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.

1. Webinar on
Performance Evaluation &
Money Management
Shaurya Chandra
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2. Building a Diversified Portfolio?
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3. • 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
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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
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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.
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d
Absolute Risk Adjusted
Return Measures
Relative Return
Measures
Relative Risk Adjusted
Return Measures
Tail Risk Measures

6. The Flaw of Averages
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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
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Strategy Analysis

8. • 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
Absolute Risk Adjusted
Return Measures
Relative Return
Measures
Relative Risk Adjusted
Return Measures
Tail Risk Measures
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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
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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
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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
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12. 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”).
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13. 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.
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14. Kelly’s Criterion for Portfolio 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)
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Portfolio Management

15. Some Advice!
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16. Thanks!
THANK YOU
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