Ratios for Managing a Trading Portfolio

Managing a Trading Portfolio

Managing a trading portfolio starts with measuring and controlling trading risk. There are quite a few tools that can help traders to measure and control their risk. However, before presenting a number of significant portfolio management ratios, it is useful to mention three fundamental investment concepts for managing any portfolio:

• Risk-Free Rate

The 'Risk-Free Rate' is the annual return that an investor can secure without taking any market risk. It is usually determined by the 3-month treasury bill.

• Standard Deviation (SD)

A standard deviation is a statistical tool that estimates the amount of variation in a set of values.

• MaxDrawdown

'MaxDrawdown' calculates the maximum historical loss of a trading portfolio compared to its maximum dollar value.

 

Portfolio Management

Portfolio management is the process that aims to achieve the highest return with the lowest risk. But if return and risk are the two key variables that determine the success of money management, then combining them into a single metric could make portfolio management much easier. This combination is called risk-adjusted portfolio return.

Here 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 the detailed presentation of each ratio separately.

(1) Sharpe ratio

The Sharpe ratio was created in 1966 by William F. Sharpe and is perhaps the most popular investment portfolio management tool. The ratio assesses management effectiveness based on performance and diversification. The return is calculated by subtracting the 'Risk-Free Rate' from the expected return, while the variance is calculated based on 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

In the event that the Sharpe ratio exceeds unity (>1) for a long period, then the management of a portfolio is considered qualitative. Conversely, when the Ratio falls significantly short of unity, then management is not considered good. It is pointed out that if the Sharpe ratio exceeds unity (>1) for a period of more than a decade, then the management of an investment portfolio is considered particularly satisfactory.

 

(2) Treynor index

The Treynor Ratio is another useful tool for evaluating a portfolio's performance. Treynor's main difference from Sharpe is the use of 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)

 

(3) Sortino index

Sortino is a ratio similar to Sharpe, except that it 'penalizes' annual returns that fall short of a predetermined percentage, and that it incorporates in the denominator a negative deviation, instead of a standard deviation like Sharpe. The Sortino Ratio can be particularly useful for investors looking for low-risk portfolios.

Sortino evaluates the performance of a portfolio based on a predetermined percentage called targeted return.

Here is Sortino's calculation formula:

■ 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 means that a portfolio's annual return does not exceed the targeted return.

Here are some conclusions, based on the indicators of the index:

• 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 index, is designed to evaluate only well-diversified portfolios. This is because it ignores portfolio variance (unsystematic risk).

Jensen's Alpha attempts to indicate a portfolio's ability to deliver returns above the market average and to achieve this, it incorporates the CAPM model. The CAPM (Capital Asset Pricing Model) model is widely used in financial analysis, as it is simple to use and allows for easy comparisons between a range of alternative investment positions.

Here is the calculation formula of 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

 

(5) MAR index

MAR is designed to assess the risk-adjusted returns of an investment strategy or hedge fund. The higher the values displayed by the MAR, the higher quality of the returns of a portfolio are considered to be. The 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 MAR:

■ 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)

 

(6) Calmar Ratio

The Calmar Ratio is designed to assess 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. Accordingly, the risk is calculated based on the maximum loss from the highs or the 'MaxDrawdown' indicator. The analysis period must include 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}.

 

 

(7) Information Ratio

The Information Ratio is a ratio designed to calculate the excess performance of a portfolio relative to a predetermined benchmark (i.e. the S&P500). This excess return is called an active return.

Here is the information ratio calculation formula:

■ 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

 

(8) Omega Ratio

The Omega Ratio is another tool for evaluating the performance of a portfolio and is considered a good alternative to the Information Ratio and Sharpe ratios. Unlike Sharpe, Omega is based on the excess returns, rather than the absolute returns, of a portfolio.

The ratio is calculated as the ratio of weighted winnings (Winning) to weighted losses (Losing) of an investment portfolio, 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

G.P. for ForexRobots.net (c) under license

 

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