Upload
quantinsti
View
358
Download
1
Embed Size (px)
DESCRIPTION
This presentation is aimed to answer the one of the most fundamental question of Trading: "How much to trade?" You might have decided what to trade but the question how much to trade raises a critical issue which needs to be handled using Statistics. This presentation take its audience through the various money management techniques and position sizing algorithms which come handy for every trader.
Citation preview
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
Shaurya Chandra
Performance Evaluation & Money Management
Webinar on
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
Building a Diversified Portfolio?
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
• Absolute Risk-adjusted Return 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
3
Strategy Analysis
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
• Sharpe ratio = (excess return over risk free rate) / (standard deviation of excess returns)
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
4
p
fp
σ
RRratio Sharpe
Absolute Risk Adjusted Return Measures
Relative Return Measures
Relative Risk Adjusted Return Measures
Tail Risk Measures
Strategy Analysis
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
• Sortino ratio = (return over target return) / (downside risk, i.e. semi deviation or variance on the downside only).
<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.
5
d
fratio Sortino
RR
Absolute Risk Adjusted Return Measures
Relative Return Measures
Relative Risk Adjusted Return Measures
Tail Risk Measures
Strategy Analysis
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
The Flaw of Averages
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
• 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
7
Absolute Risk Adjusted Return Measures
Relative Return Measures
Relative Risk Adjusted Return Measures
Tail Risk Measures
Strategy Analysis
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
• Up Capture Ratio = (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
8
Absolute Risk Adjusted Return Measures
Relative Return Measures
Relative Risk Adjusted Return Measures
Tail Risk Measures
Strategy Analysis
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
• Treynor ratio = (excess return over risk free rate)/ beta of portfolio
ri = Average Return of the PortfolioRf = Average Return of the Risk-Free Rateβ = 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’.
9
Absolute Risk Adjusted Return Measures
Relative Return Measures
Relative Risk Adjusted Return Measures
Tail Risk Measures
i
fi RrratioTreynor
Strategy Analysis
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
• RAROC (Risk Adjusted Return on Capital) = (expected return) / (Value at Risk)
RE = Expected Return VaR = Value at Risk
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.
10
Absolute Risk Adjusted Return Measures
Relative Return Measures
Relative Risk Adjusted Return Measures
Tail Risk Measures
VaR
RAROC ER
Strategy Analysis
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
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
Methods that Don’t Work• 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
Why They Don’t Work• 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
Kelly’s Criterion for Portfolio ManagementIt 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)/BWhere,f = optimal fixed fractionP = Winning ProbabilityB = Win/Loss Rate ( Average Gain on +ve Trades/ Average Loss on –ve Trades)
14
Portfolio Management
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
Some Advice!
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited
Thanks!
THANK YOU
Contact us at: Email: [email protected]: +91-22-61691400, +91-9920448877