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Risk

· 21-day option

Distributions, tail measures and portfolio sensitivities — VaR, CVaR, drawdown, the Greeks and duration. The risk-desk toolkit.

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01Probability & Distributions

21
Coin Toss — Two Heads
ProbabilityJane Street
53%Easy28
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
55%Medium176
Central Limit Theorem
StatisticsGoldman SachsMorgan Stanley
74%Easy173
Variance of Uniform(0,1)
StatisticsGoldman SachsCitadel
71%Easy175
Variance of a Sum
StatisticsGoldman SachsMorgan Stanley
63%Easy

02Portfolio & Risk Metrics

157
Value at Risk (Normal)
Portfolio & RiskGoldman SachsMorgan StanleyMillennium Management
54%Medium158
CVaR / Expected Shortfall
Portfolio & RiskAQR CapitalTwo Sigma
52%Medium160
Maximum Drawdown
Portfolio & RiskCitadelTwo SigmaMan Group
52%Medium155
Sharpe Ratio
Portfolio & RiskGoldman SachsAQR Capital
83%Easy159
Diversification & Sharpe
Portfolio & RiskAQR CapitalCitadel
52%Medium156
Two-Asset Portfolio Volatility
Portfolio & RiskGoldman SachsAQR Capital
44%Medium161
Kelly Criterion
Portfolio & RiskCitadelJane Street
59%Medium162
VaR Time Scaling
Portfolio & RiskGoldman SachsMorgan Stanley
52%Medium163
Minimum-Variance Weight
Portfolio & RiskAQR CapitalBlackRock
52%Medium164
Portfolio Beta
Portfolio & RiskGoldman SachsAQR Capital
86%Easy170
Beta of a Portfolio
Portfolio & RiskJ.P. MorganBlackRock
76%Easy169
Information Ratio
Portfolio & RiskBlackRockMillennium Management
76%Easy171
Sortino Ratio
Portfolio & RiskMan GroupMillennium Management
76%Easy167
Minimum-Variance Hedge Ratio
Portfolio & RiskGoldman SachsPIMCO
52%Medium168
Two-Asset Risk Parity
Portfolio & RiskAQR CapitalMan Group
52%Medium166
The Diversification Floor
Portfolio & RiskBlackRockAQR Capital
52%Medium

03Options & Greeks

121
Delta of an ATM Call
Options & GreeksOptiverIMC Trading
61%Easy123
Gamma Near Expiry
Options & GreeksOptiverIMC Trading
66%Medium122
Delta of a Forward
Options & GreeksOptiverIMC Trading
73%Easy124
Most Negative Put Delta
Options & GreeksGoldman SachsOptiver
66%Easy125
Sign of Theta
Options & GreeksOptiverSIG / Susquehanna
71%Medium

04Fixed Income

109
Duration & Price Sensitivity
FinanceGoldman SachsJ.P. MorganPIMCO
72%Easy107
Zero-Coupon Bond Price
FinanceGoldman SachsPIMCO
63%Easy

05Markets & Pricing

104
Put-Call Parity
FinanceGoldman SachsMorgan Stanley
66%Easy108
Futures Fair Value
FinanceGoldman SachsOptiver
63%Easy105
Black-Scholes ATM Call
FinanceGoldman SachsMorgan Stanley
72%Medium106
Risk-Neutral Probability
FinanceGoldman SachsJ.P. Morgan
81%Medium
Follow as a 21-day schedule

Interleaved, easy → hard, mixed daily

1
Day 1

Finance · Portfolio

155
Sharpe Ratio
Portfolio & RiskGoldman SachsAQR Capital
83%Easy104
Put-Call Parity
FinanceGoldman SachsMorgan Stanley
66%Easy
2
Day 2

Options · Portfolio

164
Portfolio Beta
Portfolio & RiskGoldman SachsAQR Capital
86%Easy121
Delta of an ATM Call
Options & GreeksOptiverIMC Trading
61%Easy
3
Day 3

Portfolio · Statistics

169
Information Ratio
Portfolio & RiskBlackRockMillennium Management
76%Easy173
Variance of Uniform(0,1)
StatisticsGoldman SachsCitadel
71%Easy
4
Day 4

Finance · Portfolio

170
Beta of a Portfolio
Portfolio & RiskJ.P. MorganBlackRock
76%Easy107
Zero-Coupon Bond Price
FinanceGoldman SachsPIMCO
63%Easy
5
Day 5

Portfolio · Probability

21
Coin Toss — Two Heads
ProbabilityJane Street
53%Easy171
Sortino Ratio
Portfolio & RiskMan GroupMillennium Management
76%Easy
6
Day 6

Options · Portfolio

122
Delta of a Forward
Options & GreeksOptiverIMC Trading
73%Easy156
Two-Asset Portfolio Volatility
Portfolio & RiskGoldman SachsAQR Capital
44%Medium
7
Day 7

Finance · Portfolio

157
Value at Risk (Normal)
Portfolio & RiskGoldman SachsMorgan StanleyMillennium Management
54%Medium108
Futures Fair Value
FinanceGoldman SachsOptiver
63%Easy
8
Day 8

Options · Portfolio

158
CVaR / Expected Shortfall
Portfolio & RiskAQR CapitalTwo Sigma
52%Medium124
Most Negative Put Delta
Options & GreeksGoldman SachsOptiver
66%Easy
9
Day 9

Portfolio · Statistics

175
Variance of a Sum
StatisticsGoldman SachsMorgan Stanley
63%Easy159
Diversification & Sharpe
Portfolio & RiskAQR CapitalCitadel
52%Medium
10
Day 10

Finance · Portfolio

109
Duration & Price Sensitivity
FinanceGoldman SachsJ.P. MorganPIMCO
72%Easy160
Maximum Drawdown
Portfolio & RiskCitadelTwo SigmaMan Group
52%Medium
11
Day 11

Options · Portfolio

161
Kelly Criterion
Portfolio & RiskCitadelJane Street
59%Medium123
Gamma Near Expiry
Options & GreeksOptiverIMC Trading
66%Medium
12
Day 12

Portfolio

162
VaR Time Scaling
Portfolio & RiskGoldman SachsMorgan Stanley
52%Medium
13
Day 13

Finance

105
Black-Scholes ATM Call
FinanceGoldman SachsMorgan Stanley
72%Medium
14
Day 14

Probability

28
Bayes — Disease Test
ProbabilityGoldman SachsTwo Sigma
55%Medium
15
Day 15

Portfolio

163
Minimum-Variance Weight
Portfolio & RiskAQR CapitalBlackRock
52%Medium
16
Day 16

Statistics

176
Central Limit Theorem
StatisticsGoldman SachsMorgan Stanley
74%Easy
17
Day 17

Portfolio

166
The Diversification Floor
Portfolio & RiskBlackRockAQR Capital
52%Medium
18
Day 18

Options

125
Sign of Theta
Options & GreeksOptiverSIG / Susquehanna
71%Medium
19
Day 19

Portfolio

167
Minimum-Variance Hedge Ratio
Portfolio & RiskGoldman SachsPIMCO
52%Medium
20
Day 20

Finance

106
Risk-Neutral Probability
FinanceGoldman SachsJ.P. Morgan
81%Medium
21
Day 21

Portfolio

168
Two-Asset Risk Parity
Portfolio & RiskAQR CapitalMan Group
52%Medium