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Performance evaluation & portfolio management
The document discusses various financial performance evaluation metrics, including the Sharpe, Sortino, Calmar, and Treynor ratios, highlighting their formulas, uses, and limitations. It emphasizes the importance of understanding absolute and relative risk-adjusted return measures, along with methods for trade sizing and cautions against certain trading strategies that assume dependencies between trades. The document also introduces Kelly's Criterion for optimal portfolio management focused on long-term capital growth.
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Performance evaluation & portfolio management
- 1. Webinar on PerformanceEvaluation & Money Management Shaurya Chandra © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
- 2. Building a DiversifiedPortfolio? © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
- 3. • Absolute Risk-adjustedReturn Measures – Sharpe Ratio – Sortino Ratio – Calmar Ratio – Sterling Ratio • Relative Return Measures – Up-Capture Ratio / Down-Capture Ratio – Up-Number Ratio / Down-Number Ratio – Proficiency Ratio (Up/Down Percentage Ratio) • Relative Risk Adjusted Return Measures – Treynor Ratio • Tail Risk Measures – RAROC-Var © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 3 Strategy Analysis
- 4. Strategy Analysis •Sharpe ratio = (excess return over risk free rate) / (standard deviation of excess returns) R R p f σ It is a measure of the excess return per unit of standard deviation in an investment asset. Sharpe ratio provides very useful information regarding the return of an asset for a given risk. Limitations – Based on historical data , assumes “Future would be same as the Past” – Poor at estimating tail risk – Normal Distribution Assumption , hence no differentiation between +ve and –ve trades – Doesn’t account for Draw-downs (leading to low volatility) and transaction costs © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 4 p Sharpe ratio Absolute Risk Adjusted Return Measures Relative Return Measures Relative Risk Adjusted Return Measures Tail Risk Measures
- 5. Strategy Analysis •Sortino ratio = (return over target return) / (downside risk, i.e. semi deviation or variance on the downside only). R R Sortino ratio f <R> = Expected Return Rf = Risk Free Rate σf = Standard Deviation of Negative Returns Unlike Sharpe ratio, Sortino ratio does not punish high variance if the returns are on the upside. © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 5 d Absolute Risk Adjusted Return Measures Relative Return Measures Relative Risk Adjusted Return Measures Tail Risk Measures
- 6. The Flaw ofAverages © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
- 7. • Calmar ratio= (return) / (maximum drawdown). Generally quoted for the last 3 years • Sterling ratio = (return) / (absolute(average drawdown – 10%)). Generally quoted for the last 3 years Absolute Risk Adjusted Return Measures Relative Return Measures Relative Risk Adjusted Return Measures Tail Risk Measures © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 7 Strategy Analysis
- 8. • Up CaptureRatio = (fund’s return when benchmark return increased) / (benchmark’s return when benchmark increased) • Up Number Ratio = (number of period when fund’s return increased when benchmark return increased) / (number of periods when benchmark’s return increased) • Up Percentage Ratio (Proficiency Ratio) = (number of period when fund’s return outperformed the benchmark when benchmark’s return increased) / (number of periods when benchmark’s return increased) • Likewise Down Capture Ratio, Down Number Ratio, Down Percentage Ratio Absolute Risk Adjusted Return Measures Relative Return Measures Relative Risk Adjusted Return Measures Tail Risk Measures © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 8 Strategy Analysis
- 9. Strategy Analysis •Treynor ratio = (excess return over risk free rate)/ beta of portfolio r R i f ri = Average Return of the Portfolio Rf = Average Return of the Risk-Free Rate β = Beta of the Portfolio It is a measure of returns earned in excess of that which could have been earned on a riskless investment per unit of market risk where β is a measure of market risk. The only difference between Sharpe Ratio and Treynor Ratio is that the later uses β as the measurement of ‘Volatility’. Absolute Risk Adjusted Return Measures Relative Return Measures Relative Risk Adjusted Return Measures Tail Risk Measures © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 9 i Treynor ratio
- 10. Strategy Analysis •RAROC (Risk Adjusted Return on Capital) = (expected return) / (Value at Risk) RE = Expected Return VaR = Value at Risk R AROC E R In any investment, risk is traded off against benefit. RAROC gives us a picture of the returns on several different investments with varying risk levels. Absolute Risk Adjusted Return Measures Relative Return Measures Relative Risk Adjusted Return Measures Tail Risk Measures © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 10 VaR
- 11. Trade Sizing •Ad hoc: trade no larger than lets you sleep at night • Margin plus drawdown • Fixed Fractional • Fixed Ratio • Hybrid fixed fractional/fixed ratio © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
- 12. Methods that Don’tWork • Martingale methods: increase position size after a loss; decrease it after a win. • Anti-Martingale methods. • Equity curve methods: increase size when your equity curve falls below its moving average (“reversion to mean”), or increase size when you cross above the moving average (“trade the trend in equity curve”). © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
- 13. Why They Don’tWork • Martingale and equity curve methods assume dependency between trades. • In most cases, trades are independent of each other. The odds of the next trade being a win are not related to whether the last trade was a win or a loss. • If trades are independent, you can’t determine the likelihood of the next trade being a win or a loss based on the previous trade. © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
- 14. Kelly’s Criterion forPortfolio Management It is a formula used to determine the optimal size of a series of bets. Focus : Long Term Capital Growth Kelly % (f) = ((B + 1)*P -1)/B Where, f = optimal fixed fraction P = Winning Probability B = Win/Loss Rate ( Average Gain on +ve Trades/ Average Loss on –ve Trades) © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited 14 Portfolio Management
- 15. Some Advice! ©Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
- 16. Thanks! THANK YOU Contact us at: Email: contact@quantinsti.com Phone: +91-22-61691400, +91-9920448877 © Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited