Risk Management: Maximising Long-Term Growth Presentation

Marco Nicolás Dibo
"Risk Management:
Maximizing Long Term Growth"

Profile
2
• Head of the Quantitative
Trading Desk at Argentina
Valores S.A.
• CEO and Co-founder of
Quanticko Trading S.A.
• Email
• LinkedIn Profile

Agenda
3
• Risk Management, real objectives.
• Optimal leverage:
• Understanding market risk: standard deviation,
Sharpe ratio, value-at-risk, maximum drawdown.
• Volatility targeting.
• Kelly formula.
• Stop loss.
• Hedging.

Risk Management, what does it means?
4
• Loss aversion, we don’t want to lose money.
• Real goal: Maximization of long term equity
growth.
• We should avoid risk only as it interferes with
this goal.
• Leverage is the key concept in risk
management.

Optimal Leverage
5
• The objective: Maximize long term wealth that is
equivalent to maximizing long term growth of
the portfolio.
• But be careful, 100% drawdown can never be
optimal!
• Assumption: probability distribution of returns is
Gaussian.
• No matter how optimal leverage is determined,
it should be kept constant in order to maximize
growth.

Volatility Targeting
6
The importance of risk targeting
• ¿Which is my overall trading risk?
1. Understand our trading system: performance,
skew, real sharpe, avoid overconfidence.
2. Understand yourself: Can you lose 20% of you
capital in a day?

Understanding Market Risk
7
Standard deviation of returns
• It’s a measure of risk.
• How dispersed some data is around its average.
• On unit of standard deviation is called sigma,
• It doesn’t increase linearly, but with the square
root of time, so the annualized standard
deviation is
Where is the period return of the asset or strategy
and is the period return of some benchmark.

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Standard deviation of returns

9
Rolling standard deviation

10
Sharpe ratio
• The ratio compares the mean average of
the excess returns of the asset or strategy with
the standard deviation of those returns. Thus a
lower volatility of returns will lead to a greater
Sharpe ratio, assuming identical returns.
Where is the mean average of the excess
returns.

11
Sharpe ratio
The Sharpe ratio mostly quoted is the Annualized
Sharpe, which depends on the trading period on
which returns are calculated. Assuming there are N
trading periods in a year,
For a strategy based on a trading period of days,

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Rolling Sharpe ratio

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Value at risk (VAR)
• VAR is a risk measure that helps us quantify the
risk of our strategy or portfolio.
• It provides an estimate, under a given degree of
confidence, of the size of a loss from a portfolio
over a given period of time.
• The given degree of confidence will be a value
like 95% or 99%.

14
Value at risk (VAR)
Example:
A VAR equal to 100,000 USD at a 95% confidence
level, for a time period of a day, simply states that
there is a 95% probability of losing no more than
100,000 USD in the next day.
More generally:
where c is the confidence level.

15
Value at risk (VAR)
assumptions:
• Standard market conditions.
• Volatilities and correlations.
• Normality of returns.
Advantages and Disadvantages:
• Easy to calculate, broken down by asset, used as
constraints, easy to interpret.
• It does not discuss magnitudes, does not take into
account extreme events, it takes historical data.

16
Maximum drawdown and drawdown duration
The maximum drawdown (md) and drawdown
duration (dd) are two measures that traders use to
assess the risk in a portfolio.
• md quantifies the highest peak-to-trough decline
in an equity curve
• dd is defined as the number of trading periods
over which the md occurs.

17
Setting a volatility target
• ¿How much risk do I want to take?
expected standard deviation = volatility target.
It can be measured in % or in cash and over
different periods.
Example: daily cash volatility target = average
expected standard deviation of the daily portfolio
returns.

18
• Volatility target is the long term average of
expected, predictable risk.
• This risk depends on the strength of your
forecasts and the current correlation of assets
prices.
• The best proxy for risk, annualized cash volatility
target (annualized expected daily standard
deviation of returns).

20
Setting your trading capital and volatility target
1) How much can you lose?
2) How much risk can you tolerate?
3) Can you realise that risk?
4) Is this level of risk right for your system?

21
1) How much can you lose?
• Invest only what you can afford to lose.
• Never trade with borrowed money!!!

22
2) How much risk can you tolerate? How much risk
can you tolerate?
Example:
• Trading capital = $200.000
• Volatility target = 200%
• Annualized cash volatility target = $400.000
• Can you tolerate a $20.000 daily loss? And a
cumulative loss or drawdown of $60.000
around 10% of the time?

23
3) Can you realize that risk?
Buying a short term bond with an expected
volatility of 5% a year, then without leverage its
impossible to create a portfolio with 50% volatility
target.
• With no leverage you are restricted to the
amount of natural risk that your instruments
have*.
*Systematic Trading, Robert Carver.

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3) Can you realize that risk?
Even if you have access to that kind of leverage to
accomplish that volatility target would be an
unwise decision.
• Ensure that your volatility target won´t wipe
out your account.

25
4) Is this the right level of risk?
• Do not ignore the compounding of returns!
• Suppose you have a very profitable strategy,
but you lose 90% of you account in the first
trade. Then a 190% return in the second trade
wont take you even closer to you initial equity.

26
4) Is this the right level of risk?
Kelly criterion: used by nearly all professional
gamblers and professional traders to maximize
profits.
• If you know your sharpe ratio you can use this
formula to determine how you should set your
volatility target and leverage.

Kelly Formula: Optimal leverage
27
• Assuming that the probability distribution of
returns is Gaussian:
Where is the optimal leverage, is the mean
excess return and is the variance of the excess
return.
• If returns are normally distributed, the
leverage will generate the highest compounded
growth rate of equity (assuming reinvestment of
all the returns).

28
• Example 1:
Ticker: JPM
1. Daily percentage change.
2. Mean return of daily percentage change.
3. Standard deviation of daily percentage change.
4. Mean excess return, rf = risk free rate.
5. Sharpe ratio.
6. Kelly fraction.
7. Levered and unlevered compounded return.

29
• Kelly criterion implies that we should set our
volatility target equal to the sharpe ratio.
• So, if we think that our sharpe ratio is 0.5, the
best performance will be achieved with a 50%
volatility target.
• Estimation errors can lead to ruin. Dangerous if
used by an over confident trader. Difficult to
know you exact sharpe ratio.
• Even if you know your expected sharpe ratio you
could end with a great loss.

30
Recommended percentage volatility targets
• Even with a Sharpe ratio of 1 we should not use
a 100% volatility target.
• The reasons:
1) Backtested Sharpe ratios are hardly achievable in
the future. Use a ratio of the observed Sharpe ratio.
2) Kelly criteria is far too aggressive. You could suffer
some large drawdowns even if your expected Sharpe
ratio is correct. Better use Half-Kelly.
3) Use it as an upper bound.

31
Recommended percentage volatility targets
Positive Skew Negative Skew
12% 6%
20% 10%
25% 13%
37% 19%
50% 25%1 or more
Realistic Backtested
Sharpe Ratio
Recommended Volatility Targets
0.25
0.40
0.50
0.75

Kelly Formula: BP Allocation
32
• Note: following the Kelly formula requires you to
continuously adjust your capital allocation as
your equity changes so that it remains optimal.
• This continuous updating should occur at least
once a day.
• We should also periodically update (20 or 60
days lookback?).

Kelly Formula: Contagion
33
• Risk management dictates that you should
reduce your position size whenever there is a
loss, even when it means taking losses.
• This is the cause of financial contagion.
• Example: summer 2007 meltdown. The
frequency of trading to rebalance the portfolio
to follow the formula may explain why traders
usually use half kelly fraction.

Kelly Formula: Contagion
34
• Even half Kelly may not be so conservative.
• Another check (additional constraints):
A = What is the maximum drawdown you would
tolerate?
B = What was the maximum loss in one period?
(week, day, hour, minute)
A/B will tell you the maximum leverage you would
tolerate. This can even be smaller than half-kelly.

35
• There is another usage of the Kelly formula:
buying power allocation between portfolios or
strategies.
• Let be a column vector
consisting of the optimal fractions of our equity
that we should allocate to each of the
strategies.
• The optimal allocation is given by:

36
• is the covariance matrix such that is the
covariance of the returns of the and
strategies.
• is the column vector of
the mean returns of the strategies.
• Example 6.3: Portfolio of 3 stocks

37
• Example 2:
Portfolio of 3 assets:
JPM, C, GS.
1. Daily returns.
2. Excess returns.
3. Excess returns mean.
4. Covariance Matrix.
5. Kelly fraction.
6. Compounded levered return.

38
• is the covariance matrix such that is the
covariance of the returns of the and
strategies.
• is the column vector of
the mean returns of the strategies.
• Example: Portfolio of 3 stocks

Stop Loss
39
• There are 2 ways to set stops:
1) Exit whenever your loss is greater than a certain
threshold (more common usage).
2) When drawdown drops below a certain threshold
(less common, hope we don’t use it never).
• If we focus in the first kind, setting a stop loss
will depend in the kind of strategy we are
running.

Stop Loss
40
Mean reversion strategies
• Should we set stop loss for these type of
strategies?
• At first it seems to contradict the idea behind
mean reversion:
- If price drops, and we expect it will mean reverse, the
probability of reversion increases, giving a better
opportunity than before.

Stop Loss
41
But what happens if mean reversion breaks?
• What was true of a price series before may not
be true in the future (CHAN).
• So a mean reverting process may become a
trending process, in this case setting a stop loss
will help us.
• This can prevent us from suffering a 100% loss.
• Be careful with survivorship bias in mean
reverting strategies!!!

Stop Loss
42
Conclusion:
• While a price series remain mean reverting a
stop loss will lower the performance.
• If price series undergo a regime change, then a
stop loss will definitely improve your
performance.
• Stop loss should be grater than the intraday
maximum drawdown from the backtest.

Stop Loss
43
Trend following strategies
• They benefit from stop loss:
- If the strategy is losing, it means momentum is no
longer there, we should exit the position.
- We can use this change in momentum to open a
new position on the other direction and as a stop loss
of the previous position.
• This is the reason why trend following strategies
do not suffer as much tail risk as mean reversion
strategies do.

Hedging
44
Hedging an Equity Portfolio
• We can use index futures to hedge our portfolio
by using the capital asset pricing model.
• The parameter beta is the slope of the best fit
line obtained when excess return on the portfolio
over the risk free rate is regressed against the
excess return of the index over the risk free rate.

Hedging
45
• If 1, the returns of the portfolio mirror the
returns of the index.
• If 2, the excess return of the portfolio tends
to be twice as great as the return on the index.
• If , the excess return of the portfolio
tends to be half as great as the return on the
index.
If = 2, our portfolio tends to be as twice as
sensitive to movements in the index (HULL).

Hedging
46
• The next equation shows the number of futures
contracts that we should short,
• Where is the current value of the portfolio and
is the current value of 1 future contract.

Hedging
47
• Example:
Value of the S&P 500 index = 2,656
ES[Z] S&P 500 dec. futures price = 2,670
Value of our portfolio = $10,000,000
Risk-free rate = 3% per annum
Dividend yield on index = 1% per annum
Beta of the portfolio = 1.75

Hedging
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• 1 future contract is for delivery of $250 times the
index.
•
• The number of contracts we should short:
contracts

Hedging
49
• Suppose the index closes at 2,496 in 2 months
and the future price is 2,510.
• The gain from the short is:

Hedging
50
• The loss in the index is 6%. The index pays a
dividend of 1% per annum, or 0.17% per 2
months.
• The investor in the index would have earned
• Expected return on portfolio – Rf =

Hedging
51
• The risk-free rate is 0.75% per 2 months.
• The expected return on the portfolio:
• The expected value of the portfolio:
• The expected value of the hedgers position:
$10,029,000

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