the portfolio (analyzed initially)
Alternatively, the Calmar Ratio can also be calculated without including the 'Risk-Free Rate' in the numerator {Calmar = P / MaxDrawdown}.
The Information Ratio measures a portfolio’s excess performance relative to a specific benchmark (such as the S&P 500). This excess return is known as the active return.
The Information Ratio is calculates as follows:
■ Information Ratio = {P - P(b)} / SD
where:
□ P = Portfolio performance
□ P(b) = Performance of benchmark (i.e. S&P500)
□ SD = Standard deviation of the performance difference
The Omega Ratio is another tool for evaluating portfolio performance and is considered a strong alternative to the Information and Sharpe ratios. Unlike Sharpe, Omega focuses on the portfolio’s excess returns rather than absolute returns.
The ratio is calculated as the proportion of weighted gains (Winning) to weighted losses (Losing) relative to a benchmark.
■ Omega Ratio = {Σ(Winning) - Benchmarking} / {Σ(Benchmarking) - Losing}
Where:
□ {Σ(Winning) - Benchmarking} = the weighted earnings of a portfolio relative to a reference performance (Benchmarking)
□ {Π(Benchmarking) - Losing} = the weighted losses of a portfolio relative to a reference performance (Benchmarking)
■ Key Ratios for Managing a Trading Portfolio
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